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.