Χ(2) and Χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities

Optics Express

Volumn 15, Issue 12, 2007, Pages 7303-7318

  Rodriguez, Alejandro ^a   Soljačić, Marin ^a   Joannopoulos, J D ^a   Johnson, Steven G ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL NONLINEARITIES; ELECTRIC POWER UTILIZATION; FINITE DIFFERENCE TIME DOMAIN METHOD; HARMONIC GENERATION; MAXWELL EQUATIONS; PARAMETER ESTIMATION;

LINEAR CAVITY EIGENMODES; NONLINEAR COUPLING COEFFICIENTS;

CAVITY RESONATORS;

EID: 34250356027     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.15.007303     Document Type: Article

References (63)

1. P. D. Druinmond, K. J. McNeil, and D. F. Walls, "Non-equilibrium transitions in sub/second harmonic generation I: Semiclassical theory," Optica Acta. 27(3), 321-335 (1980).
2. L.-A. Wu, M. Xiao, and H. J. Kimble, "Squeezed states of light from an optical parametric oscillator," JOSA-B 4, 1465-1476 (1987).
3. Z. Y. Ou and H. J. Kimble, "Enhanced conversion efficiency for harmonic generation with double resonance," Opt. Lett. 18, 1053-1055 (1993).
4. R. Paschotta, K. Fiedler, P. Kurz, and J. Mlynek, "Nonlinear mode coupling in doubly resonant frequency doublers," Appl. Phys. Lett. 58, 117 (1994).
5. V. Berger, "Second-harmonic generation in monolithic cavities," J. Opt. Soc. Am. B 14, 1351 (1997).
6. I. I. Zootoverkh, K. N. V., and E. G. Lariontsev, "Enhancement of the efficiency of second-harmonic generation in microlaser," Quantum Electron. 30, 565 (2000).
7. B. Maes, P. Bienstman, and R. Baets, "Modeling second-harmonic generation by use of mode expansion," J. Opt. Soc. Am. B 22, 1378 (2005).
8. M. Liscidini and L. A. Andreani, "Second-harmonic generation in doubly resonant microcavities with periodic dielectric mirrors," Phys. Rev. E 73, 016, 613 (2006).
9. Y. Dumeige and P. Feron, "Wispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation," PRA 74, 063, 804 (2006).
10. G. T. Moore, K. Koch, and E. C. Cheung, "Optical parametric oscillation with intracavity second-harmonic generation," Opt. Commun. 113, 463 (1995).
11. M. Liscidini and L. A. Andreani, "Highly efficient second-harmonic generation in doubly resonant planar microcavities," Appl. Phys. Lett. 85, 1883 (2004).
12. L. Fan, H. Ta-Chen, M. Fallahi, J. T. Murray, R. Bedford, Y. Kaneda, J. Hader, A. R. XZakharian, J. Moloney, S. W. Koch, and W. Stolz, "Tunable watt-level blue-green vertical-external-cavity surface-emitting lasers by intracavity frequency doubling," Appl. Phys. Lett. 88, 2251, 117 (2006).
13. P. Scotto, P. Colet, and M. San Miguel, "All-optical image processing with cavity type II second-harmonic generation," Opt. Lett. 28, 1695 (2003).
14. G. McConnell, A. I. Ferguson, and N. Langford, "Cavity-augmented frequency tripling of a continuous wave mode-locked laser," J. Phys. D: Appl.Phys 34, 2408 (2001).
15. G. S. Dutta and J. Jolly, "Third harmonic generation in layered media in presence of optical bistability of the fundamental," Pramana J. Phys. 50, 239 (1988).
16. (2) interactions in finite multi-layered structures," J. Opt. Soc. Am. B 19, 2111-2122 (2002).
17. A. R. Cowan and J. F. Young, "Mode matching for second-harmonic generation in photonic crystal waveguides," Phys. Rev. E 65, 085, 106 (2002).
18. A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizzeti, L. C. Andreani, F. Romanato, L. Businaro, E. D. Fabrizio, A. Passaseo, and M. D. Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161, 306 (2003).
19. S. Pearl, H. Lotem, and Y. Shimony, "Optimization of laser intracavity second-harmonic generation by a linear dispersion element," J. Opt. Soc. Am. B 16, 1705 (1999).
20. A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, and A. P. Shkurinov, "Enhancement of sum frequency generation near the photonic band edge under the quasiphase matching condition," Phys. Rev. E 63, 046,609 (2001).
21. (2) interactions," Phys. Rev. E 64, 016, 609 (2001).
22. A. H. Norton and C. M. de Sterke, "Optimal poling of nonlinear photonic crystals for frequency conversion," Opt. Lett. 28, 188 (2002).
23. J. A. Armstrong, N. Ioembergen, J. Duelling, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
24. A. Ashkin, G. D. Boyd, and J. M. Dziedzic, "Resonant optical second harmonic generation and mixing," IEEE J. Quantum Electron. 2, 109-124 (1966).
25. R. G. Smith, "Theory of intracavity optical second-harmonic generation," IEEE J. Quantum Electron. 6, 215-223 (1970).
26. A. I. Gerguson and M. H. Dunn, "Intracavity second harmonic generation in continuous-wave dye lasers," IEEE J. Quantum Electron. 13, 751-756 (1977).
27. M. Brieger, H. Busener, A. Hese, F. V. Moers, and A. Renn, "Enhancement of single frequency SHG in a passive ring resonator," Opt. Commun. 38, 423-426 (1981).
28. J. C. Berquist, H. Hemmati, and W. M. Itano, "High power second harmonic generation of 257 nm radiation in an external ring cavity," Opt. Commun. 43, 437-442 (1982).
