Calculating the modes of a photonic-crystal lightguide by a difference method

This paper discusses a fast and efficient method of detecting the modes of a lightguide that is inhomogeneous in cross section, based on the use of finite-difference approximations to the wave equations, separately for the electric and magnetic components of the field. The matrix of the eigenvalue difference problem is fully displayed for the electric component of the electromagnetic field. The features of the implementation of the method in the MATLAB medium are discussed. The method is used to calculate the fundamental mode and several higher-order modes of a photonic-crystal lightguide. A graph of the dispersion parameter, which characterizes the temporal broadening of the pulse in the lightguide, is obtained for the selected model. (C) 2007 Optical Society of America.