SPIE Press Book

Tutorials in Complex Photonic Media

The field of complex photonic media encompasses many leading-edge areas in physics, chemistry, nanotechnology, materials science, and engineering. In Tutorials in Complex Photonic Media, leading experts have brought together 19 tutorials on breakthroughs in modern optics, such as negative refraction, chiral media, plasmonics, photonic crystals, and organic photonics.

This text will help students, engineers, and scientists entering the field to become familiar with the interrelated aspects of the subject. It also serves well as a supplemental text in introductory and advanced courses on optical materials, nanotechnology, physical optics, or photonic metamaterials.

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Foreword
Introduction
List of Contributors
1 Negative Refraction: 1.1 Introduction; 1.2 Background; 1.3 Beyond natural media: waves that run backwards; 1.4 Wires and rings; 1.5 Experimental confirmation; 1.6 The perfect lens; 1.7 The formal criterion for achieving negative phase velocity propagation; 1.8 Fermat's principle and negative space; 1.9 Cloaking; 1.10 Conclusions; 1.11 Appendices; Appendix I: The ε(ω) of a square wire array; Appendix II: Physics of the wire array's plasma frequency and damping rate; References
2 Optical Hyperspace: Negative Refractive Index and Subwavelength Imaging: 2.1 Introduction; 2.2 Nonmagnetic Negative Refraction; 2.3 Hyperbolic Dispersion: Materials; 2.4 Applications; 2.4.1 Waveguides; 2.4.2 The hyperlens; 2.4.2.1 Theoretical description; 2.4.2.2 Imaging simulations; 2.4.2.3 Semiclassical treatment; 2.5 Conclusion; References
3 Magneto-optics and the Kerr Effect with Ferromagnetic Materials: 3.1 Introduction to Magneto-optical Materials and Concepts; 3.2 Reflection of Light from a Plane Ferromagnetic Surface; 3.2.1 Single-surface polar orientation; 3.2.2 Kerr rotation; 3.3 Enhancing the Kerr Effect with Attenuated Total Reflection; 3.4 Numerical Investigations of Attenuated Total Reflection; 3.5 Conclusions; References
4 Symmetry Properties of Nonlinear Magneto-optical Effects: 4.1 Introduction; 4.2 Nonlinear Optics in Magnetic Materials; 4.3 Magnetic-field-induced SHG; 4.4 Effects Due to an Optical Magnetic Field or Magnetic Dipole Moment Transition; 4.5 Experiments; References
5 Optical Magnetism in Plasmonic Metamaterials: 5.1 Introduction; 5.2 Why Is Optical Magnetism Difficult to Achieve?; 5.3 Effective Quasistatic Dielectric Permittivity of a Plasmonic Metamaterial; 5.3.1 The capacitor model; 5.3.2 Effective medium description through electrostatic homogenization; 5.3.3 Eigenvalue expansion approach; 5.4 Summary; Appendix: Electromagnetic red shifts of plasmonic resonances; References
6 Chiral Photonic Media: 6.1 Introduction; 6.2 Stratified Anisotropic Media; 6.2.1 Biaxial material; 6.2.2 Propagation and basis fields; 6.2.3 Field transfer matrices; 6.2.4 Reflectance and transmittance; 6.3 Chiral Architectures and Characteristic Matrices; 6.3.1 Five chiral architectures; 6.3.2 Matrix for a continuous chiral film; 6.3.3 Matrix for a biaxial film; 6.3.4 Matrix for an isotropic film; 6.3.5 Matrix for a stack of films; 6.3.6 Matrices for discontinuous and structurally perturbed films; 6.3.7 Herpin effective birefringent media; 6.4 Reflectance Spectra and Polarization Response Maps; 6.4.1 Film parameters; 6.4.2 Standard-chiral media; 6.4.3 Remittance at the Bragg wavelength; 6.4.4 Modulated-chiral media; 6.4.5 Chiral-isotropic media; 6.4.6 Chiral-birefringent media; 6.4.7 Chiral-chiral media; 6.5 Summary; References
7 Optical Vortices: 7.1 Introduction; 7.2 Locating Vortex Lines; 7.3 Making Beams Containing Optical Vortices; 7.4 Topology of Vortex Lines; 7.5 Computer Simulation of Vortex Structures; 7.6 Vortex Structures in Random Fields; 7.7 Experiments for Visualizing Vortex Structures; 7.8 Conclusions; References
8 Photonic Crystals: From Fundamentals to Functional Photonic Opals: 8.1 Preface; 8.2 Principles of Photonic Crystals; 8.2.1 Electromagnetism of periodic dielectrics; 8.2.2 Maxwell's equations; 8.2.3 Bloch's theorem; 8.2.4 Photonic band structure; 8.3 One-Dimensional Photonic Crystals; 8.3.1 Bragg's law; 8.3.2 One-dimensional photonic band structure; 8.4 Generalization to Two-Dimensional and Three-Dimensional Photonic Crystals; 8.4.1 Two-dimensional photonic crystals; 8.4.2 Three-dimensional photonic crystals; 8.5 Physics of Inverse-Opal Photonic Crystals; 8.5.1 Introduction; 8.5.2 Inverse opal with moderate-refractive-index contrast; 8.5.3 Toward a higher-refractive-index contrast; 8.6 Tuning and Switching the Photonic Band Gap; 8.6.1 Introduction: double-inverse-opal photonic crystals; 8.6.2 Photonic band gap switching via symmetry breaking; 8.6.3 Tuning of the partial photonic band gap; 8.6.4 Switching of the complete photonic band gap; 8.7 Conclusion; Appendix; References
9 Wave Interference and Modes in Random Media: 9.1 Introduction; 9.2 Wave Interference; 9.2.1 Weak localization; 9.2.2 Coherent backscattering; 9.3 Modes; 9.3.1 Quasimodes; 9.3.2 Localized and extended modes; 9.3.3 Statistical characterization of localization; 9.3.4 Time domain; 9.3.5 Speckle; 9.4 Conclusion; References
10 Chaotic Behavior of Random Lasers: 10.1 Introduction; 10.1.1 Multiple scattering and random lasing; 10.1.2 Mode coupling; 10.2 Experiments on Emission Spectra; 10.2.1 Sample preparation and setup; 10.2.2 Emission spectra; 10.3 Experiments on Speckle Patterns; 10.4 Modeling; 10.4.1 Monte Carlo simulations; 10.4.2 Results and interpretation; 10.5 Lévy Statistics in Random Laser Emission; 10.6 Discussion; References
11 Lasing in Random Media: 11.1 Introduction; 11.1.1 "LASER" versus "LOSER"; 11.1.2 Random lasers; 11.1.3 Characteristic length scales for the random laser; 11.1.4 Light localization; 11.2 Random Lasers with Incoherent Feedback; 11.2.1 Lasers with a scattering reflector; 11.2.2 The photonic bomb; 11.2.3 The powder laser; 11.2.4 Laser paint; 11.2.5 Further developments; 11.3 Random Lasers with Coherent Feedback; 11.3.1 "Classical" versus "quantum" random lasers; 11.3.2 Classical random lasers with coherent feedback; 11.3.3 Quantum random lasers with coherent feedback; 11.3.3.1 Lasing oscillation in semiconductor nanostructures; 11.3.3.2 Random microlasers; 11.3.3.3 Collective modes of resonant scatterers; 11.3.3.4 Time-dependent theory of the random laser; 11.3.3.5 Lasing modes in diffusive samples; 11.3.3.6 Spatial confinement of lasing modes by absorption; 11.3.4 Amplified spontaneous emission (ASE) spikes versus lasing; peaks; 11.3.5 Recent developments; 11.4 Potential Applications of Random Lasers; References
12 Feedback in Random Lasers: 12.1 Introduction; 12.2 Concept of a Laser; 12.3 Lasers with Nonresonant Feedback and Random Lasers; 12.4 Photon Diffusion and Localization in Scattering Media and Their Applications to Random Lasers; 12.4.1 Diffusion; 12.4.2 Prediction of stimulated emission in a random laser operating in the diffusion regime; 12.4.3 Modeling of stimulated emission dynamics in neodymium random lasers; 12.4.4 Stimulated emission in a one-dimensional array of coupled lasing volumes; 12.4.5 Random laser feedback in a weakly scattering regime: space masers and stellar lasers; 12.4.6 Localization of light and random lasers; 12.5 Neodymium Random Lasers with Nonresonant Feedback; 12.5.1 First experimental observation of random lasers; 12.5.2 Emission kinetics in neodymium random lasers; 12.5.3 Analysis of speckle pattern and coherence in neodymium random lasers; 12.6 ZnO Random Lasers with Resonant Feedback; 12.6.1 Narrow modes in emission spectra; 12.6.2 Photon statistics in a ZnO random laser; 12.6.3 Modeling of a ZnO random laser; 12.7 Stimulated Emission Feedback: From Nonresonant to Resonant and Back to Nonresonant; 12.7.1 Mode density and character of stimulated emission feedback; 12.7.2 Transition from the nonresonant to the resonant regime of operation; 12.7.3 Nonresonant feedback in the regime of ultrastrong scattering: electron-beam-pumped random lasers; 12.8 Summary of Various Random Laser Operation Regimes; 12.8.1 Amplification in open paths: the regime of amplified stimulated emission without feedback; 12.8.2 Extremely weak feedback; 12.8.3 Medium-strength feedback: diffusion; 12.8.4 The regime of strong scattering; References
13 Optical Metamaterials with Zero Loss and Plasmonic Nanolasers: 13.1 Introduction; 13.2 Magnetic Plasmon Resonance; 13.3 Electrodynamics of a Nanowire Resonator; 13.4 Capacitance and Inductance of Two Parallel Wires; 13.5 Lumped Model of a Resonator Filled with an Active Medium; 13.6 Interaction of Nanontennas With an Active Host Medium; 13.7 Plasmonic Nanolasers and Optical Magnetism; 13.8 Conclusions; References
