Preface
Werner S Weiglhofer and A Lakhtakia

1. Separating field and constitutive equations in electromagnetic theory
Evert J Post

2. Constitutive characterization of simple and complex mediums
Werner S Weiglhofer

3. Isotropic chiral materials
Craig F Bohren

4. Point group symmetries
Daniel B Litvin

5. Nonresonant nonlinear optics in semiconductor quantum wells
John M Arnold

6. Organic thin-film photorefractive materials
Partha P Banerjee

7. Optical energy harvesting materials
David L Andrews

8. Magnetoelectric effects in insulating magnetic materials
Hans Schmid

9. Magneto-optics: a critical review
Allan D Boardman and Ming Xie

10. Static and dynamic magnetoelasticity
Graeme Dewar

11. Electromagnetic response of a dynamic magnetized plasma
Dikshitulu K Kalluri

12. Magnetoimpedance in multilayered films for miniature magnetic sensors
Larissa V Panina and and Dmitriy P Makhnovskiy

13. Metamaterials: An introduction
Rodger M Walser

14. Homogenization of linear and nonlinear complex composite materials
Tom G Mackay

15. Negative phase-velocity materials
Akhlesh Lakhtakia, Martin W McCall and Werner S Weiglhofer

16. Scattering theory of photonic crystals
Didier Felbacq and Frederic Zolla

17. Optical properties of metal-dielectric films
Andrey K Sarychev and and Vladimir M Shalaev

18. Nanostructured thin films
Geoffrey B Smith

19. The past, the present, and the future of sculptured thin films
Akhlesh Lakhtakia and Russell F Messier

20. Electromagnetics of carbon nanotubes
Sergey A Maksimenko and Gregory Ya Slepyan

21. Models and applications of chiral sculptured thin films
Martin W McCall

22. Randomness in complex materials
H John Caulfield, Don O Henderson and Mikhail A Noginov

23. Nonlinear spatial structures
William J Firth and John M McSloy

24. Statistical approaches to scattering
Walid Tabbara, Veronique Rannou and Stefano Salio

25. Elastic orthonormal beams and localized fields with applications to control laser radiation
George N Borzdov

26. Polarimeter for anisotropic optically active materials
Toru Asahi

27. Generalized ellipsometry
Mathias Schubert

Tributes to Werner Weiglhofer

Index

Preface

"So, what is a complex medium?" Had you asked me this question in 1990, I would not have been able to give you a coherent answer. Although by then I had studied electromagnetic fields in materials with complicated response properties for about seven years, my understanding of electromagnetics lacked the necessary breadth. Furthermore, electromagnetics researchers studying diverse types of response properties were just beginning to interact with each other.

A decade later, the subdiscipline of complex-mediums electromagnetics (CME) has taken shape. At least two series of conferences on CME are held regularly, and many scientific and technical meetings have special sessions devoted to CME. Among other complex mediums, carbon nanotubes, metamaterials, materials in which light bends "differently", and materials in which light "rotates" are commonly written about in science magazines (such as Nature, Science and Materials Today), as well as in monthly organs of learned societies (such as OE Magazine, Optics and Photonics News and IEEE Antennas and Propagation Magazine).

In 2003, I can give two answers to your question: a short answer, and a long one. The short answer is that a positive definition of complex mediums still remains elusive. The consensus among CME researchers is that a complex medium is not a simple medium; and that the response properties of any complex medium must be different from linear, isotropic dielectric. The long answer? Well, read on ...

Giant strides were made during much of the 20th century in understanding and commercially exploiting the electromagnetic properties of our atmosphere and virtually matter-free space. Yet materials research for the most part remained confined to simplified (preferably dielectric) response properties. The situation began to change during the 1980s. Scientific and technological progress came to be dominated by the conceptualization, characterization, fabrication, and application of many different classes of materials. Although some of these materials are found in nature, laboratory processing is often needed for efficient use. Others are entirely synthetic, created by chemical and physical processes. Certain materials are multiphase composites designed for certain desirable response properties otherwise unavailable. Multifunctional materials as well as functional gradient materials are needed for special purposes. Nanoengineering is often used to make material samples with the same chemical composition but different response characteristics. Thus, novel fabrication techniques and a multifarious understanding of the relationship between the macroscopic properties and the microstructural morphology of materials led to rapid progress in research on the interaction of the electromagnetic field and matter.

