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Applied Optics

Applied Optics


  • Vol. 39, Iss. 25 — Sep. 1, 2000
  • pp: 4629–4637

Analysis and design of almost-periodic vertical-grating-assisted codirectional coupler filters with nonuniform duty ratios

Gia-Wei Chern and Lon. A. Wang  »View Author Affiliations

Applied Optics, Vol. 39, Issue 25, pp. 4629-4637 (2000)

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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

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(130.2790) Integrated optics : Guided waves
(230.7400) Optical devices : Waveguides, slab

Original Manuscript: January 24, 2000
Revised Manuscript: May 17, 2000
Published: September 1, 2000

Gia-Wei Chern and Lon. A. Wang, "Analysis and design of almost-periodic vertical-grating-assisted codirectional coupler filters with nonuniform duty ratios," Appl. Opt. 39, 4629-4637 (2000)

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