Numerical Analysis of Lamellar Grating Type Three-Dimensional Optical Waveguides with Periodic Structure, Using Fourier Series Expansion Method

摘要

Three-dimensional optical waveguides with periodic structure promise to play an important role in optical IC, and more accurate analysis of such waveguides is required. In this paper, an improved, more accurate Fourier series expansion method for an arbitrary number of grating periods making use of Floquet's theorem is applied to the numerical analysis of lamellar grating-type periodic optical waveguides with rectangular cross section (glass substrate). In the numerical results, the characteristics of the reflected and transmitted powers of the guided and radiation fields versus wavelength are investigated when the depth of the grating grooves and the number of grating periods are varied. The effects of the groove depth and the number of periods on the powers of each mode are elucidated and the appropriate parameters for dominant guided mode propagation in the periodic waveguide are identified.