Exploring the limits of near-field fluorescence microscopy: toward molecular-scale imaging of biological systems

This dissertation describes the advancements made towards the implementation of Tip-Enhanced Fluorescence Microscopy (TEFM) in imaging biological specimens. This specialized type of microscopy combines the chemical specifi city of optical microscopy techniques with the resolution of atomic force microscopy (AFM). When an AFM probe is centered in the focal spot of an excitation laser with axial polarization, the probe concentrates the optical field such that it can be used to induce nanometer scale fluorescence. The physical mechanisms of this optical field enhancement are set forth in detail. The feasibility of this technique for imaging bimolecular networks is discussed in regard to the requirements for adequate image contrast, as well as for obtaining fi eld enhancement in aqueous environments. A semianalytical model for image contrast for TEFM has been developed. This model shows that using demodulation techniques greatly increases the image contrast attainable with this technique, and is capable of predicting the requisite enhancement factors to achieve imaging of biomolecular networks at good contrast levels. This model predicts that signal enhancement factors on the order of 20 are needed to image densely packed samples. This dissertation also highlights a novel tomographical imaging approach. By timestamping the fluorescence photon arrival times, and subsequently correlating them to the timestamped motion of a vertically oscillating probe, a three-dimensional map of tip-sample interactions can be constructed. The culmination of these advancements has led to the ability to map the interactions between single carbon nanotubes and single fluorescent nanocrystals (quantum dots). Various attempts at using TEFM in water have been thus far unsuccessful. Several explanations for this shortfall have been identi ed|understanding these shortcomings has helped to identify the optimal excitation conditions for field enhancement.

EXPLORING THE LIMITS OF NEAR-FIELD FLUORESCENCE MICROSCOPY: TOWARD MOLECULAR-SCALE IMAGING OF BIOLOGICAL SYSTEMS by Benjamin Daniel Mangum A dissertation submitted to the faculty of The University of Utah in partial ful llment of the requirements for the degree of Doctor of Philosophy Department of Physics and Astronomy The University of Utah May 2010 Copyright c Benjamin Daniel Mangum 2010 All Rights Reserved STATEMENT OF DISSERTATION APPROVAL The dissertation of Benjamin Daniel Mangum has been approved by the following supervisory committee members: Jordan Gerton , Chair March 17, 2010 Date Approved Yong-Shi Wu , Member March 11, 2010 Date Approved Andrey Rogachev , Member March 11, 2010 Date Approved John Conboy , Member March 11, 2010 Date Approved Markus Babst , Member March 11, 2010 Date Approved and by David Keida , Chair of the Department of Physics and Astronomy and by Charles A. Wight, Dean of The Graduate School. ABSTRACT This dissertation describes the advancements made towards the implementation of Tip-Enhanced Fluorescence Microscopy (TEFM) in imaging biological speci- mens. This specialized type of microscopy combines the chemical speci city of op- tical microscopy techniques with the resolution of atomic force microscopy (AFM). When an AFM probe is centered in the focal spot of an excitation laser with axial polarization, the probe concentrates the optical eld such that it can be used to induce nanometer scale uorescence. The physical mechanisms of this optical eld enhancement are set forth in detail. The feasibility of this technique for imaging bimolecular networks is discussed in regard to the requirements for adequate image contrast, as well as for obtaining eld enhancement in aqueous environments. A semianalytical model for image contrast for TEFM has been developed. This model shows that using demodulation techniques greatly increases the image contrast attainable with this technique, and is capable of predicting the requisite enhancement factors to achieve imaging of biomolecular networks at good contrast levels. This model predicts that signal enhancement factors on the order of 20 are needed to image densely packed samples. This dissertation also highlights a novel tomographical imaging approach. By timestamping the uorescence photon arrival times, and subsequently correlat- ing them to the timestamped motion of a vertically oscillating probe, a three- dimensional map of tip-sample interactions can be constructed. The culmination of these advancements has led to the ability to map the interactions between single carbon nanotubes and single uorescent nanocrystals (quantum dots). Various attempts at using TEFM in water have been thus far unsuccessful. Several expla- nations for this shortfall have been identi ed|understanding these shortcomings has helped to identify the optimal excitation conditions for eld enhancement. For my patient wife, Dawn. CONTENTS ABSTRACT : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : iii LIST OF FIGURES: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : viii ACKNOWLEDGMENTS: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : xii CHAPTERS 1. INTRODUCTION : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 What Is a Microscope? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.1 Di raction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.2 Resolution Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Classi cation of Microscopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.1 Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.2 Chemical Speci city . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.5 Breaking the Di raction Barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.5.1 Near-Field Scanning Optical Microscopy . . . . . . . . . . . . . . . . . . 16 1.6 TEFM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2. ENHANCEMENT VSQ_ UENCHING : : : : : : : : : : : : : : : : : : : : : : : 24 2.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2 Enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3 Plasmon Resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.4 Optical Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.5 Fluorescence Quenching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.6 Field Enhancement vs. Signal Enhancement . . . . . . . . . . . . . . . . . . . 41 2.6.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.7 Tip Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3. EXPERIMENTAL SETUP: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 52 3.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.2 AFM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.2.1 Tip Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2.2 AFM Scanning Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.3 The Optical Train . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.4 Transverse ElectroMagnetic Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.5 Gaussian Illumination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.6 Axial Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.6.1 Radial Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.6.2 The Evanescent Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.6.3 Wedge Illumination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.7 Beam Pro les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.8 Tip-Laser Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.9 System Speci cations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.9.1 Radial Illumination Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.9.2 Linear/Gaussian Illumination Path . . . . . . . . . . . . . . . . . . . . . . 78 3.9.3 Illumination Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.9.4 Detection Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4. IMAGE CONTRAST : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 80 4.1 Optics Express Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.1.2 Contrast in TEFM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.1.3 Improving Contrast via Phase Sensitive Demodulation . . . . . . . 87 4.1.4 Optimizing Tip Oscillation Amplitude . . . . . . . . . . . . . . . . . . . 93 4.1.5 Summary of Contrast Limitations . . . . . . . . . . . . . . . . . . . . . . . 95 4.1.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.2 Clari cations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.3 Negative Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.4 Enhancement vs. Quenching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5. TOMOGRAPHY : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 102 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.3 Tomographical Slices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.4 Image Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.6 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 6. AQUEOUS IMAGING : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 122 6.1 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 6.2 Early E orts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6.3 Permittivity Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 6.4 Oxide Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 6.5 Diminished Evanescent Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 6.6 Success in Other Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 6.7 Quenching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 6.8 Embedded Worms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 6.9 Fluorescence Correlation of VSV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 6.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 vi 7. CARBON NANOTUBES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 149 7.1 Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 7.2 Pickup and Shortening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 7.3 Fluorescence Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 7.4 Asymmetric Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 7.5 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 8. CONCLUSIONS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 161 8.1 Enhancement vs. Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 8.2 Image Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 8.3 Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 8.4 Aqueous Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 8.5 Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 APPENDICES A. SOLUTION OF A DIELECTRIC SPHERE IN AN OTHERWISE UNIFORM ELECTRIC FIELD : : : : : : : : : : : : : : : : : : : : : : : : : : : : 164 B. SPHERICAL SHELLS: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 168 C. TIME STAMPING CIRCUIT : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 171 D. DETAILED SMOOTH COVERSLIP CLEANING PROCEDURE173 E. CONJUGATING LATEX BEADS TO AMINE COATED SLIDES175 F. GROWTH OF NANOTUBES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 177 G. ALIGNING THE TEFM SYSTEM : : : : : : : : : : : : : : : : : : : : : : : : 183 REFERENCES: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 186 vii LIST OF FIGURES 1.1 Demonstration of the di erence between magni cation and resolution. 4 1.2 Raytracing diagram for a simple lens. . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Computer generated di raction pattern of plane waves entering a marina. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 An example of an Airy pattern, representative of a typical signal in a di raction limited imaging system. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5 Examples of two identical Airy disks separated by various distances in terms of the radius of the disk r = 0:61 =NA. . . . . . . . . . . . . . . . . . 10 1.6 Several various microscopy techniques are compared in a plot of chem- ical speci city vs. resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.7 Tree of related microscopy techniques. . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.8 Cartoon overview of TEFM.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.9 Short fragments of DNA labeled with uorescent dye molecules on either side, creating DNA \dumbbells." . . . . . . . . . . . . . . . . . . . . . . . . 19 1.10 Scanning electron microscope (SEM) image of a typical AFM tip. . . . 20 1.11 TEFM images of quantum dots on a glass surface using a silicon AFM probe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1 Experimental realization of a uorescence apertureless-NSOM setup. . 26 2.2 A dielectric sphere (Si) placed in a vertically oriented uniform electric eld. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3 Enhanced intensity decay of silicon ( 543nm Si = 17:6 + 0:12i) spheres. . . 28 2.4 A three-dimensional electrostatic nite element calculation of the max- imum eld enhancement for prolate spheroids of varying aspect ratios. 29 2.5 A 3D electrostatic calculation of eld enhancement around a near- eld probe was performed in Comsol. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.6 Peak eld enhancement as a function of tip height. . . . . . . . . . . . . . . . 31 2.7 Role of plasmonic energy dissipation and initial quantum yield in a lossy metal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.8 Role of plasmonic energy dissipation in a lossless metal. . . . . . . . . . . . 40 2.9 Calculation of eld-volume overlap integrals. . . . . . . . . . . . . . . . . . . . . 42 2.10 Approach curve of a Pt/Ir tip on a 4 9 nm CdSe/ZnS quantum dot. 44 2.11 Approach curve of a Pt/Ir tip on a 20 nm diameter dye-doped latex bead. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.12 Real and imaginary permittivities plotted for some more common dielectric materials used for AFM probes. . . . . . . . . . . . . . . . . . . . . . . 48 2.13 Real and imaginary permittivities plotted for some more common metal materials used for AFM probes. . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.14 Fluorescence rate as a function of particle-surface distance z for a vertically oriented molecule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.1 Photograph of experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.2 Cartoon of AFM feedback mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.3 Computer generated images of TEM modes of Hermite-Gaussian beams calculated from Eq. 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.4 A computer generated cross section of a radially polarized beam. . . . . 59 3.5 Cartoon diagramming the production of quasi-radial polarization. . . . 61 3.6 Cartoon diagramming the production of quasi-radial polarization us- ing polarizers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.7 Relative evanescent intensities plotted as a function of incident angle. 65 3.8 Diagram detailing the polarization state of the evanescent eld. . . . . . 67 3.9 Raytracing schematic of several di erent epi-illumination con gurations. 68 3.10 Beam masks for creating wedge illumination pro les. . . . . . . . . . . . . . 69 3.11 Beam pro les for Gaussian and radial excitation con gurations. . . . . . 72 3.12 Image of a di raction pattern around a tip under side illumination. . . 