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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 21 — Oct. 16, 2006
  • pp: 9864–9872

Optimization-based calculation of optical nonlinear processes in a micro-resonator

Guy Klemens and Yeshaiahu Fainman  »View Author Affiliations

Optics Express, Vol. 14, Issue 21, pp. 9864-9872 (2006)

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We present a new method of calculating the performance of nonlinear processes in a resonator. An optimization-based approach, conceptually similar to techniques used in nonlinear circuit analysis, is formulated and used to find the wave magnitudes that satisfy all of the boundary conditions and account for nonlinear optical effects. Unlike previous solution methods, this technique is applicable to any nonlinear process (second-order, third-order, etc.) and multiple coupled resonators, maintains the phase relations between the waves, and is exact. Examples are given for second-order nonlinear processes in a one-dimensional resonator.

© 2006 Optical Society of America

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4360) Nonlinear optics : Nonlinear optics, devices
(230.3990) Optical devices : Micro-optical devices

ToC Category:
Nonlinear Optics

Original Manuscript: August 14, 2006
Revised Manuscript: September 25, 2006
Manuscript Accepted: September 25, 2006
Published: October 16, 2006

Guy Klemens and Yeshaiahu Fainman, "Optimization-based calculation of optical nonlinear processes in a micro-resonator," Opt. Express 14, 9864-9872 (2006)

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962). [CrossRef]
  2. A. Ashkin, G. D. Boyd, and J. M. Dziedzic, "Resonant optical second harmonic generation and mixing," IEEE J. Quantum Electron. QE-2, 109-124 (1966). [CrossRef]
  3. V. Berger, "Second-harmonic generation in monolithic cavities," J. Opt. Soc. Am. B 14, 1351-1360 (1997). [CrossRef]
  4. C. Simonneau,  et al, "Second-harmonic generation in a doubly resonant semiconductor microcavity," Opt. Lett. 22, 1775-1777 (1997). [CrossRef]
  5. G. Klemens, C.-H. Chen, and Y. Fainman, "Design of optimized dispersive resonant cavities for nonlinear wave mixing," Opt. Express 13, 9388-9397 (2005). [CrossRef] [PubMed]
  6. D. S. Bethune, "Optical harmonic generation and mixing in multilayer media: analysis using optical transfer matrix techniques," J. Opt. Soc. Am. B 6, 910-916 (1989). [CrossRef]
  7. A. Calderone and J. Vigneron, "Computation of the electromagnetic harmonics generation by stratified systems containing nonlinear layers," Int. J. Quantum Chem. 70, 763-770 (1988). [CrossRef]
  8. M. G. Martemyanov, T. V. Dolgova and A. A. Fedyanin,"Optical third-harmonic generation in one-dimensional photonic crystals and microcavities," J. Exp. Theor. Phys. 98, 463-477 (2003). [CrossRef]
  9. S. El-Rabaie, V. F. Fusco, and C. Stewart,"Harmonic balance evaluation of nonlinear microwave circuits-a tutorial approach," IEEE Trans. on Education 31, 181-192 (1988). [CrossRef]
  10. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane and R. Ito, "Absolute scale of second-order nonlinear-optical coeffients," J. Opt. Soc. Am. B 14, 2268-2294 (1997). [CrossRef]
  11. W. J. Tropf, M. E. Thomas, and T. J. Harris, "Properties of crystals and glasses," in Handbook of Optics: Volume II, (McGraw-Hill 1995).
  12. K. E. Atkinson, An Introduction to Numerical Analysis, (John Wiley 1989), Chap. 8.
  13. C. H. Chen, K. Tetz,W. Nakagawa, and Y. Fainman, "Wide-field-of-view GaAs/AlxOy one-dimensional photonic crystal filter," Appl. Opt. 44, 1503-1511 (2005). [CrossRef] [PubMed]
  14. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992). [CrossRef]

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