Editor: Matthias Ehrhardt

Series Title: Progress in Computational Physics (PiCP)

Wave Propagation in Periodic Media

Volume 1

eBook: US $44 Special Offer (PDF + Printed Copy): US $141
Printed Copy: US $119
Library License: US $176
ISSN: 1879-4661 (Print)
ISBN: 978-1-60805-383-4 (Print)
ISBN: 978-1-60805-150-2 (Online)
Year of Publication: 2010
DOI: 10.2174/97816080515021100101


Progress in Computational Physics is a new e-book series devoted to recent research trends in computational physics. It contains chapters contributed by outstanding experts of modeling of physical problems. The series focuses on interdisciplinary computational perspectives of current physical challenges, new numerical techniques for the solution of mathematical wave equations and describes certain real-world applications.

With the help of powerful computers and sophisticated methods of numerical mathematics it is possible to simulate many ultramodern devices, e.g. photonic crystals structures, semiconductor nanostructures or fuel cell stacks devices, thus preventing expensive and longstanding design and optimization in the laboratories.

In this book series, research manuscripts are shortened as single chapters and focus on one hot topic per volume.

Engineers, physicists, meteorologists, etc. and applied mathematicians can benefit from the series content. Readers will get a deep and active insight into state-of-the art modeling and simulation techniques of ultra-modern devices and problems.

Periodic structure problems arise quite often in many modern application areas like semiconductor nanostructures (e.g. quantum dots and nanocrystals), semiconductor superlattices, photonic crystals structures, meta materials or Bragg gratings of surface plasmon polariton waveguides.

This first volume treats both mathematical analysis of periodic structure problems and state-of-the art numerical techniques, such as frequency domain methods, beam propagation methods and eigenmode expansion methods. Several chapters are devoted to concrete applications of periodic media simulation. The book is a useful resource for individuals interested in complex wave mechanics of unique physical structures.

Indexed in: EBSCO, Ulrich's Periodicals Directory.


Wave propagation in periodic media has attracted much attention from the scientists for a very long time. Forward or backward propagation regimes, refraction and diffraction properties, all these subjects are theoretically formalized and experimentally investigated since many centuries… Nevertheless, a renewed interest for this domain exists for a few decades with the emergence of the field of metamaterials and/or photonic crystals. The origin of this renewal can be found in the theoretical works of V. Veselago in the late 1960’s, followed by the proposals of E. Yablonovitch for photonic crystals in the 1980’s and of J. Pendry for meta-materials in the 1990’s. The promise is the opportunity to design original devices built with artificial materials, metallic or dielectric, with extraordinary propagation properties (that is to say not found in nature). The most popular new effect is undoubtedly the “negative refraction” that can be obtained either by using specific propagation regimes in periodic structures or by creating double negative media in terms of permittivity and permeability. Such a concept has allowed generalizing the famous Snell-Descartes law for refraction at the interface of two propagating media to any arbitrary values of the refractive index, positive or negative, greater or lower than unity… Moreover, as it can be shown that most of the concepts do not depend on wavelength scale, they can be potentially applied from microwave to optical waves. The main limiting factor is the patterning scale of the supporting artificial materials which is proportional to the targeted wavelength of operation. Fortunately, owing to the progress in fabrication technology down to the nanometer scale, it is now possible to bring to reality most of the theoretical predictions.

At present, this research field is very attractive as shown by the huge literature devoted to meta-materials or photonic crystals. Perfect lenses, hyperlenses, cloaking or invisibility devices are widely investigated, exploiting the fact that intrinsic materials parameters as refraction index, impedance, permittivity and permeability can be locally modulated to any positive, near zero or negative values. Open theoretical problems also re-appear following some “advanced” proposals and “lively” debates occasionally occur within the scientific community. As the field gains in maturity, devices become more complex and new modeling approaches are now required to interpret and understand properly the underlying effects. That is why the field becomes more and more multidisciplinary with mathematicians, numericians and physicists for theory and concepts, applied physicists for fabrication and measurements in connection with chemists, telecommunication engineers or biologists for original applications.

The book edited by Prof. Matthias Ehrhardt provides some particularly interesting keys to enter in this vast and exciting research domain. By focusing on specific advanced subjects related to wave propagation in periodic media from the different viewpoints of analysis, numerical techniques and practical applications with chapters written by experts in their respective fields, the reader will find an overview of state-of-the-art research results over a wide range of approaches from theory and concepts to real devices. As such, the volume will be very useful to Ph.D. students and lecturers of computational physics and numerical mathematics, and also to applied by physicists searching for accurate theoretical models to support their tremendous imagination.

Olivier Vanbésien, Professor
IEMN, University of Lille
Villeneuve d'Ascq