75 3.13 Illumination and detection paths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.1 Simulated superposition of near- eld and far- eld signal components in apertureless NSOM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2 Experimental setup for TEFM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.3 Cartoon of a uorescent particle imaged by TEFM . . . . . . . . . . . . . . . 84 4.4 Phase-space plot showing how photon arrivals are correlated to tip- oscillation phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.5 Expected phase dependency of lock-in signal. . . . . . . . . . . . . . . . . . . . 89 4.6 TEFM images of a high-density quantum dot sample. . . . . . . . . . . . . . 92 4.7 TEFM image contrast and signal-to-noise ratio for isolated quantum dots as a function of the tip oscillation amplitude. . . . . . . . . . . . . . . . . 94 4.8 An example of negative near- eld contrast. . . . . . . . . . . . . . . . . . . . . . 100 ix 5.1 Schematic of experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.2 Tomographical reconstruction of a 20-nm diameter uorescent sphere. 108 5.3 Comparison of approach curves at two di erent wavelengths. . . . . . . . 110 5.4 Comparison of di erent illumination and scan conditions from Figure ??. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.5 Three-dimensional tomographic reconstruction of a 20-nm diameter uorescent sphere using a silicon tip. . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.6 Comparison of tomographical and lock-in analyses. . . . . . . . . . . . . . . . 116 5.7 A comparison of cross sections over the uorescent bead taken from images found in Figure ??. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5.8 A wedge illumination simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 6.1 Cartoon diagram of imaging ESCRT protein complexes with TEFM. . 123 6.2 An example of a uorescent sample becoming attached to the AFM tip in water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 6.3 Histograms of TEFM in water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 6.4 Analytic electrostatic peak intensity enhancement values. . . . . . . . . . . 131 6.5 IVO values for Si spheres surrounded by both air and water with varying oxide thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6.6 3D electrostatic COMSOL simulation of an Si tip with a 3 nm layer of SiO2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6.7 An electrostatic COMSOL calculation of IVO values calculated for a 20 nm diameter sphere located beneath a Si tip with varying oxide thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6.8 Axial components of evanescent intensities plotted as a function of incident angle for both air and water. . . . . . . . . . . . . . . . . . . . . . . . . . 135 6.9 TEFM imaging of Calcium channels. . . . . . . . . . . . . . . . . . . . . . . . . . . 138 6.10 TEFM images of single ATTO-740 molecules in water. . . . . . . . . . . . . 140 6.11 Apparent quantum yield plotted as a function of q0. . . . . . . . . . . . . . . 142 6.12 X-Z tomographical slice demonstrating quenching in water. . . . . . . . . 143 6.13 X-Y slices of a full tomographical data set taken as a Au tip scans over a uorescent latex bead. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 6.14 Fluorescence image of a C. elegans section in plastic. . . . . . . . . . . . . . 145 6.15 AFM image of a VSV virion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 7.1 AFM topography and phase images obtained while AFM is scanned from top to bottom over a nanotube-covered silicon wafer. . . . . . . . . . 151 7.2 SEM image of a CNT probe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 x 7.3 Approach curves of nanotube shortening. . . . . . . . . . . . . . . . . . . . . . . . 153 7.4 X-Z tomographical slice of CNT tip scanning over a quantum dot. . . . 154 7.5 Blinking analyses of a single CdSe/ZnS QD interacting with a CNT probe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 7.6 Approach curve and corresponding phase histogram of a CNT buck- ling event on a QD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 C.1 Time-stamping circuit diagram for tip-oscillations. . . . . . . . . . . . . . . . 172 G.1 Numbered photo of TEFM system. . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 xi ACKNOWLEDGMENTS First and foremost I would like to thank Dr. Jordan Gerton, who has been equal parts advisor and friend. He has provided a positive work environment|it has always been a pleasure to go to work with Jordan as a boss. His e orts in procuring grant money to keep our lab running and the paychecks coming are truly appreciated. Thanks especially for allowing me so much creative freedom in my research, giving me a chance to reason out what the logical next step might be. Many thanks go out to the various lab members I have worked with throughout my time in the lab. Thanks to my predecessors in the lab, Chang-an Xie, Chun Mu, and Jon Cox, who helped train me on the system. Several undergraduates in the lab o ered help along the way: Jason Ho, Je Jensen, and Rachel Anderson. Thanks also to the more recent students, Ben Martin, Carl Ebeling and Anil Ghimire, for their helpful discussions and willingness to help in any way possible. A special thanks to Carl who has also provided his expertise in the preparation and plotting of many of the gures presented in this work. Charles McGuire did the thankless dirty work in the lab of providing a never-ending supply of glass coverslips, clean glassware, and custom machined parts, as well as for running my time-consuming COMSOL simulations. I appreciate Jessica Johnston for her nanotube troubleshooting and help in preparing a recent book chapter, which was a starting point for this dissertation. Thanks to graduate student collaborators in the biology department: Shigeki Watanabe for his worm samples and Betsey Ott has been a top notch consultant for quite some time. Last but not least, thanks to Eyal Shafran, who has been the cause of and solution to many of the problems in the lab. He has been instrumental in the development of our data acquisition and analysis programs, for which I am indebted. I have always enjoyed our many heated arguments, which in the end have yielded both better science and hopefully better scientists. I could not have made it this far in my academic career with an always sup- portive family. Thank you to my parents for providing my family a home. Thanks also to loving grandparents who have always shown interest in my work. A special thanks to my sister Liz, who has been an excellent proofreader. My super-great wife Dawn, who has always supported me in all my endeavors, deserves thanks most of all for at least pretending to care about the details of what I do in the lab each day. Her willingness to take care of life at home when I was working long hours has de nitely not gone unnoticed. xiii CHAPTER 1 INTRODUCTION This dissertation will discuss my research involving a rather specialized form of microscopy, which falls into the general category of near- eld optics. While the term \microscope" is familiar to most people, the type of instrument I use may seem quite far removed from the mental picture most people envision. In that regard, I will give a brief overview of what exactly constitutes a microscope and how my device ts into that framework. This chapter will provide a brief introduction to near- eld microscopy, accessible to both new students in the lab as well as non-physicists, who will be able to gain a better understanding of my research. The following chapters will detail the experimental apparatus used and the basic principles behind near- eld microscopy; these chapters will require some background in physics/optics. The latter chapters in this work will include much of the results, data, and conclusions I have produced while working over the last several years. 1.1 Motivation Biological cells fabricate and assemble proteins and other biomolecules into diverse networks with striking complexity and functionality. Such networks are critical components in the complicated machinery of the cell as they participate in a host of cellular functions and are important for protection against many diseases. In general, the structure of the networks plays a large role in their functionality. Thus, nanoscale-resolution imaging of intact networks in their native conformation should yield information that could create the ability to optimize speci c cellular functions, to engineer new functions, and to strengthen a cell's defense against disease. Fur- ther, these networks are prototypical nanosystems and should be studied in detail 2 for insight into the rational design of synthetic molecular systems for a multitude of technological applications. To study biomolecular systems in this context, it is crucial to observe their molecular machinery at work in a physiologically relevant environment. Currently, there are no techniques that can accomplish this. While existing techniques such as electron microscopy, x-ray crystallography, and nuclear magnetic resonance spectroscopy can yield structural information with exquisite detail, these techniques are not well suited for in vitro studies of complex molecular networks. In comparison, optical microscopy is minimally perturbative and is routinely used under physiological conditions. Fluorescence microscopy in particular is very powerful for studying biological systems because it can be used to detect and image single molecules and to distinguish between the chemical identities of those molecules based on their spectrum (color). The major limitation of traditional optical microscopy is the limited resolution ( 250 nm) imposed by classical light di raction. A new type of imaging system was organized at Caltech in the lab of Stephen Quake several years ago that was able break the di raction limit and achieve optical resolution below 10 nm [1, 2, 3]. That system combined the bene ts of scanning probe microscopy and optical microscopy. This work is really an extension of their original work. Our goal in the lab has been to further develop and re ne a similar microscope system that is capable of imaging biomolecular networks at physiologically relevant conditions, at a resolution comparable to that of single proteins (< 10 nm). 1.2 What Is a Microscope? The term microscope comes from the Greek mikr os, meaning \small", and skope^ n, meaning \to see," or simply a device to see small things. In science terminology the pre x \micro" refers to a unit of measure meaning 10􀀀6, or one part in a million; one micrometer (a.k.a. micron) is one millionth of a meter. To appreciate how small this is, the width of a human hair is about 100 micrometers (100 m), a red blood cell has a diameter of about 10 m, and spider silk has a 3 width of 3 m. In this respect, items that are roughly a \micro"-meter in size are too small to be seen without the aid of a \micro"-scope. In fact, using the same convention, the near- eld microscope employed in our lab can really be considered to be a \nanoscope" in that it allows for visualization of things on the scale of one nanometer (10􀀀9 m or one billionth of a meter). Perhaps the simplest of all microscopes is a magnifying glass. Light re ecting o a sample travels through a lens where the resulting image is magni ed. Much more complicated systems using multiple lenses have been developed to achieve very high magni cations; the magni cation of most commercially available microscopes can easily be over 1000 , meaning that the object would appear 1000 times larger under the microscope than it would with the naked eye. 1.3 Resolution As mentioned, commercially available light microscopes can easily provide mag- ni cation of over 1000 ; however, a related but separate issue is that of resolution. Resolving power for a lens refers to its ability to distinguish detail. The classic example is that of a car's headlights. As an oncoming vehicle approaches at night from very far away the headlights are noticeable; however, if the car is su ciently far away it is impossible to tell if it is a car with two headlights or rather a motorcycle with one. As the vehicle approaches, it can be seen that the two lights gradually start to appear to be separate. This phenomenon is due to the limited resolving power of the human eye. Many people have some experience with digital cameras; once a picture is taken the image can be magni ed to your heart's content on a computer. However, at some point the ne details become less clear. As seen in Figure 1.1, a portion of the image has been magni ed so it is seven times larger than the original. The magni ed portion of the image, while larger, provides no new information about the object. Magni cation can be essentially unlimited and is easily achieved, although without resolution to go along with it, magni cation can be useless. Magni cation of digital images can be done after the fact on a computer. Resolution on the other 4 Figure 1.1. Demonstration of the di erence between magni cation and resolution. The picture of my son on the left is at full size, while on the right his eye has been magni ed by a factor of 7. Notice that the magni ed image, while larger, does not provide any extra detail not already seen in the original image. hand is expensive, and relies upon the lens used to take the picture. Likewise, in microscopes magni cation is cheap: rather inexpensive systems can boast high magni cation. On the other hand, resolution is expensive: it is determined only by the lens closest to the sample, which is responsible for gathering light (the information) and is called the objective lens. Now we have some small sample that we would like to put under our microscope to observe, such as very small grains of sand spread out on a piece of glass. Should we want to look in the microscope to count the grains of sand, an important question to ask is: how powerful of a microscope is needed? The answer is based not strictly on the size of the grains but also the spacing. For counting, we are not interested in the structure of each grain; we simply want to know how many there are. To accurately count them all, the resolving power of the microscope will need to be better than the smallest distance between two grains, lets call it L. Lord Rayleigh calculated that the best resolution a microscope can give is based on the properties of its objective lens. Namely, L = 0:61 NA ; (1.1) 5 where is the wavelength, or color, of the light being used, and NA is the Numerical Aperture of the lens. More often, this resolution limit is expressed in terms of the Numerical Aperture (NA) of the objective lens. Simply put, the numerical aperture de nes the light gathering ability of a lens. Again think of a magnifying glass, this time used to burn ants. While a bit sadistic, it is easy to visualize. To e ciently burn an ant, a high NA lens is desirable as it would gather a lot of sunlight and concentrate it to a tight (and deadly) spot. A more technical de nition of NA is actually: NA = n sin ; (1.2) where n is the index of refraction of the media the lens operates in1, and is the maximum angle from which light rays can enter the lens. Numerical aperture is related to the diameter of the lens D, as well as its focal length (f): NA n D 2f (1.3) This can be visualized via Figure 1.2; formally tan = r=f, where r is the radius of the lens, is the angle indicated, and f is the focal length of the lens. For