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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 10 — May. 20, 2013
  • pp: 11952–11964

Efficient numerical method for analyzing optical bistability in photonic crystal microcavities

Lijun Yuan and Ya Yan Lu  »View Author Affiliations


Optics Express, Vol. 21, Issue 10, pp. 11952-11964 (2013)
http://dx.doi.org/10.1364/OE.21.011952


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Abstract

Nonlinear optical effects can be enhanced by photonic crystal microcavities and be used to develop practical ultra-compact optical devices with low power requirements. The finite-difference time-domain method is the standard numerical method for simulating nonlinear optical devices, but it has limitations in terms of accuracy and efficiency. In this paper, a rigorous and efficient frequency-domain numerical method is developed for analyzing nonlinear optical devices where the nonlinear effect is concentrated in the microcavities. The method replaces the linear problem outside the microcavities by a rigorous and numerically computed boundary condition, then solves the nonlinear problem iteratively in a small region around the microcavities. Convergence of the iterative method is much easier to achieve since the size of the problem is significantly reduced. The method is presented for a specific two-dimensional photonic crystal waveguide-cavity system with a Kerr nonlinearity, using numerical methods that can take advantage of the geometric features of the structure. The method is able to calculate multiple solutions exhibiting the optical bistability phenomenon in the strongly nonlinear regime.

© 2013 OSA

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(190.1450) Nonlinear optics : Bistability
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: February 15, 2013
Revised Manuscript: April 12, 2013
Manuscript Accepted: April 24, 2013
Published: May 8, 2013

Citation
Lijun Yuan and Ya Yan Lu, "Efficient numerical method for analyzing optical bistability in photonic crystal microcavities," Opt. Express 21, 11952-11964 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-11952


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