14 Resonance Energy Transfer: Theoretical Foundations and Developing Applications: 14.1 Introduction; 14.1.2 The nature of condensed phase energy transfer; 14.1.3 The Förster equation; 14.1.4 Established areas of application; 14.2 Electromagnetic Origins; 14.2.1 Coupling of transition dipoles; 14.2.2 Quantum electrodynamics; 14.2.3 Near- and far-field behaviour; 14.2.4 Refractive and dissipative effects; 14.3 Features of the Pair Transfer Rate; 14.3.1 Distance dependence; 14.3.2 Orientation of the transition dipoles; 14.3.3 Spectral overlap; 14.4 Energy Transfer in Heterogeneous Solids; 14.4.1 Doped solids; 14.4.2 Quantum dots; 14.4.3 Multichromophore complexes; 14.5 Directed Energy Transfer; 14.5.1 Spectroscopic gradient; 14.5.2 Influence of a static electric field; 14.5.3 Optically controlled energy transfer; 14.6 Developing Applications; 14.7 Conclusion; References
15 Optics of Nanostructured Materials from First Principles: 15.1 Introduction; 15.2 Optical Response from First Principles; 15.3 Effect of the Local Field in Optics; 15.3.1 Local field effect in classical optics; 15.3.2 Optical local field effects in solids from first principles; 15.4 Electrons in Quantum Confined Systems; 15.4.1 Electron energy structure in quantum confined systems; 15.4.2 Optical functions of nanocrystals; 15.5 Cavity Quantum Electrodynamics; 15.5.1 Interaction of a quantized optical field with a two-level atomic system; 15.5.2 Interaction of a quantized optical field with quantum dots; 15.6 Optical Raman Spectroscopy of Nanostructures; 15.6.1 Effect of quantum confinement; 15.6.2 Surface-enhanced Raman scattering: electromagnetic mechanism; 15.6.3 Surface-enhanced Raman scattering: chemical mechanism; 15.7 Concluding Remarks; Appendix A: Electron Energy Structure and Standard Density Functional Theory; Appendix B: Optical Functions within the Perturbation Theory; Appendix C: Evaluation of the Polarization Function Including the Local Field Effect; Appendix D: Optical Field Hamiltonian in Second Quantization Representation; References
16 Organic Photonic Materials: 16.1 Preface; 16.2 Introduction; 16.3 Effects of Dielectric Permittivity and Dispersion; 16.4 Complex Dendrimer Materials: Effects of Covalent Bonds; 16.5 Binary Chromophore Organic Glasses; 16.5.1 Optimizing EO activity and optical transparency; 16.5.2 Laser-assisted poling (LAP); 16.5.3 Conductivity issues; 16.6 Thermal and Photochemical Stability: Lattice Hardening; 16.7 Thermal and Photochemical Stability: Measurement; 16.8 Devices and Applications; 16.9 Summary and Conclusions; Appendix: Linear and Nonlinear Polarization; References
17 Charge Transport and Optical Effects in Disordered Organic Semiconductors: 17.1 Introduction; 17.2 Charge Transport; 17.2.1 Energy bands; 17.2.2 Dispersive charge transport; 17.2.3 Hopping mobility; 17.2.4 Density of states; 17.3 Impedance Spectroscopy: Bias and Temperature Dependence; 17.4 Transient Spectroscopy; 17.5 Thermoelectric Effect; 17.6 Exciton Formation; 17.7 Space-Charge Effect; 17.8 Charge Transport in the Field-Effect Structure; References
18 Holography and Its Applications: 18.1 Introduction; 18.2 Basic Information on Holograms; 18.2.1 Hologram types; 18.3 Recording Materials for Holographic Metamaterials; 18.4 Computer-Generated Holograms; 18.5 Simple Functionalities of Holographic Materials; 18.6 Phase Conjugation and Holographic Optical Elements; 18.7 Related Applications and Procedures; 18.7.1 Holographic photolithography; 18.7.2 Copying of holograms; 18.7.3 Holograms in nature and general products; References; In Memoriam: Chandra S. Vikram
19 Slow and Fast Light: 19.1 Introduction; 19.1.1 Phase velocity; 19.1.2 Group velocity; 19.1.3 Slow light, fast light, backward light, stopped light; 19.2 Slow Light Based on Material Resonances; 19.2.1 Susceptibility and the Kramers-Kronig relations; 19.2.2 Resonance features in materials; 19.2.3 Spatial compression; 19.2.4 Two-level and three-level models; 19.2.5 Electromagnetically induced transparency (EIT); 19.2.6 Coherent population oscillation (CPO); 19.2.7 Stimulated Brillouin and Raman scattering; 19.2.8 Other resonance-based phenomena; 19.3 Slow Light Based on Material Structure; 19.3.1 Waveguide dispersion; 19.3.2 Coupled-resonator structures; 19.3.3 Band-edge dispersion; 19.4 Additional Considerations; 19.4.1 Distortion mitigation; 19.4.2 Figures of merit; 19.4.3 Theoretical limits of slow and fast light; 19.4.4 Causality and the many velocities of light; 19.5 Potential Applications; 19.5.1 Optical delay lines; 19.5.2 Enhancement of optical nonlinearities; 19.5.3 Slow- and fast-light interferometry; References

