Preface: phys. stat. sol. (b) 244/10
Authors: Busch Kurt , Chigrin Dmitry N. 
Published: September 2007

The past years have witnessed dramatic progress and interest in the micro‐ and nano‐fabrication techniques of complex photonic systems. These structures are characterized by controlled feature sizes of the order of or even below the wavelength of light. As a consequence, multiple scattering and near field effects have a profound influence on the propagation of light and light–matter interaction in these systems. In turn, this leads to novel regimes for basic research as well as to novel applications in many disciplines. For instance, the modified dispersion relation of photonic crystals and photonic crystal fibers lead to novel nonlinear wave propagation effects such as gap solitons and supercontinuum generation with applications in telecommunication, metrology, medical diagnostics, and many other areas. Similar statements fully apply to linear, nonlinear and quantum optical phenomena in photonic metamaterials and plasmonic systems.

Owing to the complex nature of wave interference and light–matter interaction processes, experimental studies of such nano‐photonic systems heavily rely on theoretical guidance both for the design of experiment as well as for the interpretation of the measurements. In almost all cases, a quantitative theoretical description has to be based on advanced computational techniques that solve the corresponding, numerically very demanding linear, nonlinear and coupled partial differential equations.

This has led the Wilhelm and Else Heraeus Foundation to devote its 386th Seminar to “Computational Nano‐Photonics”. This seminar has been held in the beautiful setting of the Physikzentrum Bad Honnef, Germany, and has brought together proponents of various computational methods. From 25–28 February 2007, 15 speakers and some 50 participants have summarized and discussed the relative merits and limitations of different methods, and have identified potential future directions. This has sparked a multitude of highly interesting debates many of which, we believe, will continue and will lead to further projects and achievements in this rapidly developing field.

This special section provides a (inevitably incomplete) cross‐sectional snapshot of what we feel
are some of the most important aspects of the vibrant and highly interdisciplinary field of “Computational Nano‐Photonics”. The contributions range from novel developments on the methodological side all the way to advanced applications of established methods to complex photonic systems and have been written by applied mathematicians, theoretical physicists and electrical engineers. Novel developments in finite element and boundary element methods are, respectively, described in the papers by J. Pomplun et al. and Ch. Hafner. This is followed by the description of the Green’s function integral equation method by T. Søndergaard. E. Popov and N. Bonod report on novel developments of the differential theory
of diffraction as applied to photonic micro‐structures. The development of a time‐domain operator‐exponential method using Krylov‐subspace techniques is presented by K. Busch et al. Further developments of the perfectly matched layer open boundary condition for the case of unconditionally stable time‐domain operator‐exponential techniques are given in the paper of H. de Raedt and K. Michielsen. D. Shyroki and A. Lavrinenko discuss how to improve the efficiency of perfectly matched layers
using coordinate transformations and the general covariance of Maxwell’s equations in the case of the finite‐difference time‐ and frequency‐domain methods. The last but certainly not least three papers of this special section are devoted to the description of light–matter interaction processes in photonic systems on different levels of sophistication. In the paper of S. Zhukovsky and D. Chigrin, a pedagogical account on the finite‐difference time‐domain and coupled‐mode theory models of simple laser micro‐structures is presented. L. C. Andreani and D. Gerace report on the application of the guided‐mode expansion method to the problem of light propagation and emission in photonic crystal slab structures. Finally, W. Hoyer and co‐workers provide a comprehensive semi‐classical analysis of plasmas in confined geometries.

All these contributions to the special section highlight one common theme which summarizes the workshop: A single universal computational method for photonics simply does not exist and a detailed knowledge of different techniques is essential in order to obtain reliable results for any given problem. It is our sincere hope that this special section helps in fostering this point of view and communicates the fascination of today’s computational photonics to a broader audience.