Electromagnetics is a science of the microscopic, though, perhaps reasonably, undergraduate textbooks rarely mention that subtlety. Many graduate textbooks also do not sufficiently emphasize that foundation. Since the 1890s, however, the Lorentz-Heaviside visualization has prevailed over earlier, even Maxwell's, understanding of electromagnetism. All matter is an ensemble of discrete charges dispersed in free space or vacuum; but an exact treatment of that kind is virtually impossible, even today, when the charge-.bearing entities exceed a few million in number. Fortunately, when electromagnetic wavelengths considerably exceed molecular dimensions, matter can be treated as a continuum for a host of technological purposes.

A simple medium---most easily exemplified by a linear, isotropic dielectric material--- affects the progress of electromagnetic signals in two ways:

* a delay is created with respect to propagation in vacuum, and

* absorption of electromagnetic energy takes place.

Both effects evince dependencies on frequency, but not on spatial direction. Calculations can be made and measurements can be interpreted on the per unit amplitude/intensity basis. An isotropic dielectric medium is thus equivalent to an isotropic contraction of space with absorption overlaid.

In complex mediums, the progress of electromagnetic signals is additionally affected in one or more of several ways:

* anisotropy: the direction-dependent contraction of space and absorption;

* chirality: the twisting of space;

* nonhomogeneity: the dispersal of energy into different directions by either interfaces between uniform mediums or continuous gradients in material dispersal; and

* nonlinearity: the emission of absorbed energy at (generally) some other frequency.

In consequence, CME research has several characteristics different from research on simple mediums.

First, CME formulations are best couched in terms of the fundamental entity in modern electromagnetics: the electromagnetic field. It happens to have two parts, named the electric field E and the magnetic field B, and identified separately for historical reasons as well as convenience. The two parts cannot be separated from the other, except after making some approximation or the other. Take a piece of a material that you think is linear, isotropic and dielectric; and make it move at a constant velocity with respect to you. You will find that it displays bianisotropic properties upon motion. A Lorentz-covariant description is therefore the only proper description of electromagnetic response properties.

Second, causality must be incorporated in CME research. Every material responds after a delay. The instantaneous part of its response properties cannot be different from that of free space; otherwise, the material would possess foreknowledge, a prospect best left for sci-fi authors to exploit. The development of femtosecond-pulse optics and the generation of attosecond pulses suggest that it is better not to cast time aside by the artifice of the Fourier transform. Even in the frequency domain, causality takes the form of dissipation and dispersion, which are the two sides of the same coin. Third, although matter is nonhomogeneous at microscopic length scales, piecewise homogeneity is commonplace at macroscopic length scales. Statistical techniques provide a bridge between the two length scales. Complicated macroscopic response properties should not be assumed casually. For instance, if a homogeneous piece of a medium with a certain set of response properties cannot be found, the existence of continuously nonhomogeneous analogs of that set at macroscopic length scales is a dubious proposition. The development of homogenization techniques for complex mediums is a major challenge today, despite very recent successes for linear bianisotropic materials.

Fourth, nonlinearity is an essential attribute of wave-material interaction. Nonlinearity introduces dependency on amplitude or strength, and is responsible for the occurrence of multiwavelength processes. It also accounts for the electromagnetic exposure histories of materials. We all know from high-school textbooks that matter modifies electromagnetic waves; but waves also modify matter. Observe how a newspaper yellows after lying in the sun for a few days. Electromagnetic waves emitted by the sun (i.e., sunlight) effect that change.

The complexity of actual materials cannot yet be handled in its entirety. Complexity is like Gulliver, while CME researchers are like the Lilliputians. Although an individual CME researcher takes only one or two meaningful steps towards the taming of complexity, different steps are taken by different CME researchers. CME commands the attentions of scientists from a wide spectrum of disciplines: from physics and optics to electrical and electronic engineering, from chemistry to materials science, to applied mathematics and even biophysics. Thus, CME is presently a multidisciplinary research area spanning basic theoretical and experimental research at universities to the industrial production of a diverse array of electrical, microwave, infrared and optical materials and devices. A recent impetus for multidisciplinarity is the unrelenting progress of nanotechnology, which is now beginning to engender mesoscopic approaches in CME.

