Progress in optics is intimately connected to the development of novel optical materials. This includes advances in synthesizing such materials as well as improvements in their theoretical understanding. Photonic Crystals represent a particularly lucid illustration of this principle: The advent of advanced microstructuring techniques has allowed the realization of two- and three-dimensional periodic arrays on sub-micron scales that provide Bragg-scattering for electromagnetic waves with frequencies in the near IR and the visible. Photonic band structure computations accurately predict crystal structures that posses complete photonic bandgaps and the minimal refractive index contrast that is needed to open them. The controlled fabrication, characterization and optimal design of cavities and waveguiding structures in photonic band gap materials represents another fascinating challenge for material scientists, spectroscopists and theorists alike. Finally, the incorporation of nonlinear and optically active materials into Photonic Crystal structures along with a detailed understanding of the optical properties of the resulting composite systems, may enhance the technological utility of Photonic Crystals over and above the conventional linear structures.

This synergetic interplay between experiment and theory together with a substantial technological potential has driven recent rapid developments in the field of Photonic Crystals. Therefore, it is time to take stock, and in the present focus issue we attempt to highlight recent advances in photonic band structure computations. This focus area lies at the heart of the entire field as it allows to characterize existing and to design novel structures and devices such as superprisms and spot convertors. In addition, photonic band structure computations provide essential input for other fields such as photonic mode structures and Green’s functions for defect calculations, as well as group velocities and local density of states for nonlinear and quantum optical calculations. Consequently, the contributions to this focus issue cover various aspects of photonic band structure computations.

It is our belief that the present focus issue covers some of the most exciting aspects of recent advances in photonic band structure computations. These range from the description of novel types of computational methods (Hermann et al.) and improvements of existing ones (Johnson et al.), to the applications of these methods to novel problems (Asatryan et al., Modinos et al. and Zhang et al.), and the identification of novel types of applications (Maystre and Toader et al.). We hope that the reader will be able to grasp a flavour of this rapidly developing area and that this focus issue may serve as a reference to the field.

Last but certainly not least, we would like to express our gratitude to the authors for their willingness to contribute to this issue and to Jennifer Martin for patiently putting up with two novice editors.

Martijn de Sterke, University of Sydney, Australia Kurt Busch, University of Karlsruhe, Germany

29 January 2001/Vol. 8, No. 3/OPTICS EXPRESS 166

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