Analytically Approximated Method to Obtain the Standard Solution on the Periodic Crystal Waveguides

The photonic crystal waveguides have attracted much interest for their properties of the photonic band gaps and the photon localizations. The numbers of periodic units become smaller and the index differences become large. Pure numerical method should be always compared with alternative methods or analytical methods. A simple analytical approach is presented to obtain the reliable standard solution. The method is based on the conventional method of separation of variables and the eigen mode expansion method. But， to treat strong multiple retlection， mode conversions， and radiation losses， it uses large numbers of transverse modes and built-in error correction procedure