This book is a collection of essays to explain complex mediums for optical and electromagnetic applications. The genesis of this book lies in a series of conferences organized at the successive Annual Meetings of SPIE from 1999 to 2002. The scope of Conference 3790, Engineered Nanostructural Thin Films and Materials, was not fully explained by its title. Subsequently, Conference 4097 was entitled Complex Mediums. Further explication being needed, Conference 4467 was named Complex Mediums II: Beyond Linear Isotropic Dielectrics and was followed by Conference 4806 Complex Mediums III: Beyond Linear Isotropic Dielectrics. All four were organized by me, very ably assisted by Werner S. Weiglhofer, Russell F. Messier, Ian J. Hodgkinson, Martin W. McCall, and Graeme Dewar. A multitude of CME researchers participated wholeheartedly.

Werner S. Weiglhofer, my co-editor, was involved in all four conferences. He and I felt that the optics community at large should benefit from a relatively broad introduction to complex mediums. Many speakers who had delivered Key Lectures and Critical Review Lectures at the conferences agreed, as also did Rick Hermann and Sharon Streams of the SPIE Optical Engineering Press. We therefore invited the presenters to update and expand their initial lectures. Other prominent researchers were invited to contribute essays on CME topics that were deemed important but had not been covered in the four conferences. The essays were edited, reviewed, revised and compiled into this book.

All contributors were requested to write with two aims: first, to educate on phenomenology and terminology; second, to provide a state-of-the-art review of a particular topic. The vast scope of CME exemplified by the actual materials covered in the essays should provide a plethora of opportunities to the novice and the initiated alike. Graduate students in the broad disciplines of electrical engineering, materials science, and physics are likely to find inspiration from one essay or another to pursue CME research; and our fondest hope is that this book would serve the next decade or so as a goldmine for dissertation topics. Experienced researchers desirous of either switching research areas or synthesizing new types of material responses may profit from this book as well. R&D engineers in industry may be able to conceptualize and actualize new types of devices, after reading certain parts of this book.

I must add here that, although Werner and I had agreed to divide editorial responsibilities equally, he was the Managing Editor. To this position, he brought his considerable organizational acumen. He interacted with all contributors and reviewers, as well as with Sharon Streams at SPIE. All contributors were supplied progress reports at suitable intervals; e-mails were promptly answered by him with unfailing courtesy; and so on. When on January 5, 2003, he asked me to initiate the writing of a preface, I replied that the end of March was far away. A week later, he was killed by an avalanche on the slopes of Bispen, a Norwegian mountain that he had ascended 29 times. I had to assume his mantle; I had to write this preface solo. This book is now a memorial to my friend Werner S. Weiglhofer, as you will notice from the inclusion of a section entitled In Memoriam.

A linguistic note: You will notice the absence in this book of Latin and Greek plurals of words from those languages commonly used in English. This was a deliberate editorial decision. During some 14 years of collaboration, both Werner and I were appalled at the widespread misuse of plurals--- such as criteria, media and spectra --- as singulars in scientific literature. Such pluralization is artificial to the native robustness of English. At best, it is an affectation. No wonder so many native and non-native speakers of this language make those mistakes! Taking a leaf from George Bernard Shaw's introductions to his plays that English spelling needs reform, in 1996 we decided in favor of the normal English pluralization of Latin and Greek singulars. Although uncommon, this practice is not new. Most journals accept it. So do the Royal Society (of London), John Wiley & Sons, and SPIE.

The cooperation that Werner and I received from all contributors and reviewers was nothing short of splendid. Ms. Sharon Streams and others at SPIE have provided unstinted support. Professors David R. Fearn and Edward Spence graciously contributed their memories of Werner; and they also assisted in the transfer of editorial correspondence from Werner's computer to me. In the latter task, they were joined by Mr. David Thom (University of Glasgow) and Professor Joseph P. Cusumano (Pennsylvania State University). I am grateful to everyone involved in this project. Complex Mediums IV: Beyond Linear Isotropic Dielectrics will be convened in August 2003, by Graeme Dewar and Martin W. McCall. I shall be delighted if a companion volume were published after another two or three editions of this conference. So would Werner, I am sure.

Akhlesh Lakhtakia
The Pennsylvania State University
University Park, PA, USA
2003