29. W. J. Kozlovsky, W. P. Risk, W. Lenth, B. G. Kim, G. L. Bona, H. Jaeckel, and D. J. Webb, "Blue light generation by resonator-enhanced frequency doubling of an extended-cavity diode laser," Appl. Phys. Lett. 65, 525-527 (1994).
30. G. J. Dixon, C. E. Tanner, and C. E. Wieman, "432-nm source based on efficient second-harmonic generation of GaAlAs diode-laser radiation in a self-locking external resonant cavity," Opt. Lett. 14, 731-733 (1989).
31. M. J. Collet and R. B. Levien, "Two-photon loss model of intracavity second-harmonic generation," PRA 43(9), 5068-5073 (1990).
32. M. A. Persaud, J. M. Tolchard, and A. I. Ferguson, "Efficient generation of picosecond pulses at 243 nm," IEEE J. Quantum Electron. 26, 1253-1258 (1990).
33. K. Schneider, S. Schiller, and J. Mlynek, "1.1-W single-frequency 532-nm radiation by second-harmonic generation of a miniature Nd:YAG ring laser," Opt. Lett. 21, 1999-2001 (1996).
34. X. Mu, Y. J. Ding, H. Yang, and G. J. Salamo, "Cavity-enhanced and quasiphase-matched mutli-order reflection-second-harmonic generation from GaAs/AlAs and GaAs/AlGaAs multilayers," Appl. Phys. Lett. 79, 569 (2001).
35. J. Hald, "Second harmonic generation in an external ring cavity with a Brewster-cut nonlinear cystal: theoretical considerations," Opt. Commun. 197, 169 (2001).
36. T. V. Dolgova, A. I. Maidykovski, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, V. A. Yakovlev, G. Mattei, N. Ohta, and S. Nakabayashi, "Giant optical second-harmonic generation in single and coupled microcavities formed from one-dimensional photonic crystals," J. Opt. Soc. Am. B 19, 2129 (2002).
37. T.-M. Liu, C.-T. Yu, and C.-K. Sun, "2 Ghz repetition-rate femtosecond blue sources by second-harmonic generation in a resonantly enhanced cavity," Appl. Phys. Lett. 86, 061, 112 (2005).
38. y tightly confining waveguides and resonant cavities," OL 31(24), 3626-3630 (2006).
39. A. Di Falco, C. Conti, and G. Assanto, "Impedance matching in photonic crystal microcavities for second-harmonic generation," Opt. Lett. 31, 250 (2006).
40. H. Schnitzler, U. Fröhlich, T. K. W. Boley, A. E. M. Clemen, J. Mlynek, A. Peters, and S. Schiller, "All-solid-state tunable continuous-wave ultraviolet source with high spectral purity and frequency stability," Appl. Opt. 41, 7000-7005 (2002).
41. F.-F. Ren, R. Li, C. Cheng, and H.-T. Wang, "Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes," PRB 70, 245, 109 (2004).
42. K. Koch and G. T. Moore, "Singly resonant cavity-enhanced frequency tripling," J. Opt. Soc. Am. B 16, 448 (1999).
43. P. P. Markowicz, H. Tiryaki, H. Pudavar, P. N. Prasad, N. N. Lepeshkin, and R. W. Boyd, "Dramatic enhancement of third-harmonic generation in three-dimensional photonic crystals," Phys. Rev. Lett. 92(083903) (2004).
44. G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, and G. Assanto, "Large nonlinear phase shifts in second-order nonlinear-optical processes," Opt. Lett. pp. 13-15 (1993).
45. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).
46. R. W. Boyd, Nonlinear Optics (Academic Press, California, 1992).
47. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1998).
48. 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).
49. N. Hashizume, M. Ohashi, T. Kondo, and R. Ito, "Optical harmonic generation in multilayered structures: a comprehensive analysis," J. Opt. Soc. Am. B 12, 1894-1904 (1995).
50. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984). Ch. 7.
51. W. Suh, Z. Wang, and S. Fan, "Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities," IEEE J. Quantum Electron. 40(10), 1511-1518 (2004).
52. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).
53. L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Butterworth-Heinemann, Oxford, 1977).
54. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984).
55. M. Soljačić M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E Rapid Commun. 66, 055,601(R) (2002).
56. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, Norwood, MA, 2000).
57. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. Burr, J. D. Joannopoulos, and S. G. Johnson, "Improving accuracy by subpixel smoothing in the finite-difference time domain," Opt. Lett. 31, 2972-2974 (2006).
58. D. D. Smith, G. Fischer, R. W. Boyd, and D. A. Gregory, "Cancellation of photoinduced absorption in metal nanoparticle composites through a counterintuitive consequence of local field effects," J. Opt. Soc. Am. B 14, 1625 (1997).
59. M. F. Yanik, S. Fan, M. Soljačic, , J. D. Joannopoulos, and Yanik, "All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry," Opt. Lett. 68, 2506 (2004).
60. S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, "Waveguide branches in photonic crystals," J. Opt. Soc. Am. B 18(2), 162-165 (2001).
61. A. Villeneuve, C. C. Yang, G. I. Stegeman, C. Lin, and H. Lin, "Nonlinear refractive-index and two-photon absorption near half the band gap in AlGaAs," Appl. Phys. Lett. 62, 2465-2467 (1993).
62. Q. Xu and M. Lipson, "Carrier-induced optical bistability in Silicon ring resonators," Opt. Lett. 31(3), 341-343 (2005).
63. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13(7), 2678-2687 (2005).