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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 21 — Oct. 13, 2008
  • pp: 17021–17030

The complex Jacobi iterative method for three-dimensional wide-angle beam propagation

Khai Q. Le, R. Godoy-Rubio, Peter Bienstman, and G. Ronald Hadley  »View Author Affiliations


Optics Express, Vol. 16, Issue 21, pp. 17021-17030 (2008)
http://dx.doi.org/10.1364/OE.16.017021


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Abstract

A new complex Jacobi iterative technique adapted for the solution of three-dimensional (3D) wide-angle (WA) beam propagation is presented. The beam propagation equation for analysis of optical propagation in waveguide structures is based on a novel modified Padé(1,1) approximant operator, which gives evanescent waves the desired damping. The resulting approach allows more accurate approximations to the true Helmholtz equation than the standard Padé approximant operators. Furthermore, a performance comparison of the traditional direct matrix inversion and this new iterative technique for WA-beam propagation method is reported. It is shown that complex Jacobi iteration is faster and better-suited for large problems or structures than direct matrix inversion.

© 2008 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(220.2560) Optical design and fabrication : Propagating methods
(350.5500) Other areas of optics : Propagation

ToC Category:
Physical Optics

History
Original Manuscript: August 1, 2008
Revised Manuscript: September 17, 2008
Manuscript Accepted: October 1, 2008
Published: October 10, 2008

Citation
Khai Q. Le, R. Godoy-Rubio, Peter Bienstman, and G. Ronald Hadley, "The complex Jacobi iterative method for three-dimensional wide-angle beam propagation," Opt. Express 16, 17021-17030 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-17021


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