Calculation of optical-waveguide grating characteristics using Green's functions and Dyson's equation

Lars Henning Rindorf, Asger Mortensen

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Abstract

We present a method for calculating the transmission spectra, dispersion, and time delay characteristics of optical-waveguide gratings based on Green's functions and Dyson's equation. Starting from the wave equation for transverse electric modes we show that the method can solve exactly both the problems of coupling of counterpropagating waves (Bragg gratings) and co-propagating waves (long-period gratings). In both cases the method applies for gratings with arbitrary dielectric modulation, including all kinds of chirp and apodization and possibly also imperfections in the dielectric modulation profile of the grating. Numerically, the method scales as O(N) where N is the number of points used to discretize the grating along the propagation axis. We consider optical fiber gratings although the method applies to all one-dimensional (1D) optical waveguide gratings including high-index contrast gratings and 1D photonic crystals.
Original languageEnglish
JournalPhysical Review E
Volume74
Issue number3
Pages (from-to)036616
ISSN2470-0045
DOIs
Publication statusPublished - 2006

Bibliographical note

Copyright 2006 American Physical Society

Keywords

  • DESIGN
  • GENERALIZED FIELD PROPAGATOR
  • INVERSE SCATTERING
  • FILTERS
  • FIBER BRAGG GRATINGS
  • MARCHENKO COUPLED EQUATIONS
  • ITERATIVE SOLUTION

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