Energy and Charge Transfer in Open Plasmonic Systems Niket Thakkar A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2017 Reading Committee: David J. Masiello Randall J. LeVeque Mathew J. Lorig Daniel R. Gamelin Program Authorized to Offer Degree: Applied Mathematics ©Copyright 2017 Niket Thakkar University of Washington Abstract Energy and Charge Transfer in Open Plasmonic Systems Niket Thakkar Chair of the Supervisory Committee: Associate Professor David J. Masiello Chemistry Coherent and collective charge oscillations in metal nanoparticles (MNPs), known as localized surface plasmons, offer unprecedented control and enhancement of optical processes on the nanoscale. Since their discovery in the 1950's, plasmons have played an important role in understanding fundamental properties of solid state matter and have been used for a variety of applications, from single molecule spectroscopy to directed radiation therapy for cancer treatment. More recently, experiments have demonstrated quantum interference between optically excited plasmonic materials, opening the door for plasmonic applications in quantum information and making the study of the basic quantum mechanical properties of plasmonic structures an important research topic. This text describes a quantitatively accurate, versatile model of MNP optics that incorporates MNP geometry, local environment, and effects due to the quantum properties of conduction electrons and radiation. We build the theory from first principles, starting with a silver sphere in isolation and working our way up to complex, interacting plasmonic systems with multiple MNPs and other optical resonators. We use mathematical methods from statistical physics and quantum optics in collaboration with experimentalists to reconcile long-standing discrepancies amongst experiments probing plasmons in the quantum size regime, to develop and model a novel single-particle absorption spectroscopy, to predict radiative interference effects in entangled plasmonic aggregates, and to demonstrate the existence of plasmons in photo-doped semiconductor nanocrystals. These examples show more broadly that the theory presented is easily integrated with numerical simulations of electromagnetic scattering and that plasmonics is an interesting test-bed for approximate methods associated with multiscale systems. To Mom and Dad, for always reminding me not to work too hard. Contents Acknowledgements 1 1 Introduction 3 1.1 List of Publications . 9 2 Quantum Plasmons in Active Environments 10 2.1 Plasmon-Electon Interaction in Isolated Nanoparticles . 11 2.2 Substrate Effects . 16 2.3 Active Environments . 19 2.4 Conclusion . 21 Mathematical Complement 23 2.A Plasmons in Isolated Nanoparticles . 23 2.B Optical Properties of the Nanosphere . 28 2.C LSP Decay in Free Space . 29 2.D Substrate Effects . 33 2.E Finite Substrates . 35 2.F Hybridized Systems . 38 2.G Bulk Dielectric Properties of Silver . 42 2.H Proof of Independence of Particular and Homogenous Solutions . 44 2.I Bulk Plasmons . 44 2.J Electron Energies, Wave Functions, and Shell Filling . 47 2.K Full wave EELS simulation . 48 2.L Data Acquisition and Analysis . 49 3 Optical Microresonators as Absorption Spectrometers 51 3.1 Photothermal absorption spectroscopy with sub-100-Hz detection limit . 52 3.2 Signatures of WGM-plasmon interaction . 56 3.3 Conclusions . 63 CONTENTS Mathematical Complement 65 3.A Methods . 65 3.B Equations of Motion . 66 3.C Absorption and Fano Interference . 67 3.D Extension to Many WGMs . 70 3.E Extension to 2 Nanorods . 71 3.F Effects of WGM Damping . 71 3.G A Numerical Approach . 72 4 Quantum Beats from Entangled Plasmons 75 4.1 Fano Resonances in the Heterodimer . 76 4.2 Single Photon Dynamics and Quantum Beats . 81 4.3 Two-Photon Dynamics and Photon Bunching . 84 4.4 Conclusion . 87 Mathematical Complement 88 4.A Plasmon-Photon Interaction Hamiltonian . 88 5 Charge-tunable Plasmons in Semiconductor Nanocrystals 90 5.1 Results and Analysis . 91 5.2 Conclusion . 99 Mathematical Complement 100 5.A Methods . 100 5.B Dielectric Model . 101 6 Concluding Remarks 104 Bibliography 105 Acknowledgements I'd like to first and foremost thank my advisor, Professor David Masiello. David has, unsurprisingly, had a huge influence on my research, but more than that, he was sure I'd be a successful scientist when no one, including me, seemed to think I would be. None of this would have been possible without David's support and belief in my potential, and even though my qualifying exams were an incredibly stressful experience, I'll never forget that David is the only reason I got the opportunity to take them at all. David's group of misfits in the chemistry department have also been amazing to work with: Charles Cherqui, Nick Bigelow, Steven Quillin, Nick Montoni, Jake Busche, Harrison Goldwyn, Claire West, and Kevin Smith have all challenged me, pushed me to grow, and supported my research efforts. Charles has had a particularly positive influence, acting