Dispersive mirrors can be designed to create cavities that resonate at set multiple frequencies while simultaneously meeting the conditions for efficient nonlinear wave mixing. We analyze the conditions that such a cavity design must meet and the free parameters that can be used for optimization. Using numerical methods, we show the benefit in conversion efficiency attained with multiple resonances, and draw conclusions concerning the design parameters. As a specific example, we consider parametric downconversion in a triply-resonant cavity.

© 2005 Optical Society of America

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]
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5. C. Simonneau, et al, �??Second-harmonic generation in a doubly resonant semiconductor microcavity,�?? Opt. Lett. 22, 1775�??1777 (1997). [CrossRef]
6. F. F. Ren, et al, �??Giant enhancement of second harmonic generation in a finite photonic ctrystal with a single defect and dual-localized modes,�?? Phys. Rev. B 70, 245109 (2004). [CrossRef]
7. R. Haidar, N. Forget, and E. Rosencher, �??Optical parametric oscillation in microcavites based on isotropic semiconductors: a theoretical strudy,�?? IEEE J. Quantum Electron. 39, 569�??576 (2003). [CrossRef]
8. 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]
9. W. Nakagawa, P. C. Sun, C. H. Chen, and Y. Fainman, �??Wide-field-of view narrow-band spectral filters based on photonic crystal nanocavities,�?? Opt. Lett. 27, 191�??193 (2002). [CrossRef]
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11. 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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15. 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]
16. K. L. Vodopyanov, et al., �??Optical parametric oscillation in quasi-phase-matched GaAs,�?? Opt. Lett. , 29 1912�??1914 (2004). [CrossRef] [PubMed]

Appl. Opt.

• 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]

Handbook of Optics: Volume II

• W. J. Tropf, M. E. Thomas, and T. J. Harris, �??Properties of crystals and glasses,�?? in Handbook of Optics: Volume II, McGraw-Hill (1995).

IEEE J. Quantum Electron.

• 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]
• R. Haidar, N. Forget, and E. Rosencher, �??Optical parametric oscillation in microcavites based on isotropic semiconductors: a theoretical strudy,�?? IEEE J. Quantum Electron. 39, 569�??576 (2003). [CrossRef]
• 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]

J. Opt. Soc. Am. B

• 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]
• V. Berger, �??Second-harmonic generation in monolithic cavities,�?? J. Opt. Soc. Am. B 14, 1351�??1360 (1997). [CrossRef]
• 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]

Opt. Lett.

• K. L. Vodopyanov, et al., �??Optical parametric oscillation in quasi-phase-matched GaAs,�?? Opt. Lett. , 29 1912�??1914 (2004). [CrossRef] [PubMed]
• C. Simonneau, et al, �??Second-harmonic generation in a doubly resonant semiconductor microcavity,�?? Opt. Lett. 22, 1775�??1777 (1997). [CrossRef]
• W. Nakagawa, P. C. Sun, C. H. Chen, and Y. Fainman, �??Wide-field-of view narrow-band spectral filters based on photonic crystal nanocavities,�?? Opt. Lett. 27, 191�??193 (2002). [CrossRef]

Phys. Rev.

• 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]

Phys. Rev. B

• F. F. Ren, et al, �??Giant enhancement of second harmonic generation in a finite photonic ctrystal with a single defect and dual-localized modes,�?? Phys. Rev. B 70, 245109 (2004). [CrossRef]

Other

• E. G. Sauter, Nonlinear Optics, pp. 55, John Wiley (1996).
• M. Born and E. Wolf, Principles of Optics, Seventh Edition, pp. 360, Cambridge (1999).
• A. Yariv, Quantum Electronics, Third Edition, pp. 147, John Wiley (1989).

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