OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 24 — Nov. 26, 2007
  • pp: 16161–16176

Enhanced nonlinear optics in photonic-crystal microcavities

Jorge Bravo-Abad, Alejandro Rodriguez, Peter Bermel, Steven G. Johnson, John D. Joannopoulos, and Marin Soljačić  »View Author Affiliations


Optics Express, Vol. 15, Issue 24, pp. 16161-16176 (2007)
http://dx.doi.org/10.1364/OE.15.016161


View Full Text Article

Enhanced HTML    Acrobat PDF (572 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Nonlinear photonic-crystal microresonators offer unique fundamental ways of enhancing a variety of nonlinear optical processes. This enhancement improves the performance of nonlinear optical devices to such an extent that their corresponding operation powers and switching times are suitable for their implementation in realistic ultrafast integrated optical devices. Here, we review three different nonlinear optical phenomena that can be strongly enhanced in photonic crystal microcavities. First, we discuss a system in which this enhancement has been successfully demonstrated both theoretically and experimentally, namely, a photonic crystal cavity showing optical bistability properties. In this part, we also present the physical basis for this dramatic improvement with respect to the case of traditional nonlinear devices based on nonlinear Fabry-Perot etalons. Secondly, we show how nonlinear photonic crystal cavities can be also used to obtain complete second-harmonic frequency conversion at very low input powers. Finally, we demonstrate that the nonlinear susceptibility of materials can be strongly modified via the so-called Purcell effect, present in the resonant cavities under study.

© 2007 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.4360) Nonlinear optics : Nonlinear optics, devices

ToC Category:
Nonlinear Optics for Functional Devices and Applications

History
Original Manuscript: September 4, 2007
Revised Manuscript: November 12, 2007
Manuscript Accepted: November 12, 2007
Published: November 21, 2007

Virtual Issues
Focus Serial: Frontiers of Nonlinear Optics (2007) Optics Express

Citation
Jorge Bravo-Abad, Alejandro Rodriguez, Peter Bermel, Steven G. Johnson, John D. Joannopoulos, and Marin Soljacic, "Enhanced nonlinear optics in photonic-crystal microcavities," Opt. Express 15, 16161-16176 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-16161


