OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 7 — Mar. 26, 2012
  • pp: 7526–7543

High-efficiency second-harmonic generation in doubly-resonant χ(2) microring resonators

Zhuan-Fang Bi, Alejandro W. Rodriguez, Hila Hashemi, David Duchesne, Marko Loncar, Ke-Ming Wang, and Steven G. Johnson  »View Author Affiliations


Optics Express, Vol. 20, Issue 7, pp. 7526-7543 (2012)
http://dx.doi.org/10.1364/OE.20.007526


View Full Text Article

Enhanced HTML    Acrobat PDF (2346 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

By directly simulating Maxwell’s equations via the finite-difference time-domain (FDTD) method, we numerically demonstrate the possibility of achieving high-efficiency second harmonic generation (SHG) in a structure consisting of a microscale doubly-resonant ring resonator side-coupled to two adjacent waveguides. We find that ≳ 94% conversion efficiency can be attained at telecom wavelengths, for incident powers in the milliwatts, and for reasonably large bandwidths (Q ∼ 1000s). We demonstrate that in this high efficiency regime, the system also exhibits limit-cycle or bistable behavior for light incident above a threshold power. Our numerical results agree to within a few percent with the predictions of a simple but rigorous coupled-mode theory framework.

© 2012 OSA

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(230.4320) Optical devices : Nonlinear optical devices

ToC Category:
Nonlinear Optics

History
Original Manuscript: January 11, 2012
Revised Manuscript: March 5, 2012
Manuscript Accepted: March 5, 2012
Published: March 19, 2012

Citation
Zhuan-Fang Bi, Alejandro W. Rodriguez, Hila Hashemi, David Duchesne, Marko Loncar, Ke-Ming Wang, and Steven G. Johnson, "High-efficiency second-harmonic generation in doubly-resonant χ(2) microring resonators," Opt. Express 20, 7526-7543 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-7526


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. Rodriguez, M. Soljačić, J. D. Joannopulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express15(12), 7303–7318 (2007). [CrossRef] [PubMed]
  2. H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljacic, and S. G. Johnson, “Nonlinear harmonic generation and devices in doubly resonant Kerr cavities,” Phys. Rev. A79(1), 013,812 (2009). [CrossRef]
  3. V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear Optics and Crystalline Whispering Gallery Mode Cavities,” Phys. Rev. Lett.92(4), 043,903 (2004). [CrossRef] [PubMed]
  4. J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally Phase-Matched Second-Harmonic Generation in a Whispering-Gallery-Mode Resonator,” Phys. Rev. Lett.104(15), 153,901 (2010). [CrossRef] [PubMed]
  5. P. S. Kuo and G. S. Solomon, “On- and off-resonance second-harmonic generation in GaAs microdisks,” Opt. Express19(18), 16,898–16,918 (2011). [CrossRef]
  6. Y. Dumeige and P. Feron, “Wispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A74, 063,804 (2006). [CrossRef]
  7. G. T. Moore, K. Koch, and E. C. Cheung, “Optical parametric oscillation with intracavity second-harmonic generation,” Optics Communications113, 463 (1995). [CrossRef]
  8. M. Liscidini and L. A. Andreani, “Highly efficient second-harmonic generation in doubly resonant planar microcavities,” Appl. Phys. Lett.85, 1883 (2004).
  9. 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. Lett88, 117–251,119 (2006). [CrossRef]
  10. P. Scotto, P. Colet, and M. San Miguel, “All-optical image processing with cavity type II second-harmonic generation,” Opt. Lett.28, 1695 (2003). [CrossRef] [PubMed]
  11. M. M. Fejer, “Nonlinear optical frequency conversion,” Phys. Today47, 25–32 (1994). [CrossRef]
  12. G. McConnell, A. I. Ferguson, and N. Langford, “Cavity-augmented frequency tripling of a continuous wave mode-locked laser,” J. Phys. D: Appl.Phys34, 2408 (2001). [CrossRef]
  13. R. G. Smith, “Theory of intracavity optical second-harmonic generation,” IEEE J. Quantum Electron.6, 215–223 (1970). [CrossRef]
  14. A. I. Gerguson and M. H. Dunn, “Intracavity second harmonic generation in continuous-wave dye lasers,” IEEE J. Quantum Electron.13, 751–756 (1977). [CrossRef]
  15. 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]
  16. S. Pearl, H. Lotem, and Y. Shimony, “Optimization of laser intracavity second-harmonic generation by a linear dispersion element,” J. Opt. Soc. Am. B16, 1705 (1999). [CrossRef]
  17. 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. E63, 046,609 (2001). [CrossRef]
  18. G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multi-layered structures,” J. Opt. Soc. Am. B19, 2111–2122 (2002). [CrossRef]
  19. A. H. Norton and C. M. de Sterke, “Optimal poling of nonlinear photonic crystals for frequency conversion,” Opt. Lett.28, 188 (2002).
  20. G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidavovic, 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 χ(2) interactions,” Phys. Rev. E64, 016,609 (2001).
  21. A. R. Cowan and J. F. Young, “Mode matching for second-harmonic generation in photonic crystal waveguides,” Phys. Rev. E65, 085,106 (2002).
  22. 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. B68, 161,306 (2003). [CrossRef]
  23. R. Paschotta, K. Fiedler, P. Kurz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. Lett.58, 117 (1994).
  24. V. Berger, “Second-harmonic generation in monolithic cavities,” J. Opt. Soc. Am. B14, 1351 (1997). [CrossRef]
  25. I. I. Zootoverkh, K. N. V, and E. G. Lariontsev, “Enhancement of the efficiency of second-harmonic generation in microlaser,” Quantum Electronics30, 565 (2000). [CrossRef]
  26. B. Maes, P. Bienstman, and R. Baets, “Modeling second-harmonic generation by use of mode expansion,” J. Opt. Soc. Am. B22, 1378 (2005). [CrossRef]
  27. M. Liscidini and L. A. Andreani, “Second-harmonic generation in doubly resonant microcavities with periodic dielectric mirrors,” Phys. Rev. E73, 016,613 (2006). [CrossRef]
  28. J. A. Armstrong, N. loembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962). [CrossRef]
  29. A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron.2, 109–124 (1966). [CrossRef]
  30. J. Bravo-Abad, A. W. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal nanocavities,” Opt. Express15(24), 16,161–16,176 (2007). [CrossRef]
  31. Z. Yang, P. Chak, A. D. Bristow, H. M. van Driel, R. Iyer, J. S. Aitchison, A. L. Smirl, and J. E. Sipe, “Enhanced second-harmonic generation in AlGaAs microring resonators,” Opt. Lett.32(7), 826–828 (2007). [CrossRef] [PubMed]
  32. L. Caspani, D. Duchesne, K. Dolgaleva, S. J. Wagner, M. Ferrera, L. Razzari, A. Pasquazi, M. Peccianti, D. J. Moss, J. S. Aitchison, and R. Morandotti, “Optical frequency conversion in integrated devices,” J. Opt. Soc. Am. B28(12), A67–A82 (2011). [CrossRef]
  33. S. Schiller, “Principles and Applications of Optical Monolithic Total-Internal-Reflection Resonators,” Ph.D. thesis, Stanford University, Stanford, CA (1993).
  34. Y. Dumeige and P. Feron, “Stability and time-domain analysis of the dispersive tristability in microresonators under modal coupling,” Phys. Rev. A84(4), 043,847 (2011). [CrossRef]
