Graduate Texts in Physics Ulrich Hohenester Nano and Quantum Optics An Introduction to Basic Principles and Theory Graduate Texts in Physics Series Editors Kurt H. Becker, NYU Polytechnic School of Engineering, Brooklyn, NY, USA Jean-Marc Di Meglio, Matière et Systèmes Complexes, Bâtiment Condorcet, Université Paris Diderot, Paris, France Sadri Hassani, Department of Physics, Illinois State University, Normal, IL, USA Morten Hjorth-Jensen, Department of Physics, Blindern, University of Oslo, Oslo, Norway Bill Munro, NTT Basic Research Laboratories, Atsugi, Japan Richard Needs, Cavendish Laboratory, University of Cambridge, Cambridge, UK William T. Rhodes, Department of Computer and Electrical Engineering and Computer Science, Florida Atlantic University, Boca Raton, FL, USA Susan Scott, Australian National University, Acton, Australia H. Eugene Stanley, Center for Polymer Studies, Physics Department, Boston University, Boston, MA, USA Martin Stutzmann, Walter Schottky Institute, Technical University of Munich, Garching, Germany Andreas Wipf, Institute of Theoretical Physics, Friedrich-Schiller-University Jena, Jena, Germany www.com Graduate Texts in Physics publishes core learning/teaching material for graduate- and advanced-level undergraduate courses on topics of current and emerging fields within physics, both pure and applied.
These textbooks serve students at the MS- or PhD-level and their instructors as comprehensive sources of principles, definitions, derivations, experiments and applications (as relevant) for their mastery and teaching, respectively. International in scope and relevance, the textbooks correspond to course syllabi sufficiently to serve as required reading. Their didactic style, comprehensiveness and coverage of fundamental material also make them suitable as introductions or references for scientists entering, or requiring timely knowledge of, a research field. More information about this series at http://www.com/series/8431 www.com Ulrich Hohenester Nano and Quantum Optics An Introduction to Basic Principles and Theory www.com Ulrich Hohenester Institut für Physik, Theoretische Physik Karl-Franzens-Universität Graz Graz, Austria ISSN 1868-4513 ISSN 1868-4521 (electronic) Graduate Texts in Physics ISBN 978-3-030-30503-1 ISBN 978-3-030-30504-8 (eBook) https://doi.1007/978-3-030-30504-8 © Springer Nature Switzerland AG 2020 This work is subject to copyright.
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Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland www.com Preface Nano optics combines the research areas of optics and nanoscience.
Through light we acquire information about the world around us, and the controlled manipulation of light forms the backbone of numerous optics applications, such as fiber-based communication or light harvesting. Nanoscience, on the other hand, deals with the controlled manufacturing and manipulation of matter at the atomic scale, and has driven the digital revolution that has irrevocably shaped our everyday life, for instance, in the form of computers or mobile phones. A combination of these areas is expected to bring together the best of two worlds. Yet, optics and nanoscience don’t come together easily.
The diffraction limit dictates that light cannot be squeezed into volumes with dimensions smaller than the wavelength, which are on the order of micrometers rather than nanometers, and conversely in optical microscopy only objects further apart than approximately the light wavelength can be spatially distinguished. Nano optics deals with the manipulation of light at length scales comparable or smaller than the light wavelength, ideally down to the nanometer scale. In the last decades, scientists have succeeded in devising schemes to let optics go nano. For instance, localization microscopy and optical tweezers have been awarded the Nobel Prizes 2014 and 2018 for light manipulations in the threshold region of the diffraction limit.
To overcome the limit, one can collect light at the nanoscale, for instance, in scanning nearfield optical microscopy, or bind within the field of plasmonics light to electron charge oscillations at the surface of metallic nanostructures, hereby squashing light into extreme subwavelength volumes. This book provides an introduction to nano optics and plasmonics. It is based on a lecture series I have taught over several years at the University of Graz and other places. My main focus is on the basic principles and the theoretical tools needed in nano optics, whereas applications are discussed only exemplary.
In this respect, the book is expected to differ from most related textbooks. I have kept references to the current research literature somewhat sparse, but have tried to cite the many excellent review articles for further information, whenever possible. I have also tried to keep the discussion self-contained, and have refrained from using the phrase “it can be shown” or equivalent whenever possible. This has made the presentation v www.com vi Preface considerably longer than I initially thought, but it will hopefully facilitate reading the book.
The book is separated into two parts. The first one deals with classical nano optics, where classical can be understood both in terms of classical electrodynamics and in terms of the classical, canonical presentation of the subject. The second part brings nano optics to the quantum realm. I have tried hard to make the presentation as entertaining as possible, but reading through the final version I realize that it has become somewhat technical and busy—apologies for that.
As always, the natural way of reading a book is from the beginning to the end, and in principle there is nothing wrong with this traditional approach. However, since I rarely stick to this order myself, I will not provide any particular advice for using the book: start reading wherever it looks interesting, and go back to the basics if needed. Many colleagues and students have helped me to bring the book to its present form; they are acknowledged separately below. I sincerely hope that this book will be helpful to both experienced researchers seeking for selected information and to beginners who are interested in a first glance of the topic.