Index

Foreword

Classical optics has been with us for some considerable time, yet the past decade has produced a cornucopia of new research, often revealing unsuspected phenomena hidden like nuggets of gold in the rich lode of optical materials. The key has often been complexity. The range of optical properties available in natural materials is limited, but by adding manmade structure to nature's offerings we can extend our reach, sometimes to achieve properties not seen before. I pick one example from the many included in this volume: negative refraction. Years ago it had been realised that a material with negative magnetic and electric responses would also have a negative refractive index. There, the idea languished for nearly half a century, lacking the naturally occurring materials to realise the effect. However by internally structuring a medium on a scale less than the relevant wavelength, it was proved possible to make a new form of material, a 'metamaterial,' which had the required negatively refracting properties. This concept alone has given rise to thousands of papers. There are other examples I could cite from the chapters in this book: exploitation of nearfield properties of nanoparticle arrays, photonic band gap waveguides, metallic nanostructures for sensing proteins, and so on. All of these examples have in common that man adds complexity to the offerings of nature.

In the face of these myriad advances, how are students or other new entrants to the field to educate themselves in the new technology? This book provides the answer, collecting together a definitive series of tutorials, each provided by an expert in the field. It is published at a time when there are many such new entrants and will be of great value.

J. B. Pendry
Imperial College London
February 2009

Preface

An increasingly large number of high- and low-tech technologies and devices benefit from employing optics and photonics phenomena, the latter originally being termed photon-based electronics. Progress in the research fields of optics and photonics, which have both experienced continuously strong growth over the last few decades, critically depends on the understanding and utilization of the physical, chemical and structural properties of optical materials. The optical materials used in traditional optics technology were macroscopically homogeneous in that their scale of inhomogeneity was much less than the wavelength. In more recent years, multiple breakthroughs have involved inhomogeneous, composite, and multiphase materials, whose structures are either photoinduced or determined by synthesis or fabrication. Examples include holography, optics of scattering media, and metamaterials. These breakthroughs make photonic materials inherently complex. The broad range of physical phenomena underlying complex photonic media makes it difficult for scientists, engineers, and students entering the field to navigate through the range of topics and to understand clearly how they relate to each other.

