Analysis and design of almost-periodic vertical-grating-assisted codirectional coupler filters with nonuniform duty ratios
Journal
Applied Optics
Journal Volume
39
Journal Issue
25
Pages
4629-4637
Date Issued
2000
Author(s)
Chern, G.W.
Abstract
A systematic approach to the analysis of almost-periodic vertical-grating-assisted codirectional couplers with nonuniform duty ratios is presented. The Poisson sum formula is used to expand rigorously a nonuniform rectangular grating into a quasi-Fourier series, and local grating parameters such as period, width, and duty ratio can be defined unambiguously in such a procedure. On the basis of this expansion the coupled-local-mode formulation is the most natural extension for the analysis of such a nonuniform grating-assisted codirectional coupler filter. By transformation of the coupled-local-mode equations into the Zakharov-Shabat system the Gel’fand-Levintan-Marchenko inverse-scattering method is then used to synthesize special grating-assisted codirectional coupler filters. The design is illustrated by two typical examples: One is a third-order Butterworth filter, and the other is a linear filter. © 2000 Optical Society of America.
Type
journal article