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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 5 — Mar. 1, 2010
  • pp: 4088–4102

Arbitrary-order interface conditions for slab structures and their applications in waveguide analysis

Yih-Peng Chiou and Cheng-Han Du  »View Author Affiliations

Optics Express, Vol. 18, Issue 5, pp. 4088-4102 (2010)

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We extend the continuity relations of field derivatives across an abrupt interface to arbitrary orders for transverse electric and magnetic waves in slab structures. Higher-order finite-difference formulation is then obtained by combining the systematically-obtained interface conditions with Taylor series expansion. Generalized Douglas scheme is also adopted to further enhance the convergence of truncation errors by two orders. We apply the derived finite-difference formulation, up to nine-points in this paper, to solve the guided modes in simple a slab waveguide and multiple quantum well waveguides. The results shows the truncation error is much higher, up to tenth order, as expected. Using those higher-order schemes, accurate results are obtained with much fewer sampled points, and hence with tremendously less computation time and memory.

© 2010 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(040.4200) Detectors : Multiple quantum well
(130.2790) Integrated optics : Guided waves
(230.7400) Optical devices : Waveguides, slab

ToC Category:
Integrated Optics

Original Manuscript: January 11, 2010
Revised Manuscript: February 11, 2010
Manuscript Accepted: February 11, 2010
Published: February 16, 2010

Yih-Peng Chiou and Cheng-Han Du, "Arbitrary-order interface conditions for slab structures and their applications in waveguide analysis," Opt. Express 18, 4088-4102 (2010)

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