small angles, tan sin , which leads to the solution of 1.3. Thus Rayleigh's formula can also be written as: L = 1:22 f D ; (1.4) which assumes imaging in air (nair = 1:0). Camera bu s will recognize the ratio f=D as the f=# of the lens. Notice that the diameter of the lens is important|the bigger the diameter, the better the achievable resolution. This is precisely why professional camera equipment seems to be so large and produces such nice results. Of course as the size of a lens is increased, the cost of the lens rises even faster. Producing and polishing high quality optics gets more expensive as the size increases, as the smoothness of 1The index of refraction can be thought of as a measure of the ability of a material to bend light. Technically it is a measure of how fast light travels in that media (v) relative to the speed of light in a vacuum (c); n = c=v. 6 f Figure 1.2. Raytracing diagram for a simple lens. Rays parallel to the optic axis (dashed line) are focused at a distance away from the lens called the focal point, f. The maximum angle is given by rays originating from the extremities of the lens. a quality lens should be much less than the wavelength of light, or should not have bumps over several tens of nanometers. The NA of a microscope objective is a very important parameter in microscopy, as it ultimately determines the maximum achievable resolution. As seen in Equation 1.2 it is limited by the index of refraction of the media, even if all possible light is collected = 90 ) sin = 1. The most common media used in microscopy are air (na = 1:0), water (nw = 1:33), and oil (no = 1:5), and thus the best objectives have NA's of 0.95, 1.20, and 1.49 for air, water, and oil respectively. Wavelengths for visible light range from 400 nm (blue) to 700 nm (red). Assuming blue light and an oil immersion numerical aperture of NA = 1:49, this limits the resolution of the best optical microscopes to 164nm. In practice such values are rarely seen as often the wavelength of light employed is much longer; more commonly, the resolution limit is generally held to be around 250 nm. In this manner, the resolution capabilities of a microscope is ultimately de- termined by the light gathering abilities of the objective lens. As the NA of the microscope objective is increased, more of the light information from the sample is collected|allowing for a more complete image reconstruction of the sample at the detector. Thus as the NA of a microscope objective is increased the better the 7 resolution will be; however, due to di raction, image patterns become distorted. 1.3.1 Di raction The ability of all waves, be they water, sound, light etc., to bend around edges is known as di raction. To quote the famous text by Landau and Lifshitz [4]: Di raction phenomena can be observed, for example, if along the path of propagation of the light there is an obstacle|an opaque body (we call it a screen) of arbitrary form. If the laws of geometrical optics were strictly satis ed, there would be beyond the screen regions of \shadow" sharply delineated from regions where the light falls. The di raction has the consequence that, instead of a sharp boundary between light and shadow, there is a quite complex distribution of the intensity of the light. These di raction phenomena appear the more strongly the smaller the dimensions of the screens and the apertures in them, or the greater the wavelength. Di raction phenomena are visible in many everyday occurrences. One example is that of waves entering a marina as seen in Figure 1.3. Marinas have rock barriers shielding the ships docked inside from large waves. As planar waves enter the marina through a narrow opening, the waves are di racted, creating a complicated pattern lling the entire marina. Notice how the waves stop traveling with planar wave fronts upon entering the marina; due to di raction, the wave fronts propagate in a circular pattern. In optics, the ability of a lens to focus light to a spot depends in part on the di raction limit. Since light waves impinging on a lens are di racted, the light can not be focused to an in nitely tight spot. Consider how the light impinging on the edges of the lens would tend to bend around the edge. Due to the bending of the light around the edges of a lens, a particular pattern known as an Airy pattern emerges (cf. Fig. 1.4), which has a central bright spot surrounded by faint rings of lower intensity. This di raction limit goes both ways: it limits the ability of a lens to focus light, but also the ability of a lens to image small objects. This means that an isolated in nitesimally small object when imaged by even the best of microscopes would appear as an Airy pattern, whose dimensions would depend on the objective 8 Figure 1.3. Computer generated di raction pattern of plane waves entering a marina. Notice how the wave di racts through the entrance of the marina. Also observable is di raction around the outer corners of the rock walls. Figure 1.4. An example of an Airy pattern, representative of a typical signal in a di raction limited imaging system. The diameter of the central disk is given by Eq. 1.5. Here a nonlinear colorscale is used to give emphasis to the outer rings. 9 lens being used. In fact, the full width of the central disk of the airy pattern has a diameter (D) given by:2 D = 1:22 NA : (1.5) For example, there is a 3-nm large single protein that is a sitting on a piece of glass that we would like to image. We put it under a microscope using a very nice objective (NA = 1.4) using red light, and the image we would get is not a 3-nm spot, but an Airy pattern (as seen in Fig. 1.4) with a diameter of D = 1:22 600nm=1:4 525nm. As Ernst Abbe was the rst to estimate the theoretical di raction limit (1872), it often bears his name (Abbe Limit). He calculated the smallest spot size would have a radius r given by: r = 0:61 NA : (1.6) The factor 1.22 is speci c to circular openings, and takes complicated mathematics to be able to derive. If this equation seems very similar to Rayleigh's, it is because Rayleigh used the di raction limited spot size to determine the resolution limit. 1.3.2 Resolution Criteria Lord Rayleigh used the known result from the Airy function and put a limit on what was considered resolvable. The limit he decided upon, for sake of simplicity, was to say when two identical Airy patterns are closer than the radius of the central disk, they are no longer resolvable. This is demonstrated in Figure 1.5 where two Airy patterns are brought increasingly close together. As seen, the point at which they can no longer be distinguished as two separate objects is actually a little ambiguous. In fact other criteria for minimally resolvable objects have also been established. For example the Sparrow criterion states that the two objects are resolvable as long as there is a saddle point between them. In other words, as long as the combined intensity pro le contains a central dip, the objects are said 2There is often some confusion with the diameter of the di raction limited spot. The diameter D given here is correct, often the Full Width Half Maximum (FWHM) of the spot is reported, which is close to the radius of the spot r, but not quite: dFWHM 0:84 r for an Airy pro le. 10 (a) (b) (c) (d) Figure 1.5. Examples of two identical Airy disks separated by various distances in terms of the radius of the disk r = 0:61 =NA. Panel (a): Airy disks separated by 1:3 r ) clearly resolved. Panel (b): Airy disks separated by r ) the Rayleigh Criterion is just met. Panel (c): Airy disks separated by 0:77 r ) the Sparrow criterion is just met. Panel (d): Airy disks separated by 0:5 r ) unresolved. to be resolvable. Without worrying about the mathematical de nition of saddle point|the criterion is also illustrated in Figure 1.5(c). The Sparrow criterion is widely regarded as a more natural de nition of resolution. The di raction limit puts a lower bound of 250 nm, meaning that features smaller than this cannot be resolved. This presents a major hurdle for scientists trying to understand the world on the nanoscale. 11 1.4 Classi cation of Microscopes A microscope that relies on light and utilizes lenses to magnify an image is an optical microscope or light microscope. While this may seem trivial, there are actually many di erent types of microscopes, some of which do not rely on light at all. Trying to categorize all existing microscopes would be a daunting task in that there are myriad variations and combinations of di erent techniques; however, in general there are three main classes: optical (or light) microscopes, electron microscopes, and scanning probe microscopes. Electron microscopes use beams of electrons that are directed onto a sample. Images can be acquired by measuring the electrons that either scatter o the sample or penetrate through it. Scanning probe microscopes use sharp probes that scan over the surface of a sample to record the topography (among other things). Each of these has speci c advantages and disadvantages. Light microscopes o er supreme chemical speci city, allowing for distinction of individual types molecules within dense ensembles of biological networks, however, with limited spatial resolution. Electron microscopes can o er excellent resolution, their downfall being a lack of chemical speci city and incompatibility with live biological specimens. Scanning probe microscopes provide resolution on almost the same scale as electron microscopy, and can be compatible with live biological specimens, but yet can only be used to probe the surface of a sample. This section will discuss how it is that light microscopes achieve their high chemical speci city, and the importance of having such a trait. 1.4.1 Fluorescence Many types of optical microscopes rely on a physical process called uorescence. Fluorescence refers to an object's ability to absorb light, only to re-emit the light at a later time. Generally speaking the light that is re-emitted is not even the same color as the absorbed light: it is less energetic (more red) and is called red-shifted. Furthermore, the light that is re-emitted is at a later time|just a very brief time later - on the order of nanoseconds (10􀀀9 s). Objects that exhibit this property are uorescent, and the part of the object where this process actually takes place is 12 called a uorophore. Many substances can be uorescent; dye molecules, single proteins, and nano- sized crystals called quantum dots (QDs) are some of the most important uorescent substances used in scienti c research. The real power of uorescence microscopy is that these uorophores can be attached to virtually anything with great speci city. The attachment of quantum dots or dye molecules can be done through chemical means, where after a series of reactions, some specimen of interest can be \tagged" or \labeled" with a uorophore. Scientists have also gured out how to label pro- teins with other uorescent proteins using genetic methods. In fact, this technique is so important that the pioneers of this method were recently awarded the 2008 Nobel prize in chemistry. Some types of jelly sh (among other animals) naturally produce uorescent proteins in their body called Green Fluorescent Protein (GFP). Scientists have the ability to remove this jelly sh DNA, which contains the code for GFP, and attach it to the DNA of some other cell. In this manner scientists can determine the function of certain parts of cells with extremely high speci city. Biologists interested in the function of a certain part of a cell - perhaps a cell membrane protein, could take the jelly sh DNA for GFP attach it to the DNA that encodes for the cell membrane protein, and inject this new DNA construct into an embryo. As it develops all the cell membranes would also have GFP attached, and thus also be uorescent. This genetically modi ed cell/animal is known as a mutant. At this point, the mutant is put under a microscope, it is illuminated with blue light, and the tagged cell membrane proteins will uoresce green. Thus, the uorescent green light will show the location of the cell membrane proteins. 1.4.2 Chemical Speci city Given this unique ability to label virtually any sample of interest, uorescence microscopy has an extremely high chemical speci city. Some microscopes o er very high resolution, but with low speci city. Scanning probe microscopes can provide very high resolution ( 1 nm) details of surface topography, but without some advanced knowledge of what to expect, all that is really seen is just bumps on a 13 surface. As scanning probes do not use light, they are not subject to the di raction limit. The resolution of scanning probes depends only upon the shape of the probe used. Extremely sharp (narrow) probes can accurately provide information on the smallest contours of a surface. Dull (fat) probes may not be able to t into small crevasses, and tend to broaden and average out surface details. While scanning probe microscopy can o er exquisite detail of a surface, the microscope itself cannot determine what the bumps mean. This can be problematic as there is no way to di erentiate between two similar sized objects. There is no way to determine which object is which. However, one nice feature of scanning probe microscopy is that it can be compatible with biological specimens, even live cells. Electron microscopes can yield even better resolution (< 1 nm), but again, with low chemical speci city. From a physicist's standpoint, electrons can also be thought of as waves, with an extremely small e ective wavelength that depends on their velocity; commercially available systems can easily reach e ective wave- lengths of 0.004 nm. Due to this small wavelength tremendous resolution can be obtained, but the information conveyed is primarily about the density of the sample. Again causing objects of similar sizes and densities to be indistinguishable. Unfortunately, electron microscopy is extremely incompatible with imaging live biological specimens. To provide adequate image contrast, cells must be xed and embedded in plastics and treated with harsh chemicals, thus live cell imaging is completely out of the question. The great virtue of light microscopy is that extremely high chemical speci city is obtainable through uorescence labeling; di erent objects of similar sizes can be labeled with di erent colored uorophores, making them now distinguishable. The ideal microscope then is one that can take advantage of the tremendous chemical speci city a orded by uorescence techniques, that is not subject to the limits of di raction, as detailed in Figure 1.6. This is the goal that I have been working toward throughout my graduate career: to combine the utilities of scanning probe microscopy with light microscopy to allow for imaging of biological samples. The hybrid technique is dubbed Near-Field Scanning Optical Microscopy (NSOM or 14 Survey of Microscopy Techniques Chemical Specificity Resolution Bright-Field Raman Fluorescence Near-Field AFM Electron Beam X-ray Crystallography Figure 1.6. Several various microscopy techniques are compared in a plot of chemical speci city vs. resolution. Increasing chemical speci city is up, while increasing resolution is to the right. Thus, the ideal microscope would be found at the top-right corner. SNOM). Its relation to other microscopy techniques is illustrated in Figure 1.7. 1.5 Breaking the Di raction Barrier While the di raction limit is still in full force for all optical microscopes, sci- entists have come up with many clever ways to eke out all the resolution possible from a system. The most obvious techniques involve not breaking the di raction limit, but simply pushing the boundaries of it. One way this is accomplished is by reducing , using bluer light, even going to UV or X-Ray wavelengths. Shorter wavelengths require specialized optical components and light sources, as most optical glass absorbs strongly at these wavelengths. Increasing the NA of a system also will lead to better resolution, but again this is limited by the index of refraction of materials. By moving to specialized high index of refraction oils and 15 MICROSCOPY Scanning Probe Optical Electron FAR FIELD Scanning Near-Field Optical Microscopy (SNOM) Atomic Force Microscopy Transmission Electron Microscopy Scanning Electron Microscopy Apertureless SNOM Aperture SNOM Fluorescence Bright Field Raman Scattering Raman Fluorescence SNOM Figure 1.7. Tree of related microscopy techniques. glass, microscope objectives can be found at ever increasing values of NA. Other techniques involve the simultaneous use of two objectives (one on either side of the sample) to make further gains in increasing the NA of the system [5]. Microscopy techniques that actually break the di raction limit are also actively being pursued. These include using tailored laser beams that have complex intensity pro les, whose envelope function is di raction limited, but has regions within the beam pro le that can be much smaller than the di raction limit [5]. Other ideas rely on the fact that we can locate the center of an object very well, but as usual this is only possible if we can resolve it, i.e., tell that there is only one object present. The method then is to only look at uorophores one at a time, by turning them on in either a random or controlled fashion, and then measuring the location before a neighboring uorophore is subsequently activated. 16 1.5.1 Near-Field Scanning Optical Microscopy Another class of optical techniques that beat the di raction limit are included in the realm of near- eld microscopy The di raction limit is actually only a far- eld phenomenon. In this regard, any technique that is a near- eld technique is inherently not subject to the far- eld di raction limit. The pre xes \near"and \far" refer to a distance relative to the wavelength of light employed. Thus \near" eld can signify that either the sample is illuminated by a light source much less than a wavelength away (d << ) or that a detector is much less than a wavelength away from the sample. Another term for the near- eld region is the Fresnel zone. Conversely, far- eld phenomena refers to both an illumination source and detector that is at a distance much longer than a wavelength away d >> . Far- eld di raction is also known as Fraunhofer di raction. For example, in the types of microscopy discussed thus far, a lens is placed quite far, relatively speaking, from a sample in order to collect light (information) coming from the sample. As the wavelength of visible light is 400 - 700 nm, even a sample placed 1 cm from a lens is 20,000 wavelengths away, and thus would have far- eld detection. If somehow a local excitation source were placed within several tens of nanometers from the sample it would have near- eld illumination. Again, even within the realm of SNOM there are many variations. NSOM is a relatively new eld, having really only existed in practice for the last 15 years, and naming conventions are still being developed. NSOM is the acronym most commonly used in North America, while SNOM is more popular in Europe. There are two main branches of NSOM: aperture type and apertureless (cf. Fig 1.7). Both rely on a particular scanning probe technique|atomic force microscopy (AFM) for ne control of a probe. Aperture type NSOM involves a hollow AFM tip with an opening at the distal end of 50-80 nm wide. Light is focused down the center of the tip until only some small fraction exits the narrow aperture as much is lost as it travels down the tip. By scanning this hollowing tip over a sample, a local light source provides near- eld detection. Either far- eld or near- eld detection can be employed with 17 this technique. Apertureless NSOM, relies on a solid AFM tip aligned within the central focus of an excitation beam. With the appropriate choice of tip, and by carefully tailoring the polarization of the laser beam, the tip can amplify the optical elds around it, such that a region of extra intensity can occur at the apex of the tip. In this way, the apex of the tip acts as a local light source as it is scanned over a sample, capable of providing near- eld illumination. Detection of light signals in this case is always done in the far- eld. Unfortunately both types of NSOM begin with the letter A, so the acronym \ANSOM" has been used to refer to both types of techniques, although it is slightly more common to use ANSOM in reference to apertureless-NSOM. Within each branch of NSOM there are several variations still of each technique. As we are interested in combining the attributes of uorescence microscopy with AFM, the particular avor we practice in our lab is uorescence-apertureless-NSOM. The term FANSOM, has been coined and used in a limited way, however, to avoid any ambiguity with a related aperture type technique, the preferred terminology in our lab is Tip-Enhanced Fluorescence Microscopy or TEFM. 1.6 TEFM Figure 1.8 represents the basic operating principles of TEFM. An AFM probe is aligned into the center of a focused laser. The AFM tip is vertically oscillating, constantly tapping the sample. The tip and laser are aligned, then the sample is scanned between the two. As the sample scans under the tip, the topography is recorded by monitoring the motion of the tip. Simultaneously uorescence signals coming from the sample are also collected. Additionally, the AFM is able to report extra information beyond simply the height, a relative measure of how hard/soft or sticky a sample is also simultaneously acquired in a separate data channel. If the tip material and laser polarization are carefully controlled, a region of enhanced local eld surrounds the apex of the tip. A uorescent sample sits atop a glass coverslip. As the sample is in the far- eld focused laser spot, it will be 18 Fluorescence Focused Laser AFM Probe Figure 1.8. Cartoon overview of TEFM. A sharp tip is positioned within the focus of an excitation beam, which causes an enhanced local eld at the apex of the tip. The sample (circle) is being illuminated by the far- eld background signal and emits uorescence photons (downward arrows). When the tip apex is near the sample, the local eld associated with the tip apex leads to extra uorescence signal but at a much higher resolution. emitting photons, which will produce a di raction limited image. As the tip is brought in close proximity to the sample the \extra" eld around the tip apex also illuminates the sample, which in turn gives o more uorescence signal. Again, the properties of the tip are very important in order to be able to observe any eld enhancement. Some materials, such as metals, can lead to a local reduction in uorescence signal via a process called quenching. Actually, near- eld signals can come from either enhancement or quenching of the far- eld uorescence signal. TEFM signals contain both a di raction limited far- eld background signal as well as a near- eld signal, whose resolution is only limited by the sharpness of the tip. In terms of optical resolution, TEFM is the world-record holder, coming in at under 10 nm [2, 3]. My advisor, Jordan Gerton, and co-workers in Stephen Quake's group at Caltech have demonstrated the extreme resolution capabilities of TEFM by imaging short strands of DNA labeled with uorescent dye molecules at either end. By measuring the distance between the two uorophores, and using a known code of DNA 60 base pairs in length, they were able to determine the length per base pair of that particular kind of DNA, as shown in Figure 1.9. While there 19 Figure 1.9. Short fragments of DNA labeled with uorescent dye molecules on either side, creating DNA \dumbbells." These dumbbells were imaged with TEFM, resulting optical images are shown in (a)-(c) with pro les shown as insets. The corresponding AFM topography images are shown in (d)-(f). Scale bars are 50 nm. The length of the DNA chain was determined optically, by the distance between uorescent centers. Panel (g) shows a histogram of these distances. Panel (h) represents a control experiment, where some single dye molecules exhibit double lobe artifacts - the resulting distances between the artifactual lobes are plotted here as a histogram. Reprinted with permission from reference [3]. Copyright (2006) by The American Physical Society. 20 are obvious limitations to TEFM in the fact that it is a surface technique, such demonstrations have shown the great promise that TEFM has towards unraveling an untold number of biological secrets. Just as AFM resolution depends on the sharpness of the probe being used, TEFM resolution scales with tip size. Thus a sharper probe (assuming it is made of the appropriate material) leads to both higher AFM and optical resolution. The sharpness of such AFM probes is often described by the radius of curvature at the apex, as at this scale there really is no such thing as a sharp corner. Commercially available AFM tips can have radii of curvature less than 10 nm. Figure 1.10 shows an SEM image of a typical AFM tip used in our lab. As mentioned, a raw, TEFM image consists of both near- eld and far- eld components, which makes such raw images messy and di cult for non-experts to interpret. Much work has been devoted to removal (or at least suppression) of the far- eld background signal, as high levels of far- eld background signal lead to worse Figure 1.10. Scanning electron microscope (SEM) image of a typical AFM tip. This type of tip (silicon) is also capable of exhibiting strong eld enhancement at the apex under appropriate illumination conditions. 21 image contrast. Some rather straightforward and very e ective techniques such as lock-in demodulation have readily been applied to tackling this problem as seen in Figure 1.11. Other more sophisticated background suppression (or near- eld isolation) techniques have also been of particular interest in our lab's research. A great deal of my work has dealt with understanding and devising means of suppressing these unwanted background signals. 1.7 Summary As mentioned we have developed a uorescence microscope in our lab that is ca- pable of nanoscale resolution imaging of single uorescent molecules ( uorophores) [2, 3, 7, 6, 8], which we call a tip-enhanced uorescence microscope (TEFM). To date, we have primarily used this instrument to image isolated uorophores in air, and have repeatedly demonstrated spatial resolution of 10 nm. The objective of my project has been to adapt the microscope for imaging in an aqueous 0 100 200 300 400 0.04 0.06 0.08 Lock In (V) Position (nm) 12 nm 200nm (a) (c) (b) 500nm Figure 1.11. TEFM images of quantum dots on a glass surface using a silicon AFM probe. (a) Fluorescence image of several isolated quantum dots with no lock-in ampli cation. The size of the far- eld spot is about 1 m 0:5 m. (b) Lock-in magnitude image of an isolated quantum dot. (c) Pro le speci ed by dashed line in (b). Reprinted with permission from reference [6], c 2008 IEEE. 22 environment, and further, to optimize its performance to enable imaging of protein networks in planar membranes assembled onto glass coverslips. To accomplish this, two benchmarks must be met. First, the contrast of the microscope must be su cient such that individual molecules within a dense ensemble can be resolved. Second, the microscope must be made to work e ciently in water. We have made substantial progress in the rst area and are now addressing the second. These have been the primary objectives of my research in the lab; some of the successes in reaching these objectives, as well as some of the remaining hurdles, will be discussed throughout the body of this dissertation. Chapter 2 will provide the background theory necessary to understand what an optical near- eld is, and how it is created. The concept of eld enhancement at a tip apex will be explored in depth. Additionally, uorescence quenching and its role in near- eld optics will also be described in detail. Finally, it also discusses optimization of probe geometries/permittivities for maximal results. Chapter 3 will discuss the experimental setup required to make TEFM a reality. This includes both the hardware requirements and some of the basic theory needed to appreciate the design of the instrument. This is a very technical chapter, explaining the particular intricacies of our imaging system, and is primarily intended for new students in the lab. TEFM as an imaging system will be discussed in Chapter 4. More particularly, attention will be focused on image contrast, and how demodulation techniques can be used to increase contrast. The primary focus will be on the near- eld enhancement of uorescence, but some discussion on uorescence quenching as a contrast mechanism is also included. This chapter has provided an important framework for the way in which we describe and discuss our system. Chapter 5 describes a particular data acquisition technique that allows for three-dimensional mapping of near- eld interactions. This near- eld tomography, as it is called, has become an important addition to the lab, allowing for unlimited post-processing possibilities of any data we collect in the lab. Results from various attempts at imaging in aqueous environments are shown 23 in Chapter 6. Thus far, we have had extremely limited success in using TEFM in water. Many explanations of why TEFM in water has been so elusive are given. As a consequence of this analysis, the optimal excitation mode is also described. Other methods for imaging biological samples at nanoscale resolution are also discussed. Finally a possible way forward for using TEFM in water is sketched out. Chapter 7 presents the latest applications of utilizing TEFM in conjunction with carbon nanotube (CNT) tips. The extreme precision of our measurement techniques are highlighted by measuring CNT-quantum dot interactions. Finally, a discussion of important future experiments using CNTs is included. CHAPTER 2 ENHANCEMENT VSQ_ UENCHING Thus far I have given a basic overview of tip-enhanced uorescence microscopy and discussed some of the requirements for achieving optical near- elds, namely that aligning a near- eld probe in the center of a laser beam with axial polarization leads to an enhanced eld at the apex of the probe. This chapter explores the particular mechanism for this creation of optical near- elds and the factors that in uence both the strength and extent of such elds. In addition to discussing the factors in uencing enhancement, this chapter also explores the opposite of enhancement: quenching. Brie y, quenching is a process leading to decreased uorescence signals as the presence of a metal structure increases the nonradiative decay rates of a uorophore. Quenching is an extremely important factor in near- eld microscopy in that any uorescence signal obtained in TEFM is the net result of a competition between enhancement and quenching. Experimentally these two e ects can be di cult to separate, as they can often be competing on similar length scales. To rst order, eld enhancement relies on only the particular details of the tip and incident eld. Quenching, on the other hand, is somewhat more complicated. Quenching is not a decrease in local eld strength, but rather it is described by nonradiative uorescence decay channels, thus its e ects cannot be determined without a knowledge of the current state of the uorophore. Factors determining the extent of quenching by a tip then include the initial radiative and nonradiative decay rates, quantum yield, tip-material, and tip-geometry. While this chapter will discuss enhancement and quenching separately, the focus will be on the importance of appreciating the interplay between the two. 25 2.1 Setup In order to properly ubicate the relevance of the theory presented in this chapter, it is rst necessary to understand the experimental setup we employ. The basic microscope schematic is shown in Figure 2.1. Brie y, illumination and detection are achieved via the same inverted microscope con guration. Axial polarization of the excitation laser is achieved by either a radial polarization state or evanescent illumination from blocking all but a small wedge of supercritical rays at the back aperture of the objective. The tip can be operated in contact mode, where is is simply dragged along the surface, or tapping mode, where it oscillates vertically, only tapping the surface intermittently. 2.2 Enhancement When a dielectric material is placed in a uniform electric eld, the applied eld polarizes the material as the electrons and ions migrate toward their respective sides of the dielectric [9]. This charge separation creates an induced electric eld, and the total eld near the surface of the material is the superposition of both the applied eld and the induced eld. For a dielectric sphere, the induced eld can be obtained analytically, as shown in Equation 2.1, and illustrated in Figure 2.2. Here, a uniform static eld is applied along the vertical axis, but the calculation is also valid for an oscillating eld with vertical polarization if the size of the sphere is much smaller than the wavelength. In this quasi-static approximation, retardation e ects can be neglected and at each point in time, the applied eld can be considered uniform. At the vertical poles of the sphere, the total electric eld is enhanced relative to the applied eld, while the total eld is reduced along the horizontal equator. E~out (r; ) = E~0 cos 1 + 2 r 􀀀 1 r + 2 R3 r3 ^r + ~ E0 sin 􀀀1 + r 􀀀 1 r + 2 R3 r3 ^ (2.1) From Equation 2.1 it can be seen that the maximum electric eld strength occurs at the poles of the sphere, and is given by: Emax = E0 1 + 2 r 􀀀 1 r + 2 ; (2.2) 26 (b) (c) 2f f OF f APD BM SF DM SM OBJ AFM Z X Y (a) Figure 2.1. Experimental realization of a uorescence apertureless-NSOM setup (a). An excitation beam exits an optical ber (OF) and goes through a beam mask (BM) in either a wedge or radial con guration. The excitation beam is re ected by a dichroic mirror (DM) and o a scanning mirror (SM) before being focused through a microscope objective (OBJ). Signals are collected through the same path and directed onto an avalanche photodiode (APD) after passing through the appropriate spectral lters (SF). Panels (b) and (c) show ray diagrams for a radial and wedge beam mask respectively. Solid arrows show the direction of beam propagation (dark arrows for excitation and lighter arrows for emission), while dashed arrows represent the polarization direction. where E0 is the applied eld and r is the permittivity of the sphere relative to that of the surrounding medium: r = dielectric= media. In principle, a dielectric sphere can be used as an apertureless NSOM probe if it can be scanned in close proximity to a sample. In this case, the enhanced eld at the distal pole of the sphere can increase the optical response. This response is generally proportional to the optical intensity or higher orders thereof depending on the particular scattering process [10], the expression in Equation 2.2 must be raised to an appropriate power to nd the expected enhancement in the scattering rate. For dielectrics, the magnitude of this e ect in some sense is independent of the size of the sphere. As shown in Figure 2.3, -f- --1- 27 0.5 1 1.5 2 20 nm 2.5 Figure 2.2. A dielectric sphere (Si) placed in a vertically oriented uniform electric eld. The dark regions correspond to elevated electric elds. The incident eld has a strength of E0 = 1V=m as can be seen on the scale shown. the peak eld enhancement for a dielectric sphere is identical, regardless of particle radius, the caveat being that the eld decays more slowly. A slowly decaying eld around a near- eld probe leads to a decrease in optical resolution, an unwanted e ect. Note also that it is in this manner that near- eld resolution is a function of tip-sharpness rather than wavelength|in general, sharper tips have a steeper eld decay. For dielectric materials, the peak intensity can be enhanced by at most a factor of nine (when r ! 1 ) for this spherical geometry. Although the spherical geome- try can be solved analytically, it often does not accurately approximate the shape of many AFM tips. Furthermore, elongated geometries can yield signi cantly larger eld enhancement. Figure 2.4 demonstrates this e ect by plotting the maximum intensity enhancement from a three-dimensional nite element calculation of prolate spheroids of increasing semiaxis ratios. In fact, Bohn et al. have shown that as the long axis of the spheroid approaches in nity, the intensity enhancement adopts the 28 0 0 5 10 15 20 25 30 35 40 45 50 1 2 3 4 5 6 7 8 Distance from tip (nm) Relative Intensity R = 10 nm R = 20 nm R = 30 nm R = 40 nm Figure 2.3. Enhanced intensity decay of silicon ( 543nm Si = 17:6 + 0:12i) spheres. The eld decay for several sized dielectric spheres is plotted taking = 0 from Eqn. 2.1 and then plotting for r R. The peak eld enhancement is independent of radius. Larger particles lead to slower eld decay and thus would yield poor optical resolution when used as a near- eld probe. analytic form [11]: Epeak = E0 r ) Ipeak = E2 0 2r ; (2.3) which is reproduced well in the numeric calculations shown in Figure 2.4. This geometry-dependent electric- eld enhancement, where the highest enhancement values occur in regions of highest curvature is known as the lightning-rod e ect. It is important to remember that Equations 2.2 and 2.3 are strictly valid for static electric elds, and thus can only be used for optical elds (resulting from either continuous wave or pulsed lasers) when retardation e ects can be neglected, namely when the size of the object is much smaller than the light wavelength. This, of course, prohibits rigorous application of Equation 2.3 for commercial AFM tips in NSOM, as the entire structure of a commercial tip, while very sharp at the apex, is an extended structure many times larger than optical wavelengths ( 10 m). . ·1 - 29 0 10 20 30 40 50 60 0 2 4 6 8 10 12 14 16 18 Axis Ratio Peak Field Enhancement Factor Figure 2.4. A three-dimensional electrostatic nite element calculation of the max- imum eld enhancement for prolate spheroids of varying aspect ratios. Spheroids were given the permittivity of silicon (17.6+0.12i @ 543 nm). Aspect ratio is calculated as the semi-major axis divided by the semi-minor axis of the prolate spheroid (short axis was kept constant). The incident eld is applied parallel to the long axis of the spheroid. The horizontal line is the theoretical limit as the ratio approaches in nity as found in Eq. 2.3. Nothing prohibits applying Equations 2.2 and 2.3 to metal nanoparticles as long as the size of the particle is no larger than the optical skin depth, = =(4 p ); otherwise, the bulk electrons are shielded and only the surface electrons experience the external driving eld. In general the dielectric function is complex valued and also frequency dependent, r(!) = 0r(!)+ 00 r (!) . Here the imaginary part relates to light absorption, which ultimately results in energy loss through ohmic dissipation (Joule heating) [12]. Metals generally have negative values for the real parts of their dielectric function throughout the visible spectrum, which also raises the possibility of exciting plasmon resonances (cf. Eq. 2.1 for r = 􀀀2) that can massively increase the enhancement factor (see below). More precise predictions of the eld enhancement for realistic tip geometries, such as the conical or pyramidal tips that are commercially available, can be ob- tained by solving Maxwell's equations on a discrete grid using a nite element anal- 30 ysis program such as COMSOL [13] or CST Microwave Studio [14]. Alternatively, a discrete dipole approximation (DDA) [15] or multiple multipoles method can also be used [16]. These previous calculations have predicted intensity enhancement factors in excess of 1,000 for metal tips and around 225 for dielectric tips [16, 11]. The previous calculations by Bohn et al. using spheroids have been readily duplicated (as evidenced by Fig. 2.4), and a slightly more realistic probe geometry is now used. Using a nite element solver (COMSOL) I have also calculated the expected eld enhancement for a dielectric tip as shown in Figure 2.5. A silicon tip is represented as a conical probe with an aspect ratio of 4:1 (equivalent to a half cone angle of 14 ). Near the apex of the probe the cone has been truncated and replaced with a symmetric quadratic B ezier curve with an identical aspect ratio in a continuous fashion. The sharpness of the tip can be considered to have a radius of 10 nm; the tip height is 10 m. The maximum intensity enhancement factor of such a probe was calculated to be nearly 3000. 5 nm Figure 2.5. A 3D electrostatic calculation of eld enhancement around a near- eld probe was performed in Comsol. A small portion of the simulation is viewable here. The modeled Si tip has a radius of 10 nm, a height of 10 m, and an aspect ratio of 4:1. The scale bar indicates the magnitude of the eld, where the incident eld is 1 V/m. 31 Such large enhancement factors have never been observed. For example, to the best of our knowledge, the largest signal enhancement factor reported for silicon tips is 20 for uorescence measurements of 4-nm diameter quantum dots [2]. This discrepancy between predicted and observed enhancement values could also be due to rapid growth of oxide layers, which have a smaller permittivity, or to irregular geometry. Furthermore, quenching, redirection of uorescence, and interference e ects can also contribute to such a discrepancy. Clearly the geometry of the probe in all aforementioned calculations is quite di erent from real probes. Furthermore, keeping the apex of the tip the same size, while changing the tip height can lead to vastly di erent values in calculated enhancement factors as shown in Figure 2.6. More properly, the amount of tip-enhancement in such electrostatic calculations 100 5 10 15 20 25 20 30 40 50 60 70 80 Tip Height ( m) Peak Field Enhancment Figure 2.6. Peak eld enhancement as a function of tip height. A 3D electrostatic calculation of eld enhancement around a near- eld probe was performed in Comsol. A silicon tip is modeled by a conical probe with an aspect ratio of 4:1. The apex of the probe the cone has been truncated and replaced with a symmetric quadratic B ezier curve. The peak enhancement factor under the tip is plotted as a function of the tip height|keeping the geometry of the apex constant. 32 scales with the volume. This can be troublesome as many calculations keep the vertical extent of the probe to a minimum in order to lower computational demands. As evidenced by the drastically di erent results reported in the literature, these calculated enhancement values must be used as only very rough estimates. 2.3 Plasmon Resonances The primary optical response of metals in the presence of a driving eld is determined by the motion of their conduction electrons, which have an e ective mass characteristic of the particular material. Neglecting the response of the valence electrons (i.e., interband transitions), we can then apply the Drude-Sommerfeld model for the free electron gas and solve for the frequency-dependent permittivity: Drude = 1 􀀀 !2 p !2 + 􀀀2 + i 􀀀!2 p ! (!2 + 􀀀2) ; (2.4) where !p = p ne2=me 0 is the bulk plasma frequency, n is the free-electron density, e and me are the electron charge and e ective mass, 􀀀 = vf =l is a damping term, and vf and l are the Fermi velocity and mean free path of the electrons. For ballistic charge transport (i.e., 􀀀 = 0), the dielectric function is zero at the plasma frequency, positive at high frequencies (i.e., UV), and negative at low frequencies (i.e., visible and IR wavelengths). Thus, bulk metals are largely re ective below the plasma frequency and largely transparent above it [17]. A plasmon at the surface of a metal is known as a surface plasmon, and from Maxwell's equations it can be shown that surface plasmons can exist only at an interface of two materials with permittivities 1 and 2 that simultaneously satisfy [18]: 1(!) 2(!) < 0 1(!) + 2(!) < 0: (2.5) These conditions are easily met at a metal-dielectric interface, when a metal has a su ciently large (and negative) permittivity compared to the dielectric; at such an interface it can be shown that the eld decays exponentially into both materials away from the interface [9]|it is in this way that a surface plasmon derives its name. Plasmons and surface plasmons have been studied extensively and more details can be found in a variety of sources [9, 17, 19, 20, 18]. 33 Surface plasmons play a large role in near- eld optics as a material excited resonantly can generate enormous eld enhancements beyond those expected from the lightning rod e ect alone. Optimal eld enhancement requires the right com- bination of material, excitation wavelength, and also extremely importantly, geom- etry. For instance, if a subwavelength sized metal sphere is illuminated with an excitation source near its plasmon resonance frequency, localized surface plasmons can greatly increase the enhancement factor. As the spherical particle is elongated along its polarization axis the eld can be enhanced even further [21]. However, while elongated particles lead to larger enhancement as compared to their spherical counterparts made of the same metal, the excitation wavelength needed to achieve the maximum enhancement may be quite di erent for the two geometries. As nanoparticles become elongated, the extinction spectrum can redshift signi cantly [15]. Furthermore, plasmon resonances for metal nanostructures redshift with increasing size [22]. Aside from having di erent extinction spectra, the particle size also matters in terms of the magnitude of obtainable eld enhancement: if the particle is larger than the skin depth, the inner electrons will be shielded, resulting in reduced enhancement. For smaller particles with large surface area-to-volume ra- tios, electron collisions with the surface become a large source of plasmon damping, thus reducing plasmonic eld enhancement [23, 24]. These geometry and size e ects can collude to make predictions about eld enhancement from metal nanoparticles challenging; for example, just because an 80-nm gold sphere leads to reasonable enhancement at = 633 nm, it should not be presumed that a much bigger and elongated gold tip should yield similar performance at the same wavelength. Bulk and surface plasmons can also play a major role in energy transfer. In particular, a photoexcited particle (e.g., quantum dot or uorophore) that would normally relax via radiative channels ( uorescence), can instead nonradiatively transfer its internal energy to a nearby plasmon-active structure. This results in a sharp reduction in the detected uorescence rate (quenching), and also in the uorescence lifetime [1, 25], as nonradiative decay channels become predom- inant. Recently, several groups have directly observed the competition between 34 eld enhancement and uorescence quenching when using metal tips in NSOM [12, 26, 27, 13, 24]. The net signal depends on the details of this competition, which in turn depends strongly on the tip geometry and size, the light wavelength and polarization, and the distance between the sample and tip. 2.4 Optical Antennas The combination of the lightning-rod e ect and plasmon resonances naturally leads to the concept of designing nanostructures with strong, shape-speci c res- onances to drastically enhance the optical eld. This is, in fact, a description of an optical antenna, which like their radio or microwave analogs, can be used to convert free propagating electromagnetic waves into localized elds and vice versa. The design and implementation of antennas for optical frequencies is highly desirable for a number of applications including NSOM, biochemical sensing, display technology, etc., and is a very active area of research. While any near- eld probe can be considered an antenna inasmuch as it can locally focus light, we will more rigorously use the term \antenna" to describe a device that exhibits shape-speci c resonances, which implies that they are made of metal. There are a number of di cult challenges associated with scaling down antennas from the macro to the nanoscale as needed for optical eld enhancement. For example, it is di cult to fabricate structures of this size using conventional lithog- raphy, so specialized techniques such as focused ion beam milling or electron beam lithography must be used. Furthermore, at optical frequencies, charge transport in nanoscale metallic structures can su er from a number of damping mechanisms, in contrast to the ideal conductors envisioned in antenna theory for the microwave and radio wave regions of the electromagnetic spectrum. Thus, the design of e cient antennas at optical frequencies requires new theories, or at least rigorous adaptation of existing microwave theories, to account for this non-ideal behavior. At optical frequencies, the skin depth of a metal can be of the same order of magnitude as the antenna size. The penetration of electromagnetic waves into the antenna creates electron oscillations inside the metal, which tends to push 35 the antenna resonance toward a higher frequency and thus a shorter e ective wavelength. For example, van Hulst and co-workers have shown that the resonant length of a linear monopole antenna is signi cantly shorter than predicted for an ideal conductor using classical antenna theory [28]. Novotny modeled the antenna as a strongly coupled plasma in order to determine the relation between the external and e ective wavelengths [29]. He found that the e ective wavelength, eff , is related to the external wavelength, , according to: eff = n1 + n2 p (2.6) where n1 and n2 are complicated expressions depending on the geometric and static dielectric properties of the antenna, and p is the plasma wavelength. The shorter e ective wavelength predicted by Novotny can be several times smaller than the free-space wavelength [30]. This correction to the wavelength is very important for antenna design since it implies that optimized antenna sizes should be shorter than what traditional antenna theories project and are dependent on the shape of the tip and the properties of the metal. A number of antenna designs have been used in NSOM to obtain large and con ned eld enhancement, thus obtaining optical resolution beyond the di rac- tion limit. For example, the monopole antenna mentioned above [28] was ac- complished with the tip-on-aperture approach developed by Guckenberger and co-workers [31, 32]. The antenna was driven with light emerging from the aperture with polarization along the antenna axis. In this work, the antenna resonances were mapped by scanning an antenna over a single molecule while monitoring its rate of uorescence emission, and repeating the experiment for di erent length antennas. The observed uorescence rate for similarly oriented molecules increased dramat- ically for the optimal antenna length. In a second experiment, the polarization of the orescence emission from single molecules was monitored while scanning an antenna in proximity to the sample plane [14]. When the antenna was directly over a molecule, its emission pattern changed to that of the coupled antenna-molecule system, illustrating that it is possible to redirect the dipole emission of a single quantum emitter to match that of a near- eld antenna. 36 Another simple antenna geometry commonly employed is a single gold nanosphere attached to the end of a dielectric probe, such as a pulled glass ber or an AFM tip [12, 26]. The spherical geometry yields plasmon resonance modes with strong eld enhancement at the poles of the sphere along the polarization direction. These antennas have been used as described above to image single molecules and to study the competition between eld enhancement and uorescence quenching. As above, the emission rate of single molecules was recorded as the spherical nanoantenna was scanned in close proximity. As the antenna approached a molecule, the emission of the molecule initially increased due to eld enhancement. At very short range ( 10 nm), uorescence quenching overwhelmed this enhancement, leading to a reduction in signal. Under similar illumination conditions using nonresonant, gold-coated AFM tips, only quenching was observed, demonstrating the importance of resonance e ects [24]. 2.5 Fluorescence Quenching When an apertureless NSOM probe is applied to a uorescent sample, the eld enhancement mechanisms discussed above can cause an increase in the detected uorescence signal. Simultaneously, the presence of the tip can decrease the de- tected uorescence signal in a variety of di erent ways. As mentioned, the tip can change the angular distribution of the emission away from the collection angle of the objective. Interference e ects from direct laser illumination and excitation light scattered from the tip can also lead to either an increase or decrease in the local eld value. Furthermore, the tip can also open up additional channels for photo-excited uorophores to relax back to the electronic ground state nonradiatively, thereby quenching the uorescence. This is particularly important for metallic NSOM probes, which can respond to a wide range of wavelengths via dipole-dipole coupling similar to uorescence (F orster) resonance energy transfer (FRET). In this process, energy is transferred from uorophore to tip via exchange of a virtual photon, which in turn creates an excitation in the metal where the energy is rapidly dissipated as heat within the tip. Thus, as a tip approaches a uorescent sample, the local 37 nonradiative relaxation rate ( NR) increases, thus decreasing the apparent quantum yield, resulting in a suppression of the detected emission [33, 34]. This uorescence quenching may be accompanied by a change in the radiative rate R, where both NR and R depend on the orientation of the molecule transition dipole moment relative to the probe geometry [34, 35]. This means that the total uorescence lifetime, = ( R + NR)􀀀1, is altered near a metal surface. By using pulsed lasers and time-correlated single photon counting (TCSPC), it is possible to measure directly, even for single molecules, by building up a histogram of uorescence photon delay times following a laser pulse. This lifetime can then be plotted pixel by pixel to build up an image, where the value of each pixel represents the uorescence lifetime of the corresponding location. Since a metal tip will alter the lifetime, it can be used as a contrast mechanism in NSOM, as has been demonstrated previously [25, 36]. This type of imaging can provide a great deal of information about near- eld interactions between the tip and sample as it provides simultaneous topography, uorescence, and lifetime data. There are two general cases to consider with regard to quenching with metal tips: 1) quenching by tips with well-de ned, closed geometries such as the spherical, or monopole antennas described above, and 2) quenching by tips with open geometries such as the metal-coated pyramidal AFM probes available commercially. Closed geometries support localized plasmons with well-de ned and relatively narrow res- onance frequencies determined by the detailed geometry and material of the probe. In this case, the uorescence quenching e ciency should depend very sensitively on the emission wavelength of the uorophore, with maximum quenching at the plasmon resonance frequency. For such closed geometry tips, however, the eld enhancement is also strongly wavelength dependent, so the competition between enhancement and quenching, and thus the net uorescence signal, is delicately balanced and can be di cult to predict. For molecular uorophores, which exhibit relatively small Stokes shifts, the excitation and emission wavelengths may only be as little as 10-20 nm apart, in which case enhancement and quenching can both be quite strong near the plasmon resonance. Colloidal quantum dots, on the other 38 hand, have a broad absorption pro le extending into the UV. Thus it is possible, in principle, to have a large imbalance between eld enhancement and quenching, as the excitation laser can be tuned far to the blue of a plasmon resonance, while the quantum dot emission can be at the resonance frequency. Varying the excitation wavelength toward the resonance frequency would then make it possible to study the competition between quenching and enhancement in detail. To our knowledge, such an experiment has not yet been reported. For the case of tips with open geometries, such as metal-coated pyramidal or conical probes, the situation can be quite di erent. These probes do not support localized plasmon resonances but can still dissipate energy via damping of traveling plasmon waves. Issa and Guckenburger recently attempted to quantify this e ect through the use of nite element analysis using COMSOL [13]. Again it is important to distinguish between two e ects: local energy transfer and plasmonic energy losses. True quenching originates from a F orster like local energy transfer from an emitter to a proximate metal structure where energy is locally dissipated through ohmic losses. Generally speaking, eld enhancement is proportional to the real part of the e ective polarizability (e.g., Equation 2.2, quantity in parentheses), while the imaginary part of the permittivity, 00, is a predictor for the quenching e ciency [12]. Plasmonic losses on the other hand, can occur even in a lossless material, 00 = 0. Energy can be transfered from an emitter to a surface plasmon on the metal structure; the energy need not be dissipated locally, the traveling plasmon may move away where it may eventually be dissipated. Figures 2.7 and 2.8 from reference [13] show the extent of this e ect. Figure 2.7 shows an approach curve as a silver tip vertically approaching a single emitting dipole as a function of initial quantum yield, q0. For large initial quantum yields, as the tip approaches the apparent quantum yield q decreases. The reverse is true when the initial quantum yield is already low; an increase in the radiative rate can be observed for intermediate tip-sample separations. Other important parameters include the fraction of power radiated into the lower half-space, #r = , the amount of power dissipated via surface plasmon polaritons, spp= , and the amount of power 39 Silver tip D (nm) D (nm) q0 = 1 q0 = 0.1 0 0.2 0.4 0.6 0.8 1 0.1 1 10 100 1000 0 0.2 0.4 0.6 0.8 1 0.1 1 10 100 1000 λ = 550 nm, εmetal = -12.9 + 0.43i q γ γSPP γ r γ γ LET γ Figure 2.7. Role of plasmonic energy dissipation and initial quantum yield in a lossy metal. Parameters plotted include the apparent quantum yield, the radiative decay rate into the lower half-space, #r = , the local energy transfer rate, let= , and the nonradiative surface plasmon polariton coupling rate, spp= . Reprinted with permission from [13]. dissipated by local energy transfer, let= . Regardless of initial quantum yield, at large tip-sample separation distances surface plasmon polariton coupling can be quite strong, while at shorter distances, the primary source of losses stems from local energy transfer. The same calculation as in Figure 2.7 is again repeated, but now assuming Ag has no losses, 00 = 0, as shown in Figure 2.8. Such a situation requires that the local energy transfer rate be exactly zero. Despite having let = 0, the apparent quantum yield still drops precipitously as the tip approaches the sample. This drop in q is due entirely to the transfer of energy to surface plasmon polaritons to the metal tip. As the plasmons propagate away from the sample they carry away energy also. Whether or not the plasmons are rapidly dissipated is a moot point as there is power ow directed away from the sample. It is of course possible that the surface plasmons could scatter o some irregularity on the tip surface and emit a real photon; however, this may or may not be detectable depending on the propagation direction of photon, the wavelength of the photon, and how high up 40 λ = 550 nm, εmetal = -12.9, q0=1 Silver tip with no loss q 0 0.2 0.4 0.6 0.8 1 0.1 1 10 100 1000 D (nm) (with loss) γ SPP γ γ r γ γ SPP γ Figure 2.8. Role of plasmonic energy dissipation in a lossless metal. Parameters plotted include the apparent quantum yield, the radiative decay rate into the lower half-space, #r = , the nonradiative surface plasmon polariton coupling rate, spp= , with no losses, and with losses as shown in Fig. 2.7 for comparison. Note that the the local energy transfer rate, let= , is exactly zero for all distances and is thus not plotted. Reprinted with permission from [13]. the tip the photon originated. The di erence between the response of the uorescence signal using tips with closed and open geometries has been demonstrated in a number of recent experi- ments. For example, Novotny and co-workers [12, 27] have shown that for spherical gold tips, eld enhancement is clearly evident leading to a strong enhancement in the uorescence signal from single molecules, which is mitigated by quenching only when the tip is brought to within 5 nm of a molecule. Using gold-coated pyramidal tips, on the other hand, switches the balance strongly in favor of quench- ing, often leading to a complete lack of observable enhancement in the uorescence 41 signal at any distance scale, as demonstrated by a number of groups [1, 25, 26, 24]. In any NSOM experiment it is important to remember that the e ect of the near- eld probe on the sample can be non-trivial, especially for metallic probes. In particular, for uorescent samples, the net detected signal is a ected by eld enhancement, quenching, and other possible mechanisms such as the redirection of uorescence. Thus, determining the eld enhancement factor of a particular probe is complicated in that it may be impossible to decouple any observed increase in uorescence signals with any quenching that may also be occurring. In general, this would require a rather sophisticated model of the system, which is highly dependent on the probe geometry and material. 