**1. Introduction**

Periodic structure plays important role with its sensitivity for frequency in microwave communication and optical integrated circuit system [1][2]. Also, in optical fiber communication[3], such periodic structure is used for supporting optical wave to be guided in core of the fiber. In such application, a defect in the structure generally works as a cavity or a waveguide by making use of its high selectivity. However, by lacking periodicity in the structure with a defect, general mathematical approaches have often difficulties, due to inconvenience in description of the problem. In such cases, computational simulation technique for electromagnetic wave propagation and scattering is very important and effective. By the recent development of computers, it is possible to model a large scale periodic structure with defect.

In simulation of electromagnetic phenomena, finite difference time domain (FDTD) method [4] [5] is most widely used. However, in numerical analysis of the wave behavior near boundary, where the dielectric constant is quite different on each side, a special care is required. Supposing in lossless dielectric medium, it is well known that wavelength of the electromagnetic wave changes due to the dielectric constant. Because of this compression of wavelength in high dielectric constant medium, grid size of space becomes rather coarse compared with material with lower dielectric constant. Therefore, accuracy of finite difference approximation deteriorate in most computation with uniform grid size. In numerical analysis of periodic structure such as photonic crystal(PC), the dielectric constant is generally quite high compared with its background medium.

A constrained interpolation profile (CIP) method[6][7] is payed much attention because of its accurate simulation result compared with conventional FDTD method. In this paper, on scattering problem by a dielectric cylinder with high contrast with its background air, performance of CIP method is compared with analytical approximated method using Hertz

potential [8] and conventional FDTD simulation [9]. As a measure of accuracy of CIP and FDTD simulation, an normalized cross correlation function is defined and compared with it, by setting analytical approximated result as a reference. Consequently, results of CIP method showed better correlation than that of FDTD method. As applications of CIP method, analysis of electromagnetic field propagation in Y-shaped branching waveguide and Mach-Zehnder interferometer in two dimensional photonic crystal structure were demonstrated. Both of analysis results showed reasonable behaviour. Especially for asymmetrical Mach-Zehnder interferometer, the measurement result by microwave model and the numerical result of CIP corresponded to each other. Complicated output characteristics of asymmetric Mach-Zhender interferometer was interpreted very well by refering to the electric field profile obtained by CIP method.