Sort:  Year  |  Journal  |  Reset  

References

  1. R. W. Boyd, Nonlinear Optics (Academic Press, California, 1992).
  2. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic Press, Orlando, FL, 1985).
  3. For a review on this topic, see K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003). [CrossRef] [PubMed]
  4. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).
  5. J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, "Photonic-bandgap microcavities in optical waveguides," Nature 390, 143-145 (1997). [CrossRef]
  6. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998). [CrossRef]
  7. O. Painter, J. Vuckovic, and A. Scherer, "Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab," J. Opt. Soc. Am. B 16, 275-285 (1999). [CrossRef]
  8. S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000). [CrossRef] [PubMed]
  9. S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, "Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78, 3388-3390 (2001). [CrossRef]
  10. T. Yoshie, J. Vuckovic, A. Scherer, H. Chen, and D. Deppe, "High quality two-dimensional photonic crystal slab cavities," Appl. Phys. Lett. 79, 4289-4291 (2001). [CrossRef]
  11. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 016608 (2002). [CrossRef]
  12. Y. Akahane, T. Asano, B. S. Song, and S. Noda), "Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 83, 1512-1514 (2003). [CrossRef]
  13. K. Srinivasan, P. E. Barclay, O. Painter, J. X. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003). [CrossRef]
  14. H. Y. Ryu, M. Notomi, and Y. H. Lee, "High-quality-factor and small-mode-volume hexapole modes in photoniccrystal-slab nanocavities," Appl. Phys. Lett. 83, 4294-4296 (2003). [CrossRef]
  15. A. Rodriguez, M. Ibanescu, J. D. Joannopoulos, and S. G. Johnson, "Disorder-immune confinement of light in photonic-crystal cavities," Opt. Lett. 30, 3192-3194 (2005). [CrossRef] [PubMed]
  16. S. Noda, M. Fujita, and T. Asano, "Spontaneous-emission control by photonic crystals and nanocavities," Nature Phot. 1, 449-458 (2007). [CrossRef]
  17. E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62, R7683-R7686 (2000). [CrossRef]
  18. M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, "Photonic-crystal slow-light enhancement of non-linear phase sensitivity," J. Opt. Soc. Am. B 19, 2052-2059 (2002). [CrossRef]
  19. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601(R) (2002). [CrossRef]
  20. S. F. Mingaleev and Y. S. Kivshar, "Nonlinear transmission and light localization in photonic crystal waveguides," J. Opt. Soc. Am. B 19, 2241-2249 (2002). [CrossRef]
  21. A. R. Cowan and J. F. Young, "Optical bistability involving photonic crystal microcavities and Fano line shapes," Phys. Rev. E 68, 046606 (2003). [CrossRef]
  22. M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan, "Nonlinear photonic crystal microdevices for optical integration," Opt. Lett. 28, 637-639 (2003). [CrossRef] [PubMed]
  23. M. Soljacic, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and Y. Fink, "Optical bistability in axially modulated OmniGuide fibers," Opt. Lett. 28, 516-518 (2003). [CrossRef] [PubMed]
  24. M. F. Yanik, S. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83, 2739-2741 (2003). [CrossRef]
  25. M. F. Yanik, S. Fan, M. Soljacic, and J. D. Joannopoulos, "All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry," Opt. Lett. 28, 2506-2508 (2003). [CrossRef] [PubMed]
  26. J. Trull, R. Vilaseca, J. Martorell, and R. Corbalan, "Second-harmonic generation in local modes of a truncated periodic structure," Opt. Lett. 20, 1746-1748 (1995). [CrossRef] [PubMed]
  27. 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, 2129-2140 (2002). [CrossRef]
  28. F. F. Ren, R. Li, C. Cheng, and H. T. Wang, J. R. Qiu, J. H. Si, and K. Hirao, "Giant enhancement of second harmonic generation in a finite photonic crystal with a single defect and dual-localized modes," Phys. Rev. B 70, 245109 (2004). [CrossRef]
  29. M. G. Martemyanov, E. M. Kim, T. V. Dolgova, A. A. Fedyanin, O. A. Aktsipetrov, and G. Marowsky, "Thirdharmonic generation in silicon photonic crystals and microcavities," Phys. Rev. B 70, 073311 (2004). [CrossRef]
  30. M. Soljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nature Mater. 3, 211-219 (2004). [CrossRef]
  31. P. E. Barclay, K. Srinivasan, and O. Painter, "Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper," Opt. Express 13, 801-820 (2005). [CrossRef] [PubMed]
  32. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, "Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip," Opt. Lett. 30, 2575-2577 (2005). [CrossRef] [PubMed]
