Abstract

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

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References

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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. 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]
  4. V. Berger, �??Second-harmonic generation in monolithic cavities,�?? J. Opt. Soc. Am. B 14, 1351�??1360 (1997).
    [CrossRef]
  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]
  10. E. G. Sauter, Nonlinear Optics, pp. 55, John Wiley (1996).
  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]
  12. M. Born and E. Wolf, Principles of Optics, Seventh Edition, pp. 360, Cambridge (1999).
  13. A. Yariv, Quantum Electronics, Third Edition, pp. 147, John Wiley (1989).
  14. W. J. Tropf, M. E. Thomas, and T. J. Harris, �??Properties of crystals and glasses,�?? in Handbook of Optics: Volume II, McGraw-Hill (1995).
  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. (1)

Handbook of Optics: Volume II (1)

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. (3)

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 (3)

Opt. Lett. (3)

Phys. Rev. (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]

Phys. Rev. B (1)

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 (3)

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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Figures (6)

Fig. 1.
Fig. 1.

Diagram of a multiply-resonant cavity used for nonlinear wavelength conversion.

Fig. 2.
Fig. 2.

The calculated conversion efficiency as a function of cavity length for a dispersive resonant cavity. Input wavelengths of 1.55 and 2.617 micrometers (μm) and an output wavelength of 3.80 μm were assumed, with GaAs as the nonlinear material. The corresponding coherence length is 25 μm. The cavity finesse is held constant at 30, 50 and 70, and the input field intensities are 0.5 W /μm 2.

Fig. 3.
Fig. 3.

The calculated conversion efficiency as a function of input power. Input wavelengths of 1.55 and 2.617 micrometers (μm) and an output wavelength of 3.80 μm were assumed, with GaAs as the nonlinear material. Ideal phase compensating mirrors were assumed, and the cavity length was held constant at 12 μm. Shown are curves for cases where (i) the pump, (ii) the signal, (iii) the pump and idler, and (iv) the pump, idler, and the signal are resonant. For the resonant beams, the finesse was set to 50, and was set to 0 for the non-resonant beams.

Fig. 4.
Fig. 4.

The calculated conversion efficiency as a function of cavity finesse. Input wavelengths of 1.55 and 2.617 micrometers (μm) and an output wavelength of 3.80 μm were assumed, with GaAs as the nonlinear material. The cavity length is 12 μm and the input field intensities are 0.5 W /μm 2. (a) Idler finesse held constant at 50 while signal and pump finesse vary, (b) pump finesse held constant at 50 while signal and idler finesse vary, (c) pump and idler finesse are set to be equal and vary together vs signal finesse.

Fig. 5.
Fig. 5.

Transmission coefficient (solid line) through the entire structure and reflection coefficient (dashed line) seen from the inside of the cavity looking out through the dielectric stack. At the three wavelengths of the nonlinear conversion, the transmission is at a peak, indicating Fabry-Perot resonance. The mirror reflectivities are at a maximum at those wavelengths to increase cavity finesse.

Fig. 6.
Fig. 6.

Layer thicknesses of alternating GaAs and AlAs for the dielectric mirrors with the response of Figure 5. Layer 1 is GaAs. The refractive indices used are 3.399, 3.343, and 3.326 for GaAs at 1.55, 2.617 and 3.8 μm, respectively, and 2.909, 2.886 and 2.880 for AlAs.

Equations (11)

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d A q ( z ) dz = i ω q χ eff c 0 n q p q P A p ( z ) exp ( i Δ k z ) exp ( i Δ ωt ) ,
Δ k = r R k r s S k s ,
Δ ω = r R ω r s S ω s ,
2 Δ kL + p P ( φ p ( left ) + φ p ( right ) ) = 2 π a ( 1 ) ,
r ( ω ) = r ( ω ) exp ( ( ω ) ) .
2 k p L = φ p left φ p right = 2 π a ( 2 ) ,
A Internal = 1 R 1 R A Incident ,
𝓕 = π R 1 R .
t c = nL π c 0 𝓕 ,
P out = C 𝓕 sin 2 ( π L c L ) ,
P NL = χ ( 2 ) E p E i * ,

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