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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

  • Editor: Franco Gori
  • Vol. 27, Iss. 11 — Nov. 1, 2010
  • pp: 2347–2353

A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects

Zhengfu Xu and Gang Bao  »View Author Affiliations


JOSA A, Vol. 27, Issue 11, pp. 2347-2353 (2010)
http://dx.doi.org/10.1364/JOSAA.27.002347


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Abstract

A numerical scheme is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a nonlinear χ ( 2 ) effect and the NLH equation modeling wave propagation in Kerr type gratings with a nonlinear χ ( 3 ) effect in the one-dimensional case. Both of these nonlinear phenomena arise as a result of the combination of high electromagnetic mode density and nonlinear reaction from the medium. When the mode intensity of the incident wave is significantly strong, which makes the nonlinear effect non-negligible, numerical methods based on the linearization of the essentially nonlinear problem will become inadequate. In this work, a robust, stable numerical scheme is designed to simulate the NLH equations with strong nonlinearity.

© 2010 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(190.0190) Nonlinear optics : Nonlinear optics
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.3270) Nonlinear optics : Kerr effect

ToC Category:
Nonlinear Optics

History
Original Manuscript: June 30, 2010
Revised Manuscript: August 30, 2010
Manuscript Accepted: September 2, 2010
Published: October 4, 2010

Citation
Zhengfu Xu and Gang Bao, "A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects," J. Opt. Soc. Am. A 27, 2347-2353 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-11-2347


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