The purpose of this book is to provide the necessary coverage and inspire the reader's curiosity about the fascinating subject of complex photonic media. All of the tutorial chapters are designed to start with the basics and gradually move toward discussion of more advanced topics. We thus envisage that students and scholars with diverse backgrounds and levels of expertise will find this text interesting and useful. The book can be used as a supplemental text in courses on nanotechnology or optical materials, or a variety of other courses. It can also be used as the main text in a more focused course aimed at fundamental properties of scattering media and metamaterials. The anticipated level of preparation is equivalent to advanced senior undergraduate level, beginning graduate level, or higher. The book covers the topics in the following (rather loose) categorization:

Negative index materials (NIMs). One of the most exciting developments in complex photonic media in recent years is the realization that the basic parameters describing the electromagnetics of simple, isotropic media can take simultaneously negative values. This leads to all kinds of interesting phenomena, from a revised understanding of Snell's law, to lenses that defeat the conventional diffraction resolution limit. In "Negative Refraction" (Chapter 1), Martin W. McCall and Graeme Dewar describe the basic theory and impetus for negative refraction research. In "Optical Hyperspace: Negative Refractive Index and Subwavelength Imaging" (Chapter 2), Leonid V. Alekseyev, Zubin Jacob, and Evgenii Narimanov explore nonmagnetic routes that exploit materials with hyperbolic dispersion relations.

Magneto-optics. The term magneto-optics is used when the direction and polarization state of light are controlled by the application of external magnetic fields, offering opportunities for optical storage and isolation in optical systems. In "Magneto-optics and the Kerr Effect with Ferromagnetic Materials" (Chapter 3), Allan D. Boardman and Neil King introduce the magneto-optics derived from air-ferroelectric interfaces and glass/ferromagnetic film/air multilayer systems. "Nonlinear Magneto-Optics" (Chapter 4) by Yutaka Kawabe gives emphasis to the relationship between the tensors describing the nonlinearity and the underlying crystal point group symmetry. In "Optical Magnetism in Plasmonic Metamaterials" (Chapter 5), Gennady Shvets and Yaroslav A. Urzhumov describe some of the difficult challenges that lie ahead for achieving magnetic activity at optical frequencies.

Chiral media and vortices. Light, being composed of unit spin photons, is inherently chiral. However, chirality in optical systems can also be engaged at structural and macroscopic electromagnetic levels. Structural chirality is covered by Ian Hodgkinson and Levi Bourke in "Chiral Photonic Media" (Chapter 6), which describes the multilayer matrix formalism for novel elliptically polarized filters. When optical beams interfere, phase singularities occur; in "Optical Vortices" (Chapter 7) Kevin O'Holleran, Mark R. Dennis, and Miles J. Padgett describe some of the remarkable topological knots and 3D twists that result.

Scattering in periodic and random media. Scattering of light is fundamental to complex photonic media. Structures that are periodic are generally referred to as photonic crystals. In "Photonic Crystals: From Fundamentals to Functional Photonic Materials" (Chapter 8), Durga P. Aryal, Kosmas L. Tsakmakidis, and Ortwin Hess describe how photonic bandstructure emerges in both 1- and 2D structures, and how optical switching is achievable in inverse-opal structures. When the material inhomogeneity is random, different methods must be employed. In "Wave Interference and Modes in Random Media" (Chapter 9), Azriel Z. Genack and Sheng Zhang describe photon transport in a medium in terms of the interference of multiply scattered partial waves as well as by considering the different spatial, spectral, and temporal characters of the electromagnetic modes.