  33. 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, 2678-2687 (2005). [CrossRef] [PubMed]
  34. F. F. Ren, R. Li, C. Cheng, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, "Low-threshold and high-efficiency optical parametric oscillator using a one-dimensional single-defect photonic crystal with quadratic nonlinearity," Phys. Rev. B 73, 033104 (2006). [CrossRef]
  35. A. Rodriguez, M. Soljacic, J. D. Joannopoulos, and S. G. Johnson, "χ(2) and χ (3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities," Opt. Express 15, 7303-7318 (2007). [CrossRef] [PubMed]
  36. P. Bermel, A. Rodriguez, J. D. Joannopoulos, and M. Soljacic, "Tailoring optical nonlinearities via the Purcell effect," Phys. Rev. Lett. 99, 053601 (2007). [CrossRef] [PubMed]
  37. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, Norwood, MA, 2000).
  38. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984).
  39. J. Bravo-Abad, S. Fan, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, "Modeling nonlinear optical phenomena in nanophotonics," J. Lightwave Technol. 25, 2539-2546 (2007). [CrossRef]
  40. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr "Improving accuracy by subpixel smoothing in the finite-difference time domain," Opt. Lett. 31, 2972-2974 (2006). [CrossRef] [PubMed]
  41. G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J.W. Haus, and M. Bertolotti, "Photonic band edge effects in finite structures and applications to |(2) interactions," Phys. Rev. E 64, 016609 (2001). [CrossRef]
  42. M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, "Slow-light, band-edge waveguides for tunable time delays," Opt. Express 13, 7145-7159 (2005). [CrossRef] [PubMed]
  43. Y. Xu, R. K. Lee, and A. Yariv, "Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide," J. Opt. Soc. Am. B 17, 387-400 (2000). [CrossRef]
  44. J. E. Heebner, R. W. Boyd, and Q. H. Park, "Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide," Phys. Rev. E 65, 036619 (2002). [CrossRef]
  45. VMODE is actually the effective modal volume (weighted by local χ(3)) but it is quantitatively very similar to the usual definition of modal volume.
  46. M. Notomi, Personal communication (2007).
  47. Q. F. Xu and M. Lipson, "Carrier-induced optical bistability in Silicon ring resonators," Opt. Lett. 31, 341-343 (2006). [CrossRef] [PubMed]
  48. S. Pearl, H. Lotem, Y. Shimony, and S. Rosenwaks, "Optimization of laser intracavity second-harmonic generation by a linear dispersion element," J. Opt. Soc. Am. B 16, 1705-1711 (1999). [CrossRef]
  49. A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, "Enhancement of sum frequency generation near the photonic band edge under the quasiphase matching condition," Phys. Rev. E 63, 046609 (2001). [CrossRef]
  50. A. H. Norton and C. M. de Sterke, "Optimal poling of nonlinear photonic crystals for frequency conversion," Opt. Lett. 28, 188-190 (2003). [CrossRef] [PubMed]
  51. G. D’ Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Generalized coupled-mode theory for |(2) interactions in finite multi-layered structures," J. Opt. Soc. Am. B 19, 2111-2121 (2002). [CrossRef]
  52. A. R. Cowan and J. F. Young, "Mode matching for second-harmonic generation in photonic crystal waveguides," Phys. Rev. E 65, 085106 (2002).
  53. A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizzetti, L. C. Andreani, F. Romanato, L. Businaro, E. Di Fabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306 (2003). [CrossRef]
  54. 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). [CrossRef] [PubMed]
  55. V. Berger, "Second-harmonic generation in monolithic cavities," J. Opt. Soc. Am. B 14, 1351-1360 (1997). [CrossRef]
  56. Y. Dumeige and P. Feron, "Wispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation," Phys. Rev. A 74, 063804 (2006). [CrossRef]
  57. 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]
  58. A. Ashkin, G. Boyd, and J. M. Dziedzic, "Resonant optical second harmonic generation and mixing," IEEE J. Quantum Electron. 2, 109-124 (1966). [CrossRef]
  59. R. Smith, "Theory of intracavity optical second-harmonic generation," IEEE J. Quantum Electron. 6, 215-223 (1970). [CrossRef]
  60. A. Ferguson and M. Dunn, "Intracavity second harmonic generation in continuous-wave dye lasers," IEEE J. Quantum Electron. 13, 751-756 (1977). [CrossRef]
  61. 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). [CrossRef]
  62. J. C. Bergquist, H. Hemmati, and W. M. Itano, "High power second harmonic generation of 257 nm radiation in an external ring cavity," Opt. Comm. 43, 437-442 (1982). [CrossRef]