2.6 Field Enhancement vs. Signal Enhancement In near- eld literature, the term enhancement is sometimes used somewhat ambiguously and at times perhaps even incorrectly. Enhancement may refer to either eld enhancement or to signal enhancement; however, it is usually incorrect to use these terms interchangeably. To rst order, eld enhancement deals simply with the interaction of the tip and laser. Signal enhancement, on the other hand, can be proportional to eld enhancement, but includes the sum of many other e ects such as uorescence quenching, redirection, interference e ects, and very importantly, the eld-sample volume overlap. Calculating the peak eld enhancement of a tip alone yields a somewhat incomplete picture; that is the spatial extent to which the eld overlaps with the volume of the sample must be taken into account to determine the amount of signal enhancement to be expected. In the same model as Figure 2.5, the intensity-volume overlap is calculated by integrating the intensity contained in several di erent spherical volumes directly under the tip as shown in Figure 2.9. This represents the integrated intensity that a spherical sample might see when the tip is directly on top of it. This integrated intensity was then normalized to both the integrated intensity under similar illumination in the absence of the tip and the peak intensity enhancement under the tip. The results are summarized in Table 2.1, where the intensity 42 5 nm Figure 2.9. Calculation of eld-volume overlap integrals. A 3D electrostatic calculation of eld enhancement around a near- eld probe was performed in Comsol as described in Fig. 2.5. The scale bar represents the magnitude of the eld, where the incident eld is 1 V/m. Integration of the intensity was performed at spheres of various sizes indicated by solid black lines. enhancement factor is reported as a percent of the peak intensity below the tip. The radii chosen for this calculation correspond to some typical samples measured in the lab: primarily 5 nm diameter quantum dots, and 20 nm diameter dye-doped latex beads. This calculation corroborates the data reported previously by Gerton et al. [2] where a 5 nm diameter quantum dot exhibited roughly 4 times the signal enhancement as a 20 nm dye-doped bead, which is similar to the predictions made in Table 2.1. While to rst-order, eld enhancement is purely a function of tip-and excitation elds, tip sample coupling can also play an important role. As a tip approaches a sample, it no longer is rigorously correct to discuss the polarizability of the tip alone, but rather, tip-sample coupling e ects require an e ective polarizability of the tip-sample complex. An analytic solution for tip-sample coupling between a spherical tip and a sample (an in nite plane) has been worked out some time ago by Knoll and Keilmann [37]. In fact for scattering SNOM this tip-sample coupling 43 Table 2.1. Intensities were integrated over the volumes of spheres of several di erent radii as shown in Fig. 2.9. This integrated result was normalized to both the value obtained in that region in the absence of a tip and to the peak intensity at the apex of the tip. The normalized intensity enhancement factor is reported as a percent of the peak intensity. The results were normalized in this fashion to ensure they are not sensitive to the particular tip height chosen for the calculation. Radius Normalized Intensity Enhancement Factor 20 nm 2% 10 nm 5% 5.0 nm 11% 2.5 nm 23% is the entire signal of interest [37]. eff = (1 + ) 1 􀀀 16 (a + z)3 􀀀1 (2.7) where is the polarizability of the tip (or the tip modeled as a sphere), = 4 a3 1 􀀀 1 1 + 2 (2.8) is the dielectric response function of the sample, = ( 2􀀀1)=( 2+1), z is the tip- sample separation distance, a is the radius of the tip, 1 is the permittivity of the tip, and 2 is the permittivity of the sample. It must be remembered that this calculation assumes the sample is an in nite plane; deviations to these approximations of course lead to nonanalytic results, however, such a calculation may still be useful. Also included in the signal enhancement is any redirection of uorescence signals by the tip. It has been demonstrated that the presence of a tip can redirect the uorescence emission of a sample [38]. Such redirection can be ampli ed if the probe exhibits a strong antenna e ect [14]. Aside from redirection, the tip can also produce long range interference e ects, also contributing to an observed signal enhancement. As the light scatters from a probe interferes with the direct laser illumination, complicated tip-geometry dependent patterns can emerge such that the uorescence signal can be either increased or decreased corresponding to regions of constructive or destructive interference from the tip [39, 40, 41, 42, 24] With 44 the signal enhancement being a function of so many di ering and widely variable parameters, it is often unclear a priori how a given tip might e ect the observed near- eld signal. 2.6.1 Examples This interplay between eld-enhancement and signal enhancement is well il- lustrated through a few examples. In particular we have observed that platinum coated tips can lead to interesting results. Using a platinum/iridium coated Si tip with a vertical wedge illumination, we expect to obtain some eld enhancement at the tip apex. However, due to the reasons just stated, we also expect strong quenching from such probes. Figure 2.10 plots the uorescence signal (normalized to the far- eld signal) as a Pt/Ir tip is lowered down onto an elongated CdSe/ZnS quantum dot, which is nominally 4 9nm. As is shown the result shows no evidence of enhancement at any distance, but rather shows strict quenching. For comparison, the same tip was also used to generate an approach curve on a 20 nm diameter dye-doped latex bead, Figure 2.11. Since the bead has a much larger 0.50 50 100 150 200 250 300 350 0.6 0.7 0.8 0.9 1.0 1.1 Tip−Sample Distance (nm) Normalized Signal Figure 2.10. Approach curve of a Pt/Ir tip on a 4 9 nm CdSe/ZnS quantum dot. Vertical wedge illumination (543 nm) was used such that some eld enhancement would be expected.The uorescence rate has been normalized to the far- eld value. 45 volume we may expect that any enhancement e ects would be reduced. However, as seen in Figure 2.11 there is some \recovery" of the uorescence signal at short length scales. Note that this recovery is not present when using horizontal wedge illumination. Since uorescence quenching is expected to dominate all interactions at the shortest length scales, this result can be even more perplexing. The explana- tion is that the sample is an extended object with a roughly uniform distribution of uorophores throughout. As the tip approaches some fraction of the uorophores are quenched to di erent extents while others are more preferentially enhanced. This of course is evidence that there is indeed some eld enhancement present in this setup, which was not at all apparent when using the quantum dot. These two competing e ects occur at roughly the same length scales [12] and thus can be very di cult to sort out experimentally The overall message is that the total near- eld signal collected can be much more complicated than estimating the eld enhancement a tip may produce. 0.40 20 40 60 80 100 120 140 160 180 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Tip−Sample Distance (nm) Normalized Fluorescence Signal Figure 2.11. Approach curve of a Pt/Ir tip on a 20 nm diameter dye-doped latex bead. Vertical wedge illumination (543 nm) was used such that some eld enhancement would be expected. The uorescence rate has been normalized to the far- eld value. 46 2.7 Tip Selection In order to obtain the strongest near- eld signal, optimization of the tip's enhancement factor is essential. There are generally three di erent types of tips em- ployed in apertureless-NSOM experiments: commercial cantilever-based AFM tips made of silicon, silicon nitride, or metal-coated silicon; spherical metal nanoparticles attached to the distal end of a pulled glass ber or commercial cantilever-based AFM tip [43]; and electrochemically sharpened metal wires (gold, tungsten, silver, etc.) [44]. These various probes have di erent strengths and weaknesses, and the choice of one over another depends in large part on the particular optical process to be employed during the experiment. The key factor in choosing the most appropriate tip in uorescence imaging is to optimize the competition between eld enhancement and quenching, as described above. Although metal tips can generate extremely high eld enhancement factors, particularly near a plasmon resonance frequency, they also quench uorescence at very short range. This competes with eld enhancement, thereby reducing the net uorescence signal. Generally speaking, eld enhancement is proportional to the real part of the e ective polarizability (e.g., Eq. 2.2, quantity in parentheses), while the imaginary part of the permittivity, 00, is a predictor for the quenching e ciency [12]. The precise dependence of quenching and enhancement on the complex permittivity is also very sensitive to geometry. For metals, both the e ective polarizability and 00 can become very large in magnitude near a plasmon resonance frequency. Thus it is di cult to predict what the net signal enhancement will be for an arbitrary geometry, and there are only a few rigorous calculations that have been compared with experiment [12, 27, 35], and only for a simple spherical geometry. Nonetheless, all uorescence experiments thus far with metal tips have exhibited strong quenching, and thus reduced signal, at very short tip-sample separation distances. Tips composed of small metal spheres (attached to dielectric probes) can support strong localized plasmon resonances, and can thus exhibit appreciable signal enhancement outside this quenching zone (see below). Metal-coated tips with extended geometries (e.g., commercial metalized 47 probes), on the other hand, do not support localized plasmon resonances, and have exhibited no net enhancement of the uorescence signal at any length scale [1, 25, 26, 24]. Silicon has a complex permittivity of Si = 17:6 + 0:12i (at = 532 nm) [45], indicating the potential for good uorescence signal enhancement, with only minimal quenching. Furthermore, silicon tips can be made quite sharp, particularly compared to metal-coated tips, so the lightning-rod enhancement and resulting increase in spatial resolution should be quite good. Indeed, silicon tips have exhibited uorescence signal enhancement factors as large as f 20 [2], and spatial resolution as small as 10 nm [46, 7, 3, 8, 24, 47]. As described above, this enhancement factor should provide adequate contrast to image even rather complex samples with high background signals. A literature search of dielectric constants at visible frequencies for commonly available materials indicates that silicon gives the largest enhancement factor, although reliable optical constants for some materials are di cult to obtain. Figures 2.12 and 2.13 highlight the permittivities for some of the more common AFM probe materials; Figure 2.12 shows dielectric materials while metals are shown in 2.13. Silicon has by far the highest 0 of the dielectrics; however, it is also the only dielectric to have a nonzero imaginary part 00 at visible wavelengths . The imaginary parts of the permittivity for SiO2, Si3N4, and diamond are exactly zero in this wavelength range and thus are not plotted. Evidently, silicon appears to be the best, or at least most straightforward, probe material for uorescence imaging, and there are a variety of probe geometries available, most of them cantilever-based. Super-sharp silicon AFM probes have been used to obtain large signal enhancement in the past [7] but they also su er from rapid wear, which leads to large variations in their performance. Metals can also yield exceedingly large eld enhancements. Metals can have high enhancement values for two reasons: rst, the real part of the permittivity can be very large (albeit usually negative at visible wavelengths), and second, the metal tip can support a plasmon resonance (cf. Fig. 2.13). In the case of a 48 −20 300 400 500 600 700 800 900 1000 −10 0 10 20 30 40 50 Wavelength (nm) Permittivity Permittivites of Several Dielectrics ' Si ' SiO2 ' Diamond ' Si3N4 '' Si Figure 2.12. Real and imaginary permittivities plotted for some more common dielectric materials used for AFM probes. Permittivity values are found in the following references: Si [45], SiO2 [48], Si3N4 [48], and diamond [49]. sphere, the plasmon resonance occurs when r = 􀀀2 (cf. Eq. 2.2). Metals also exhibit considerable quenching as the imaginary parts of their permittivities can be considerable (cf. Fig. 2.13). In our experience, standard silicon\tapping mode" probes yield very acceptable and repeatable results. One problem with silicon probes is the growth of oxide layers, which do not exhibit strong polarizability at optical frequencies, as compared to Si. All silicon tips have some native oxide layer, but as tips age this layer thickens. Using fresh probes alleviates this problem somewhat, but it can be di cult to determine their exact date of manufacture. Storing tips in vacuum chambers is de nitely recommended, and some manufacturers have begun shipping probes in hermetically sealed packages of fewer quantities to avoid unnecessary oxidation. Some studies have also indicated that contaminants from gel-pack o -gassing may """",.",".",".",.",".",".,".",".",.",".",".",.",".",".,".",".",.",".",".,".",".",".,".",".",.",".",".",.",". 49 300 400 500 600 700 800 900 1000 0 5 10 15 20 25 30 35 40 45 50 Wavelength (nm) Permittivity Imaginary Permittivites ( '') of Several Metals '' Au '' Ag '' Al '' W 300 400 500 600 700 800 900 1000 −100 −90 −80 −70 −60 −50 −40 −30 −20 −10 0 10 Wavelength (nm) Permittivity Real Permittivites ( ') of Several Metals ' Au ' Ag ' Al ' W Figure 2.13. Real and imaginary permittivities plotted for some more common metal materials used for AFM probes. Permittivity values are found in the following references: Au [50], Ag [48], Al [48], W [51]. , ... ," , "".".."."..".".."." """""""",,"""""""""""""""""""" •• [... ] ,.,., ""'" [... ] ,.,., ""'" •• ........