Photonic media with gain and lasing phenomena. Photonic media with gain and lasing phenomena represents the generic class of active photonic media. "Chaotic Behavior of Random Lasers" (Chapter 10) by Diederik Wiersma, Sushil Mujumdar, Stefano Cavalieri, Renato Torre, Gian-Luca Oppo, and Stefano Lepri examines the irreproducibility of experimental emission spectra and the change of statistics at near threshold. "Lasing in Random Media" (Chapter 11) by Hui Cao provides a detailed review of the concepts and advances in the field of random lasers. "Feedback in Random Lasers" (Chapter 12) by Mikhail A. Noginov emphasizes the significance of the strength of scattering and/or feedback in determining the properties of random lasers. In "Optical Metamaterials with Zero Loss and Plasmonic Nanolasers" (Chapter 13), Andrey Sarychev discusses how nano-horseshoe inclusion in an active host medium results in a plasmonic nanolaser.

Fundamentals. In "Resonance Energy Transfer: Theoretical Foundations and Developing Applications" (Chapter 14), David L. Andrews explores how the intricate interplay between quantum mechanical and electromagnetic medium properties leads to schemes for energy transfer and all-optical switching. In "Optics of Nanostructured Materials from First Principle Theories" (Chapter 15) Vladimir I. Gavrilenko provides a tutorial on the microscopic modelling of optical response functions using density functional theory and related approaches.

Organic photonic materials. Materials whose nonlinear coefficients often exceed their inorganic counterparts both in magnitude and response rate are examined in "Organic Photonic Materials" (Chapter 16) by Larry R. Dalton, Philip A. Sullivan, Denise H. Bale, Scott R. Hammond, Benjamin C. Olbricht, Harrison Rommel, Bruce Eichinger, and Bruce H. Robinson. These authors explore organic optical material design in terms of critical structure/function relationships. "Charge Transport and Optical Effects in Disordered Organic Semiconductors" (Chapter 17) by Harry H. L. Kwok, You-Lin Wu, and Tai-Ping Sun highlights how, as with regular semiconductors, charge transport can be modified by doping in organic materials, which possess enhanced carrier mobilities.

Holographic media. "Holography and Its Applications" (Chapter 18) by H. John Caulfield and Chandra S. Vikram discusses holograms used as parts of complex light-controlled or light-defined systems that manipulate the direction, spectrum, polarization, or speed of pulse propagation of light in a medium.

Slow and fast light. Slow and fast light is an intriguing topic demystified by Joseph E. Vornehm, Jr. and Robert W. Boyd in the final chapter "Slow and Fast Light" (Chapter 19). The authors show how manipulation of the material dispersion can lead to very slow, halted, or even backward propagating optical pulses.

The conception of Tutorials in Complex Photonic Media lies in an effort to consolidate the conference series, Complex Mediums: Light and Complexity, a subconference of the annual SPIE Optics and Photonics meeting held over the years 2003-2006¹. Incentive for this book was also largely compelled by Introduction to Complex Mediums for Optics and Electromagnetics, edited by Werner S. Weiglhofer and Akhlesh Lakhtakia, SPIE Press (2003), which is a consolidation of the Complex Mediums conferences from 1999 to 2002. We have taken special emphasis in this book to avoid the somewhat disjointed presentation that often accompanies books based on conferences. To this end, all of the chapters underwent round-robin reviews by several editors and coauthors who were frequently not directly involved in the research area. Much "back and forth" has hopefully ironed out the specialist's tendency to dive headlong into details that can only be appreciated once sufficient underpinning motivational material has been presented. Another issue is notation. Eventually, we decided that keeping a consistent notation throughout the book would be self-defeating, as anyone entering a new area must, to a certain extent, be flexible to individual authors' preferences. Nevertheless, we went to some lengths to ensure that the notation within each chapter is consistent.

The four editors who undertook this project have had a unique opportunity to work with some of the leading specialists in the field. Of course, there have been frustrations, but in the end, we hope that that this book presents a broad and balanced summary that will lead many others to take up the exciting challenges of working in complex photonic media. In the introduction to the predecessor volume noted above, Akhlesh Lakhtakia wrote 'I shall be delighted if a companion volume were published after another two or three editions of this conference.' Well, here it is.

Mikhail A. Noginov
Graeme Dewar
Martin W. McCall
Nikolay I. Zheludev
September 2009

¹ In 2003 the conference was titled Complex Mediums IV: Beyond Linear Isotropic Dielectrics; in 2006 it was titled Complex Photonic Media.

Tutorials in Complex Photonic Media

Contents

Foreword

Preface