For the field of nano optics as a whole, I hope that its future will be as bright and shiny as its past has been. Graz, Austria Ulrich Hohenester June 2019 www.com Acknowledgements This book presents my personal account of nano optics and plasmonics, but my way of seeing the field has been strongly influenced by many colleagues and predecessors. I thank all of them. My first encounter with the topic has been through the NANOOPTICS group headed by Joachim Krenn at the University of Graz who has worked in the field of plasmonics long before it has become fashionable and has been given this name.
I have strongly benefited from their deep insights as well as their serenity in judging novel developments in the light of the long history of the field. I am indebted to my long-term collaborator Andi Trügler who has accompanied me for more than a decade on our joint nano optics and plasmonics activities. Many thanks also to the numerous experimental and theoretical collaborators for sharing their results and opinions, as well as for making science such an exciting and pleasant undertaking. Teaching the subject has been always important to me, unfortunately, it has never come easy.
In 2011, Jussi Toppari invited me to teach a course at a summer school in Jyväskylä, Finland, where I enjoyed both the interactions with the students in the class room and the traditional Finnish sauna. However, I had to realize that I should probably spend more time with the basic things, which one often erroneously calls “simple” after having employed them for a sufficiently long time. For several years, I have used the loose collection of slides compiled for this summer school as lecture notes for a course I have taught at Graz University. The kind invitation of Guido Goldoni and Elisa Molinari for teaching a course on “Nano and Quantum Optics” at the University of Modena and Reggio Emilia in the spring of 2018 finally triggered my (surprisingly spontaneous) decision to start writing a textbook on the subject.
The conveniences of the superb Modenese food, the beautiful bike tours to the Apennin, as well as a class of extremely bright students helped me to make the start as enjoyable as possible. Of course, I have completely underestimated writing a textbook, and after having worked on it for about one and a half years my emotions towards the project have remained as mixed and diverse as they have been from the beginning. Special thanks go to my wife Olga Flor, among many other things for organizing during my stay at Modena, a memorable trip to the eroding castle of Canossa, vii www.com viii Acknowledgements which has been given up by the Italian state but is kept alive by a few brave volunteers, as well as a visit together with Elisa to the Osteria Francescana, and for showing me how to write real books. I am indebted to numerous colleagues who have read through specific parts of the book and have given most valuable feedback.
In alphabetic order, I wish to thank Javier Aizpurua, Stefano Corni, Hari Ditlbacher, Hans Gerd Evertz, Antonio Fernández-Domínguez, Christian Hill, Mathieu Kociak, Joachim Krenn, Olivier Martin, Walter Pötz, Stefan Scheel, and Gerhard Unger. They have helped me to detect the most obvious errors and mistakes in the manuscript. I will provide an updated list of errata on my homepage at the University of Graz, and I invite all readers to inform me about possible errors and to provide feedback on how the presentation could be made even more clear.com Contents 1 What Is Nano Optics? .3 The Realm of Nano Optics. 14 2 Maxwell’s Equations in a Nutshell .1 The Concept of Fields .3 Maxwell’s Equations in Matter .4 Time-Harmonic Fields .5 Longitudinal and Transverse Fields.
40 3 Angular Spectrum Representation .1 Fourier Transform of Fields .2 Far-Field Representation .3 Field Imaging and Focusing .4 Paraxial Approximation and Gaussian Beams .5 Fields of a Tightly Focused Laser Beam .6 Details of Imaging and Focusing Transformations. 60 4 Symmetry and Forces .4 Optical Cross Sections .5 Conservation of Momentum .6 Optical Angular Momentum .1 What Are Green’s Functions? .2 Green’s Function for the Helmholtz Equation .3 Green’s Function for the Wave Equation .5 Details for Representation Formula of Wave Equation. 108 6 Diffraction Limit and Beyond .1 Imaging a Single Dipole .2 Diffraction Limit of Light.3 Scanning Nearfield Optical Microscopy .1 Drude–Lorentz and Drude Models .2 From Microscopic to Macroscopic Electromagnetism .3 Nonlocality in Time .4 Reciprocity Theorem in Optics .3 Transfer Matrix Approach .5 Green’s Function for Stratified Media .2 Spheres and Ellipsoids in the Quasistatic Limit .3 Boundary Integral Method for Quasistatic Limit .6 Boundary Integral Method for Wave Equation .7 Details of Quasistatic Eigenmode Decomposition. 251 10 Photonic Local Density of States .1 Decay Rate of Quantum Emitter.2 Quantum Emitter in Photonic Environment.3 Surface-Enhanced Raman Scattering.4 Förster Resonance Energy Transfer .5 Electron Energy Loss Spectroscopy.
281 11 Computational Methods in Nano Optics .1 Finite Difference Time Domain Simulations .2 Boundary Element Method .4 Boundary Element Method Approach (Galerkin) .5 Finite Element Method .6 Details of Potential Boundary Element Method .com Contents xi 12 Quantum Effects in Nano Optics .1 Going Quantum in Three Steps .2 The Quantum Optics Toolbox .3 Summary of Book Chaps. 349 13 Quantum Electrodynamics in a Nutshell .