- ---­•• •• •• •• •• •• ••• 50 also contribute to a reduction in enhancement factor [46]. It is widely agreed that oxidized or contaminated tips may be \revived" to some extent via etching in hydro uoric acid (HF) [46, 41]. Standard bu ered oxide etch (BOE) procedures prescribe the rate at which silicon oxide layers can be eaten away [52]. This procedure, while e ective in removing oxide layers, can also dull the AFM tip, and it should thus be applied carefully and conservatively. Other cantilever-based probes of interest that have currently become available include diamond-like carbon (Mikromasch) and carbon nanotube tips (nanoScience). While more di cult to produce, metal nanospheres attached to dielectric tips [43] can also yield excellent results [12, 26, 27]. Because these probes can support localized plasmon resonances, they can yield very large eld-enhancement factors that can overcome the reduced signal caused by uorescence quenching beyond some critical tip-sample separation distance. This is clearly the case in Figure 2.14 where an 80-nm gold sphere is used to probe a vertically oriented single molecule; at very close range quenching overpowers the eld enhancement. Thus, to optimize image contrast, these tips should be maintained at this critical height from the sample ( 5 nm), where the signal enhancement is maximized (cf. [12]). To maintain a constant tip-sample gap, the AFM should be operated in shear-force rather than tapping mode. When using tips composed of spherical nanoparticles, both the size of the particle and the metal to be employed should be chosen so that the localized plasmon resonance frequency is close to the absorption peak of the uorophore: the resonance frequency is determined by both the size and permittivity of the particle. It has been shown that gold nanoparticles perform better at red wavelengths and silver nanoparticles at blue wavelengths [27]. Smaller particles yield higher resolution but also smaller enhancement [12, 23]: most reports utilize diameters in the 40-80 nm range [12, 26, 18, 27, 53]. 51 z (nm) z 80nm Au 0 20 40 60 0 10 20 30 0 2 4 6 8 count rate (kHz) γem γem o Figure 2.14. Fluorescence rate as a function of particle-surface distance z for a vertically oriented molecule. Dots represent experimentally observed count rates (left axis). The solid curve shows the theoretical normalized emission rate compared to free space, em= 0 em (right axis). The horizontal dashed line indicates the background level. Reprinted with permission from [12]. Copyright (2006) by The American Physical Society. CHAPTER 3 EXPERIMENTAL SETUP Ordinarily a section on the experimental setup may not receive its own chapter, but due to the large amount of e ort and constant re nement needed for TEFM, I will dedicate an entire chapter to that end. As alluded to earlier, in order for TEFM to work, a nanoscale probe needs to be aligned to the central 100 nm of a laser spot. Furthermore, the polarization state of this excitation beam needs to be both carefully controlled and alterable. The microscope system developed in our lab is a multipurpose imaging tool with several distinct functionalities. It has the ability to operate as an inverted confocal microscope in both sample scanning and laser scanning con gurations. It can be used as a standalone Atomic Force Microscope (AFM) and most signi cantly as an apertureless Near-Field Scanning Optical Microscope. This microscope system has been designed in such a way that switching between di erent imaging modes is meant to be a relatively straightforward task; however, as with any system, increasing functionality necessarily goes hand in hand with increasing complexity. Thus in order to understand the operation of the system, a knowledge of both some basic theory and engineering limitations must be obtained. 3.1 Setup The basis for the system is an AFM sitting atop a custom built inverted optical microscope (see Fig. 3.1). The AFM is a commercially available system (Asylum Research) that includes a high precision piezo-actuated X-Y scanning stage and an AFM head. This AFM head controls the movement of nanoscale probes that scan the sample and is capable of moving the AFM probe only in the vertical (Z) dimension. As seen in Figure 2.1, the inverted optical microscope has a choice 53 Figure 3.1. Photograph of experimental setup. of di erent illumination pathways depending on the polarization state required. Excitation pathways for either a radial polarization state or a linearly polarized polarization state (both of which will be described in greater detail below) can be implemented through the use of removable face-plate mirrors. 3.2 AFM The AFM is a commercial cantilever based unit from Asylum Research (MFP3D). Again, there are two essential components of this system: the AFM head itself, along with a piezo-actuated scanning stage. The AFM employed in our lab is cantilever based, meaning that the probes themselves are mounted at the end of a long (usually 200 m) thin plank. A feedback laser re ects o the backside of the cantilever onto a segmented photodiode. The laser is weakly focused so 54 that the spot size is about the same size as the width of the cantilever, but as the laser bounces o the cantilever it is divergent. After re ecting o the cantilever, the beam strikes a photodiode with four segments (see Fig. 3.2); each segment puts out a voltage relative to the incident light intensity. Since the beam acts as a long lever arm, small displacements of the tip result in large displacements of the beam on the quadrant photodiode; in this manner, minuscule tip-sample interactions are measured faithfully, thus the name Atomic Force Microscope. The two main modes of operation of the AFM are contact mode, where the probe is simply dragged across the surface, and tapping mode, where the tip undergoes rapid vertical oscillations only tapping the sample surface intermittently. Tapping mode is used almost exclusively in our lab for two important reasons: it can be employed in such a manner that it is much gentler on the sample (also leading to less tip-wear), and it can lead to higher near- eld contrast as will be explained in later chapters. While most of the important details of operation of the AFM can be found in the operation manual, I will discuss a few important points that are A B C D A B C D A B C D neutral de ection positive de ection negative de ection Figure 3.2. Cartoon of AFM feedback mechanism. A laser is incident on the back side of a cantilever based probe. The beam re ects o the probe onto a segmented photodiode. Each segment produces a voltage in proportion to the amount of light detected. Small changes in the cantilever de ection lead to large changes in beam displacement on the detector, thus yielding high sensitivity. Positive or negative de ections can be monitored via the photodiode output signals and converted into real displacement when a probe is properly calibrated. 55 important in our research. 3.2.1 Tip Calibration The primary mode of AFM operation in our lab is tapping mode (other monikers include AC mode or intermittent contact mode). The amplitude of these tip- oscillations must be carefully calibrated: the amplitude determines the force applied when tapping, the amount of near- eld contrast we can obtain, and is important for understanding the length scales of optical responses on the nanometer scale. The oscillation amplitude can be set through the software user interface and is in volts; however, an important conversion factor needed is the Inverse Optical Lever Sensitivity or InvOLS. This conversion factor can vary depending on the particular brand (geometry) of tip being used and how it is mounted. Furthermore, it depends on the sum signal from the quadrant photodiode (VA + VB + VC + VD); the larger the sum signal the smaller the InvOLS value. The largest di erence comes from the fact that some cantilevers are bare silicon, while others are metal coated and thus much more re ective|leading to a larger sum signal. From much practice we can get a rough estimate of the InvOLS based on the sum alone, the results are summarized in Table 3.1. While Table 3.1 may be used a starting point, it must be remembered that these are only estimates and an InvOLS measurement should Table 3.1. AFM Sum signal and corresponding approximate InvOLS values. Two classes of tips are routinely used in the lab, Si tips with no backside coating and metallic tips, or tips with a metal backside coating. These two classes typically give Sum values of 3-4 and 9 respectively, which is why no data are shown for intermediate Sum values. Note, the InvOLS values listed here are for converting the oscillation amplitude in volts to nm|the peak to peak amplitude being twice the values listed here. The de ection InvOLS can be calibrated in a similar way. As a rule of thumb: AmpInvOLS = 1:09 De InvOLS. Sum Amplitude InvOLS 9 70 nm/V 8 90 nm/V 5 170 nm/V 4 210 nm/V 3 240 nm/V 56 be performed for each tip used. 3.2.2 AFM Scanning Stage The scanning stage is a two-layer system. Adjustment of the lower layer keeps the AFM and sample registered together but moves them both relative to an opening on the bottom allowing for optical measurements, while adjustment of the upper layer of the stage moves only the sample It is this upper layer of the stage that scans the sample during AFM operation. This upper stage is operated in closed loop mode and has a maximum scannable area of 90 m 90 m but also has hand adjustable micrometer screws for coarse positioning. The lower stage, which adjusts the AFM head and sample in tandem, relative to the optic axis originally came with only hand adjustable micrometer screws. These have been replaced with piezo-actuated micrometers (Pico-motors from New Focus), which work by rapidly turning a drive screw then slowly relaxing back into place. The total travel of the screw can be quite large; we have purchased models with both 1=2 inch and 1 inch travel, while the minimum step of each piezo movement is 20 nm. The picomotors can be actuated remotely via a computer interface or by a joystick. Tip-sample alignment can be achieved using these picomotor actuators and will be discussed in more detail later in this chapter. 3.3 The Optical Train As mentioned, multiple excitation paths allow for easy selection of various polarization states and spatial modes for the excitation laser beam. The two options primarily employed are radial polarization and linearly polarized light; however, in each such path further changes to the spatial mode of the beam are also often made such that the beam is clipped or masked in particular ways. In order to understand the motivation behind the tailoring of the laser beams in our system, I will brie y discuss the fundamental di erences between some the basic laser modes. 57 3.4 Transverse ElectroMagnetic Modes In laser cavities there can exist both longitudinal modes and transverse modes of oscillation. The longitudinal modes correspond to standing waves in the cavity. For cavities with rectangular symmetry (containing Brewster windows or prisms), the transverse modes are usually called TEMmn modes, TEM standing for Transverse Electric and Magnetic, while the m and n subscripts refer to number of nodal lines in the X and Y directions of the beam respectively [54]. Mathematically these beams can be described by: Im;n(x; y) = I0 " Hm p2x w ! exp 􀀀x2 w2 #2 " Hn p2y w ! exp 􀀀y2 w2 #2 (3.1) where the subscripts m and n refer to the order of the Hermite polynomial H, and w is the width of the Gaussian pro le. The corresponding intensity pro les can be seen in Figure 3.3. The TEM00 mode is a standard laser mode produced by most commercially available lasers; it has a Gaussian pro le and linear polarization state. Of special importance to our lab is the TEM01 mode. The superposition of the TEM01 mode with another TEM01 mode rotated at 90 to the rst creates a beam with a radially shaped polarization pro le as seen in Figure 3.4. This mode is often described as a \doughnut" mode as the intensity at the center of the pro le is exactly zero; oftentimes it is simply referred to as a TEM01 mode. Note that the TEM01 beam is sometimes described to be a superposition of a TEM01 beam with a TEM10 beam, which is incorrect. It is also important to bear in mind that the electric eld of the beam is of course oscillating. That is, while Figure 3.4 portrays a snapshot of the cross section of a collimated TEM10 beam at one moment in time as pointing radially outward, it is actually rapidly oscillating between radially outward and radially inward at the optical frequency. 3.5 Gaussian Illumination The most common illumination scheme in many di erent types of microscope con gurations is to illuminate a sample with a linearly polarized Gaussian pro led 58 00 10 20 01 11 21 20 12 22 Figure 3.3. Computer generated images of TEM modes of Hermite-Gaussian beams calculated from Eq. 3.1. The subscripts m,n refer to the horizontal and vertical number of nodal lines respectively. Arrows representing the instantaneous polarization direction have been overlaid. 59 Figure 3.4. A computer generated cross section of a radially polarized beam. Arrows represent the polarization direction (the instantaneous direction of electric eld vectors). laser beam, or in other words a TEM00 mode beam. This type of beam is found at the output of most commercially available lasers. This mode also couples very e ciently to single mode optical bers, whose output again is a TEM00 beam. The Gaussian path is the simplest to achieve in that the output of a single mode ber is simply collimated using a short focal length lens to achieve the correct beam diameter. A commercially available out-coupler is currently used for this purpose (Optics For Research PAF-X15); however, the lens used in this commercial ber out-coupler is extremely non-achromatic, meaning that when changing between di erent wavelengths, considerable adjustments must be made to reachieve a collimated beam, which consequently may change the diameter as well. Inasmuch as all commercially available out-couplers seem to su er from 60 such problems, we have created a custom-built out-coupler consisting of a slightly larger focal length achromatic lens, mounted in a lens tube and screwed onto a exure mount where the optic ber terminates. Due to geometrical constraints focal lengths of 30 mm are most appropriate, but consequently produce a large beam diameter 14 mm. Due to this large beam diameter, the custom out-coupler is not currently used in the Gaussian beam path, but is used on the radial beam path. For all paths used in our setup linearly polarized TEM00 laser beams are coupled into polarization maintaining optical bers (OZ Optics) using berports of various focal lengths from OFR. Following the out-coupler, the next two elements in the Gaussian optical path are a half-wave plate followed by a linear polarizer. By rotating the wave plate and polarizer appropriately, the direction of the polarization can be changed to any arbitrary angle without reducing intensity. 3.6 Axial Polarization The two basic requirements to make most near- eld optical measurements a reality include rst, positioning the near- eld probe into the focus of a laser beam as discussed above, and second, the excitation beam must have axial polarization; That is, the electric eld direction must be pointed parallel to the long axis of the probe. Several di erent illumination schemes have been introduced to achieve such a requirement. One such con guration is to illuminate the probe and sample from the side at a shallow angle such that a linearly pol