as my second advisor, challenging me to make my work better, and teaching me approaches to problem solving and mathematical modeling that I would never have learned otherwise. Looking at his thesis, it's pretty obvious how much influence he's had on this one: I can't thank him enough for that. I've had the incredible pleasure of working with a lot of experimentalists whose data is featured prominently throughout this dissertation. Professor Daniel Gamelin and (now) Professor Alina Schimpf were my first experimental collaborators, and I'll always be thankful that they were willing to put up with my inexperience in our work together. I'm also deeply grateful to Professor Randall Goldsmith and his students, Kevin Heylman, Erik Horak, and Morgan Rea, who have been so great to work with that I've considered staying in graduate school longer to continue (I won't though). I also want to thank my committee members: Professors Randy LeVeque, Matt Lorig, Arka Majumdar, and Daniel Gamelin. All of them have been encouraging, happy to listen to me, and supportive of my work, and I'm thankful to have had such diverse and discerning perspectives on my research. I've had a lot of useful conversations about research that have made their way into my thesis as well. Donsub Rim, Akash Sheth, Scott Moe, Devin Light, Dr. Robert L. Cook, Professor Hrvoje Petek, and many others have edited my writing, talked to me about statistics or linear algebra, or listened to me complain about all the devils in all the details that make research complicated. I'm very grateful for all of those conversations. Last and most importantly, I want to thank my family and friends. I've had endless support from my mom, Trupti Thakkar, and my dad, Harshad Thakkar, and even though I pretend to be annoyed when they 1 2 ACKNOWLEDGEMENTS brag about me to their friends, I'm secretly incredibly flattered. Nipa Eason, my sister, not only taught me algebra over a summer in middle school, but also contributed significantly to the graphics throughout my thesis - this work is as much hers as it is mine, and I would never have gotten this far without her. Nehal Thakkar, my other sister, is easily so much smarter than me and an endless source of inspiration. When I was 3 and she was 6, she was the one to remind me to curb my spending habits so our parents could save for our college educations, so I suppose I have her to thank for still being trapped in school 23 years later. Finally, I want to thank Caitlin Cornell, Ty Kunovsky, Chardon Stuart, Jeff Wheatley, and Kevin Zimmerman for being my closest friends and strongest supports throughout the ups and downs of this entire process. Research is difficult, and it's people like these that make it worth all the trouble. Chapter 1 Introduction Understanding and controlling light has historically been a significant problem, and few technologies and discoveries are independent of innovations in optics [1]. The study of light dates back to fifth century BC, when Empedocles postulated that Aphrodite lit a fire within all human eyes, and that fire radiated out, allowing humans to see. He noted that if that were true, humans could see in the night just as well as in the day, so rays from the eyes and rays from sun must interact in some way to explain the difference [2]. Over time, this ray representation of light gave way to particle and wave representations, all of which were finally reconciled some 2000 years later with the discovery of quantum mechanics [3]. Along the way, studies of light and optics have inspired the invention of a variety of technologies, from the telescope to the microscope and beyond, all of which have pushed the limits of what the fires in people's eyes are capable of seeing. To that end, this text is an attempt to develop mathematical models of the electromagnetic and quantum mechanical properties of nanoscale pieces of metal. These so-called metal nanoparticles (MNPs) support collective and coherent oscillations of conduction electrons known as localized surface plasmons (LSPs, see Fig 1.1), which offer unprecedented control of light [4, 5], heat [6, 7], and charge [8, 9] at sub-diffraction-limited length scales [5]. Recent advances in methods for manufacturing MNP systems of nearly arbitrary shape and aggregation scheme have made once idealized plasmonic structures realizable, pushing the field of plasmonics into a golden age. Since MNP aggregates offer the possibility of focusing laser light onto the nanoscale, they represent a frontier in optics and studies of their basic properties continue to promise new applications in a range of fields, such as biosensing [10], solar energy [11], cancer therapy [12], and selective catalysis [13]. The term surface plasmon was originally coined by Stern and Ferrell [14], but the study of plasmons dates back to the 1950's works of Bohm and Pines, who were able to formulate a theory describing the existence of collective plasma oscillations in bulk metals [15, 16, 17].