OPTICAL SUPER-RESOLUTION AND PERIODICAL FOCUSING EFFECTS BY DIELECTRIC MICROSPHERES by Arash Darafsheh A dissertation submitted to the faculty of The University of North Carolina at Charlotte in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Optical Science and Engineering Charlotte 2013 Approved by: ______________________________ Dr. Vasily N. Astratov ______________________________ Dr. Michael A. Fiddy ______________________________ Dr. Gregory J. Gbur ______________________________ Dr. Angela D. Davies ______________________________ Dr. Christopher J. Evans ii ©2013 Arash Darafsheh ALL RIGHTS RESERVED iii ABSTRACT ARASH DARAFSHEH. Optical super-resolution and periodical focusing effects by dielectric microspheres. (Under the direction of DR. VASILY N. ASTRATOV) Optical microscopy is one of the oldest and most important imaging techniques; however, its far-field resolution is diffraction-limited. In this dissertation, we proposed and developed a novel method of optical microscopy with super-resolution by using high- index dielectric microspheres immersed in liquid and placed on the surface of the structures under study. We used barium titanate glass microspheres with diameters of D~2-220 μm and refractive indices n~1.9-2.1 to discern minimal feature sizes ~/4 (down to ~/7) of various photonic and plasmonic nanostructures, where is the illumination wavelength. We studied the magnification, field of view, and resolving power, in detail, as a function of sphere sizes. We studied optical coupling, transport, focusing, and polarization properties of linear arrays of dielectric spheres. We showed that in arrays of spheres with refractive index n=√3, a special type of rays with transverse magnetic (TM) polarization incident on the spheres under the Brewster’s angle form periodically focused modes with radial polarization and 2D period, where D is the diameter of the spheres. We showed that the formation of periodically focused modes in arrays of dielectric spheres gives a physical explanation for beam focusing and extraordinarily small attenuation of light in such chains. We showed that the light propagation in such arrays is strongly polarization- dependent, indicating that such arrays can be used as filters of beams with radial polarization. The effect of forming progressively smaller focused beams was experimentally observed in chains of sapphire spheres in agreement with the theory. iv We expanded the concept of periodically focused modes to design a practical device for ultra-precise contact-mode laser tissue-surgery, with self-limiting ablation depth for potential application in retina surgery. By integrating arrays of dielectric spheres with infrared hollow waveguides and fibers, we fabricated prototypes of the designs and tested them with an Er:YAG laser. Furthermore, we proposed another design based on conical arrays of dielectric spheres to increase the coupling efficiency of the probe. v ACKNOWLEDGMENTS I am very thankful to my advisor, Dr. Vasily N. Astratov, for his advice and support; for his constructive criticisms on my presentations, papers, and dissertation; and for the scientific discussions we had during my study at the University of North Carolina at Charlotte. Without his help, this dissertation work would have not been possible. I thank members of my committee, Dr. Michael A. Fiddy, Dr. Gregory J. Gbur, Dr. Angela D. Davies, and Dr. Christopher J. Evans for accepting to serve in the committee and their time and comments. I am grateful to Dr. Nathaniel M. Fried for his guidance in surgical applications of lasers and fruitful discussions, to Dr. Michael A. Fiddy for discussions which initiated the work on super-resolution imaging, and to Dr. Angela D. Davies for sharing high numerical-aperture microscope objectives. During my graduate studies, I enjoyed discussing scientific issues with my fellow Mesophotonics Laboratory members, Dr. Oleksiy Svitelskiy, Kenneth W. Allen, S. Adam Burand, and Yangcheng Li. I am grateful for the opportunity to be involved in a number of collaborations with different groups with which Mesophotonics laboratory has collaborative works. I also would like to thank fellow graduate students Thomas C. Hutchens and Mona Mayeh for productive discussions. I am thankful to Dr. Lou Deguzman, Scott Williams, Dr. Awad Gerges, and Dr. Robert Hudgins for showing me how to operate the equipment in the Optics center at the UNCC. I would like to thank the staff of the Physics department and the Optics center, Wendy Ramirez and Mark Clayton, for helping me with the administrative issues. vi I was supported through a fellowship from TIAA-CREFF for Fall 2008 and Spring 2009 and by GASP award from Fall 2008 to Spring 2013. My graduate assistantship in Dr. Astratov’s Mesophotonics Laboratory was supported through his grants from NSF, NIH, and ARO. I am grateful to Dr. Faramarz Farahi and Dr. Mohammad A. Kazemi for their guidance and introducing the UNCC Optical Science and Engineering graduate program to me. I deeply thank my family for their endless love and support which motivated me to pursue my academic education up to this level. vii DEDICATION To my parents, Dr. Rafat Rafiei and Dr. M. Reza Darafsheh, for their endless love and support. viii TABLE OF CONTENTS LIST OF FIGURES xii LIST OF ABBREVIATIONS xxiii CHAPTER 1: INTRODUCTION 1 1.1: Outline and Overview of the Dissertation 1 1.2: Super-resolution Microscopy Techniques 3 1.2.1: Diffraction Limit and Resolution Criteria 4 1.2.2: Near-field Techniques 10 1.2.3: Immersion Microscopy Techniques 11 1.2.4: Microsphere Nanoscope 13 1.3: Resonant and Non-resonant Optical Properties of Dielectric Spheres 17 1.3.1: Whispering Gallery Modes in Spherical Cavities 17 1.3.2: Photonic Nanojets and Nanojet Induced Modes 23 1.4: Focusing Surgical Microprobes 42 1.4.1: Erbium:YAG Laser for Medical Applications 46 1.4.2: Infrared Waveguides 48 1.4.2.1: Classification of Infrared Fibers and Waveguides 48 1.4.2.2: Infrared Hollow Waveguides 50 1.4.2.3: Quantitative Parameters of Infrared Waveguides 51 1.5: Summary 53 CHAPTER 2: SUPER-RESOLUTION IMAGING BY LIQUID-IMMERSED 57 HIGH-INDEX MICROSPHERES 2.1: Introduction 57 ix 2.2: Samples 59 2.3: Microscopy Technique 64 2.4: Spatial Resolution 67 2.5: Lateral Magnification and Field-of-View 69 2.6: Polarization Effects 72 2.7: Resolution Gain and Effect of the NA of the Objective Lens 73 2.8: Comparison with Solid Immersion Lens Microscopy 76 2.9: Comparison with Confocal Microscopy 80 2.10: Conclusions 82 CHAPTER 3: OPTICAL CHARACTERISTICS OF LINEAR ARRAYS OF 84 DIELECTRIC SPHERES 3.1: Introduction 84 3.2: Periodically Focused Modes 88 3.3: Description of the Modeling Technique 94 3.4: Optical Characteristics 97 3.4.1: Optical Power Transport 98 3.4.2: Focusing 101 3.4.3: State of Polarization 105 3.5: Disorder Effects 110 3.5.1: Shape Disorder (Deviation from a Perfect Sphere) 111 3.5.2: Spacing Disorder (Presence of Gap between Spheres) 112 3.5.3: Scattering inside Spheres and from Their Surfaces 112 3.5.4: Size Disorder 113 3.6: Experimental Results 116 x 3.6.1: Assembly of Sphere-chains 116 3.6.2: Focusing Properties 118 3.6.3: Optical Power Transport 123 3.6.4: Phase Properties 126 3.7: Conclusions 130 CHAPTER 4: DESIGN, FABRICATION, AND TESTING OF FOCUSING 133 MULTIMODAL MICROPROBES 4.1: Introduction 133 4.2: Fiber-integrated Microprobes Formed by Uniform Sphere-arrays 136 4.2.1: Modeling Technique 136 4.2.2: Optical Properties 140 4.2.2.1: Fiber-to-microsphere Separation 140 4.2.2.2: Optical Focusing and Power Transport 143 4.2.2.3: Self-limiting Mechanism 147 4.2.2.4: Polarization Properties 151 4.2.3: Fabrication and Testing 153 4.3: A Sub-optimal Microprobe Design for Preliminary ex vivo Testing 158 4.4: Microprobe Designs Using Conical Arrays of Spheres 160 4.4.1: Modeling Technique 161 4.4.2: Optical Properties 163 4.5: Conclusions 167 CHAPTER 5: CONCLUSIONS AND FUTURE DIRECTIONS 169 REFERENCES 175 APPENDIX A: LIST OF PUBLICATIONS 195 xi APPENDIX B: SOME APPLICATIONS OF PHOTONIC NANOJETS 199 APPENDIX C: DERIVATION OF PFMS CONDITIONS 211 APPENDIX D: MATRIX OPTICS FOR SPHERE-CHAINS 215 APPENDIX E: SPHERES SIZES IN A CONICAL DESIGN 223 xii LIST OF FIGURES FIGURE 1.1 Numerical aperture (NA) of a lens. 4 FIGURE 1.2 Illustration of the Abbe’s theory where diffraction orders pass 6 through (a) or stopped by (b) the lens pupil [42]. Reprinted with permission. © 2003 Imperial College Press. FIGURE 1.3 Rayleigh criterion for a (a) square and (b) circular aperture. 8 FIGURE 1.4 (a) An objective lens, (b) a hemispherical solid immersion lens 12 (h-SIL), and (c) a super-spherical solid immersion lens (s-SIL). FIGURE 1.5 (a) Schematic of an optical nanoscope with microspheres 14 placed on top of the sample. The spheres collect the near-field object information and form virtual images that are captured by the objective lens. (b) Optical microscopy of a Blu-ray® disk without SIL or sphere, (c) with a 0.5 mm SIL, (d) with a 2.5 mm SIL, and (e) with a 4.74 μm silica microsphere [63]. Reprinted with permission. © 2011 Macmillan Publishers Ltd: Nature Communications. FIGURE 1.6 (a) Super-resolution strength vs. size parameter q. (b) Intensity 15 distributions calculated for a freestanding s-SIL, a freestanding sphere, and a sphere on surface of a 40-nm-thick gold film (D=4.74 μm, n=1.46, and λ=600 nm). (c) FWHM of foci for s- SIL (blue), sphere (red), and sphere on substrate (green). (d) Virtual image magnification vs. sphere diameter D [63]. Reprinted with permission. © 2011 Macmillan Publishers Ltd: Nature Communications. FIGURE 1.7 (a-c) Schematics of a single sphere on a substrate illustrating 21 intensity maxima distributions for WGMs with different m.