  63. 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). [CrossRef]
  64. 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). [CrossRef] [PubMed]
  65. M. J. Collett and R. B. Levien, "Two-photon loss model of intracavity second-harmonic generation," Phys. Rev. A 43, 5068-5072 (1991). [CrossRef] [PubMed]
  66. 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). [CrossRef]
  67. Z. Y. Ou and H. J. Kimble, "Enhanced conversion efficiency for harmonic generation with double resonance," Opt. Lett. 18, 1053-1055 (1993). [CrossRef] [PubMed]
  68. G. T. Moore, K. Koch, and E. C. Cheung, "Optical parametric oscillation with intracavity second-harmonic generation," Opt. Commun. 113, 463-470 (1995). [CrossRef]
  69. K. Schneider, S. Schiller, J. Mlynek, M. Bode, and I. Freitag, "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). [CrossRef] [PubMed]
  70. X. Mu, Y. J. Ding, H. Yang, and G. J. Salamo, "Cavity-enhanced and quasiphase-matched mutli-order reflectionsecond-harmonic generation from GaAs/AlAs and GaAs/AlGaAs multilayers," Appl. Phys. Lett. 79, 569-571 (2001). [CrossRef]
  71. J. Hald, "Second harmonic generation in an external ring cavity with a Brewster-cut nonlinear cystal: theoretical considerations," Opt. Commun. 197, 169-173 (2001). [CrossRef]
  72. 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, 2408-2413 (2001). [CrossRef]
  73. 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, 061112 (2005). [CrossRef]
  74. L. Scaccabarozzi, M. M. Fejer, Y. Huo, S. Fan, X. Yu, and J. S. Harris, "Enhanced second-harmonic generation in AlGaAs/AlxOy tightly confining waveguides and resonant cavities," Opt. Lett. 31, 3626-3628 (2006). [CrossRef] [PubMed]
  75. A. Di Falco, C. Conti, and G. Assanto, "Impedance matching in photonic crystal microcavities for secondharmonic generation," Opt. Lett. 31, 250-252 (2006). [CrossRef] [PubMed]
  76. K. Koch and G. T. Moore, "Singly resonant cavity-enhanced frequency tripling," J. Opt. Soc. Am. B 16, 448-459 (1999). [CrossRef]
  77. E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681-686 (1946).
  78. D. Kleppner, "Inhibited spontaneous emission," Phys. Rev. Lett. 47, 233-236 (1981). [CrossRef]
  79. H. Y. Ryu and M. Notomi, "Enhancement of spontaneous emission from the resonant modes of a photonic crystal slab single-defect cavity," Opt. Lett. 28, 2390-2392 (2003). [CrossRef] [PubMed]
  80. P. Bermel, J. D. Joannopoulos, Y. Fink, P. A. Lane, and C. Tapalian, "Properties of radiating pointlike sources in cylindrical omnidirectionally reflecting waveguides," Phys. Rev. B 69, 035316 (2004). [CrossRef]
  81. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, "Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal," Phys. Rev. Lett. 95, 013904 (2005). [CrossRef] [PubMed]
  82. S. John and T. Quang, "Resonant nonlinear dielectric response in a photonic band gap material," Phys. Rev. Lett. 76, 2484-2487 (1996). [CrossRef] [PubMed]
  83. D. Miller, S. Smith, and B. Wherrett, "The microscopic mechanism of 3rd-order optical nonlinearity in InSb," Opt. Commun. 35, 221-226 (1980). [CrossRef]
  84. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
  85. J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, Reading, MA, 1994).
  86. G. Lenz, J. Zimmermann, T. Katsufuji, M. E. Lines, H. Y. Hwang, S. Spalter, R. E. Slusher, S. W. Cheong, J. S. Sanghera, and I. D. Aggarwal, "Large Kerr effect in bulk Se-based chalcogenide glasses," Opt. Lett. 25, 254-256 (2000). [CrossRef]
  87. V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, "Quantum well excitons in semiconductor microcavities: unified treatment of weak and strong coupling regimes", Solid State Comm. 93, 733-739 (1995). [CrossRef]
  88. X. Brokmann, L. Coolen, M. Dahan, and J. P. Hermier, "Measurement of the radiative and nonradiative decay rates of single CdSe nanocrystals through a controlled modification of their spontaneous emission," Phys. Rev. Lett. 93, 107403 (2004). [CrossRef] [PubMed]
  89. H. Shinojima, "Optical nonlinearity in CdSSe microcrystallites embedded in glasses," IEICE Trans. Electron.E 90-C, 127-134 (2007). [CrossRef]
  90. D. V. Talapin, A. L. Rogach, A. Kornowski, M. Haase, and H. Weller, "Highly luminescent monodisperse CdSe and CdSe/ZnS nanocrystals synthesized in a hexadecylamine-trioctylphosphine oxide-trioctylphospine mixture," Nano Lett. 1, 207-211 (2001). [CrossRef]
  91. N. M. Litchinitser, A. Abeeluck, C. Headley, and B. Eggleton, "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1592-1594 (2002). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited