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

Full Article  |  PDF Article
OSA Recommended Articles
Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures

Giuseppe D’Aguanno, Marco Centini, Michael Scalora, Concita Sibilia, Mario Bertolotti, Mark J. Bloemer, and Charles M. Bowden
J. Opt. Soc. Am. B 19(9) 2111-2121 (2002)

Collinear terahertz generation in photonic crystal structures via difference-frequency generation

Nadia Mattiucci, Giuseppe D'Aguanno, Michael Scalora, Mark J. Bloemer, Neset Akozbek, and J. W. Haus
J. Opt. Soc. Am. B 23(1) 168-178 (2006)

Non-reciprocal transmission and Schmitt trigger operation in strongly modulated asymmetric WBGs

Masafumi Fujii, Ayan Maitra, Christopher Poulton, Juerg Leuthold, and Wolfgang Freude
Opt. Express 14(26) 12782-12793 (2006)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (5)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (28)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription