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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 3 — Feb. 2, 2009
  • pp: 1299–1307

Modulation instability in nonlinear coupled resonator optical waveguides and photonic crystal waveguides

Chih-Hsien Huang, Ying-Hsiuan Lai, Szu-Cheng Cheng, and Wen-Feng Hsieh  »View Author Affiliations

Optics Express, Vol. 17, Issue 3, pp. 1299-1307 (2009)

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Modulation instability (MI) in a coupled resonator optical waveguide (CROW) and photonic-crystal waveguide (PCW) with nonlinear Kerr media was studied by using the tight-binding theory. By considering the coupling between the defects, we obtained a discrete nonlinear evolution equation and termed it the extended discrete nonlinear Schrödinger (EDNLS) equation. By solving this equation for CROWs and PCWs, we obtained the MI region and the MI gains, G(p,q), for different wavevectors of the incident plane wave (p) and perturbation (q) analytically. In CROWs, the MI region, in which solitons can be formed, can only occur for pa being located either before or after π/2, where a is the separation of the cavities. The location of the MI region is determined by the number of the separation rods between defects and the sign of the Kerr coefficient. However, in the PCWs, pa in the MI region can exceed the π/2. For those wavevectors close to π/2, the MI profile, G(q), can possess two gain maxima at fixed pa. It is quite different from the results of the nonlinear CROWs and optical fibers. By numerically solving the EDNLS equation using the 4th order Runge-Kutta method to observe exponential growth of small perturbation in the MI region, we found it is consistent with our analytic solutions.

© 2009 Optical Society of America

OCIS Codes
(130.2790) Integrated optics : Guided waves
(190.0190) Nonlinear optics : Nonlinear optics
(230.7370) Optical devices : Waveguides
(230.5298) Optical devices : Photonic crystals

ToC Category:
Nonlinear Optics

Original Manuscript: November 17, 2008
Revised Manuscript: January 12, 2009
Manuscript Accepted: January 12, 2009
Published: January 22, 2009

Chih-Hsien Huang, Ying-Hsiuan Lai, Szu-Cheng Cheng, and Wen-Feng Hsieh, "Modulation instability in nonlinear coupled resonator optical waveguides and photonic crystal waveguides," Opt. Express 17, 1299-1307 (2009)

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