  35. Z. Y. Ou and H. J. Kimble, “Enhanced conversion efficiency for harmonic generation with double resonance,” Opt. Lett.18, 1053–1055 (1993). [CrossRef] [PubMed]
  36. M. Tabor, Chaos and Integrability in Nonlinear Dynamics: An Introduction (Wiley, New York, 1989).
  37. J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express19(12), 11,415–11,421 (2011). [CrossRef]
  38. C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express19(11), 10,462–10,470 (2011). [CrossRef]
  39. M. Gandomkar and V. Ahmadi, “Design and analysis of enhanced second harmonic generation in AlGaAs/AlOx microring waveguide,” Opt. Express19(10), 9408–9418 (2011). [CrossRef] [PubMed]
  40. G. Nielson, D. Seneviratne, F. Lopez-Royo, P. Rakich, Y. Avrahami, M. Watts, H. Haus, H. Tuller, and G. Barbastathis, “Integrated wavelength-selective optical MEMS switching using ring resonator filters,” Photonics Technology Letters, IEEE17(6), 1190 –1192 (2005). [CrossRef]
  41. R. W. Boyd, Nonlinear Optics (Academic Press, California, 1992).
  42. M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quant. Elec.28(11), 2631–2654 (1992). [CrossRef]
  43. A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Letters to Nature391, 463–466 (1997).
  44. T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q ring resonators in thin silicon-on-insulator,” Appl. Phys. Lett.85(16), 3346–3347 (2004). [CrossRef]
  45. I. Tomita, M. Asobe, H. Suzuki, J. Yumoto, and Y. Yoshikuni, “Broadband quasi-phase-matched second-harmonic generation in a nonlinear photonic crystal,” J. of Appl. Phys.100(2), 023,120 (2006). [CrossRef]
  46. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008). URL http://ab-initio.mit.edu/book .
  47. K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett.99(1), 013,114 (2011). [CrossRef]
  48. K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant photonic crystal nanocavities for nonlinear frequency conversion,” Opt. Express19(22), 22,198–22,207 (2011). [CrossRef]
  49. K. Rivoire, Z. Lin, F. Hatami, and J. Vuckovic, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett.97(4), 043,103 (2010). [CrossRef]
  50. K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vuckovic, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express17(25), 22,609–22,615 (2009). [CrossRef]
  51. K. Rivoire, S. Buckley, F. Hatami, and J. Vuckovic, “Second harmonic generation in GaP photonic crystal waveguides,” Appl. Phys. Lett.98(26), 263,113 (2011). [CrossRef]
  52. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Steven, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm.181, 687–702 (2010). [CrossRef]
  53. V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys.107(17), 6756–6769 (1997). See erratum. [CrossRef]
  54. V. A. Mandelshtam and H. S. Taylor, “Erratum: “Harmonic inversion of time signals and its applications”,” J. Chem. Phys.109, 4128 (1998). [CrossRef]
  55. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express8(3), 173–190 (2001).
  56. W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. O. H. Suche, R. Nouroozi, and Y. Min, “Integrated Optical Devices in Lithium Niobate,” Opt. Photon. News19(1), 24–31 (2008). [CrossRef]
  57. Q. Xu and M. Lipson, “Carrier-induced optical bistability in Silicon ring resonators,” Opt. Lett.31(3), 341–343 (2005). [CrossRef]
  58. R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, 2002).
  59. C. L. Chen, Foundations for Guided-Wave Optics (Wiley, 2006). [CrossRef]
  60. K. K. Y. Lee, Y. Avniel, and S. G. Johnson, “Rigorous sufficient conditions for index-guided modes in microstructured dielectric waveguides,” Opt. Express16, 9261–9275 (2008). [CrossRef] [PubMed]
  61. P. D. Drummond, 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). [CrossRef]
  62. K. Grygiel and P. Szlatchetka, “Chaos in second-harmonic generation of light. The case of a strain of pulses.”Opt. Comm.91, 241–246 (1992). [CrossRef]
  63. E. D. Palik, ed., Handbook of optical constants of solids II (Academic Press, 1991).
  64. M. Ohashi, T. Kondo, and R. Ito, “Determination of quadratic nonlinear optical coefficient of AlxGa1−xAs system by the method of reflected second harmonics,” J. Appl. Phys.74(1), 596–601 (1993). [CrossRef]
  65. C. W. Wong, P. T. Rakich, S. G. Johnson, M. Qi, H. I. Smith, E. P. Ippen, L. C. Kimerling, Y. Jeon, G. Barbastathis, and S.-G. Kim, “Strain-tunable silicon photonic band gap microcavities in optical waveguides,” Appl. Phys. Lett.84, 1242–1245 (2004). [CrossRef]
  66. D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Postfabrication fine-tuning of photonic crystal microcavities in InAs/InP quantum dot membranes,” Appl. Phys. Lett.87(15), 151,107 (2005). [CrossRef]
  67. H. Lohmeyer, J. Kalden, K. Sebald, C. Kruse, D. Hommel, and J. Gutowski, “Fine tuning of quantum-dot pillar microcavities by focused ion beam milling,” Appl. Phys. Lett.92(1), 011,116 (2008). [CrossRef]
  68. J. Pan, Y. Hio, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett.92(10), 103,114 (2008). [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