Introduction

Photonic band structures or photonic crystals are periodic dielectric structures that have variations in two or three dimensions but also include the familiar one-dimensional layered dielectric structures. Photonic crystals are developing potential technological solutions to some perplexing problems in optoelectronics, and in microwave or RF detection. The complex nature of the field dynamics in these structures necessitates the development of numerically intensive computations that can provide answers to design problems.

The four papers in this focus issue represent a selection of topics not counted among the traditional applications in the field. Three of them rely upon the use of mode symmetries, and the computational methods employed show a shift away from plane-wave calculations, which have limited use, to the more intensive finite-difference (volume)-finite-time algorithm and the transfer matrix method. This is an indication that the simulation tools are now available for accurate calculations of a complicated geometry.

The channel drop filter designs of Fan, Villeneuve, Joannopoulos and Haus demonstrate a new application by considering waveguides with local defect modes to function as a wavelength division demultiplexer. The symmetry of the defect mode is important in determining whether the channel will be transmitted or reflected in the drop waveguide. Sakoda and Kawamata formulated a general method for calculating the dispersion relations and observing the mode symmetry in photonic crystals with frequency-dependent dielectric functions. Yuan, Haus and Sakoda combine the plane-wave calculations for a three-dimensional simple cubic lattice with group theory to determine the mode symmetry and compare these results with transmission spectra determined by using a transfer matrix method developed by Pendry. Scholz, Hess, and Ruhle develop a finite-volume time domain algorithm and applying it to a nonlinear switching problem.