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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 19, Iss. 6 — Jun. 1, 2002
  • pp: 1120–1128

Efficient analysis of periodic dielectric waveguides using Dirichlet-to-Neumann maps

Johannes Tausch and Jerome Butler  »View Author Affiliations


JOSA A, Vol. 19, Issue 6, pp. 1120-1128 (2002)
http://dx.doi.org/10.1364/JOSAA.19.001120


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Abstract

We present a numerical scheme for the analysis of periodic dielectric waveguides using Floquet–Bloch theory. The problem of finding the fundamental propagation modes is reduced to a nonlinear eigenvalue problem involving Dirichlet-to-Neumann maps. This approach leads to much smaller matrix problems than the ones that have appeared previously. By an increase of the discretization fineness, any desired precision of the method can be achieved. We discuss an eigensolver and extend the conventional rule to choose the branches of the transverse wave numbers. This ensures analytic dependence on the Floquet multiplier and convergence of the nonlinear solver. We demonstrate that even for a complicated multilayer waveguide structure the propagation factors can be calculated within seconds to several digits of accuracy.

© 2002 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(050.2770) Diffraction and gratings : Gratings
(130.2790) Integrated optics : Guided waves

History
Original Manuscript: February 5, 2001
Revised Manuscript: November 13, 2001
Manuscript Accepted: November 13, 2001
Published: June 1, 2002

Citation
Johannes Tausch and Jerome Butler, "Efficient analysis of periodic dielectric waveguides using Dirichlet-to-Neumann maps," J. Opt. Soc. Am. A 19, 1120-1128 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-6-1120


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