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Optics Express

Optics Express

| THE INTERNATIONAL ELECTRONIC JOURNAL OF OPTICS

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 11 — May. 25, 2009
  • pp: 9241–9251

Difference-frequency generation with quantum-limited efficiency in triply-resonant nonlinear cavities

Ian B. Burgess, Alejandro W. Rodriguez, Murray W. McCutcheon, Jorge Bravo-Abad, Yinan Zhang, Steven G. Johnson, and Marko Lončar

Optics Express, Vol. 17, Issue 11, pp. 9241-9251        doi:10.1364/OE.17.009241

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  • OCIS Codes:
  • (190.4410) Nonlinear optics : Nonlinear optics, parametric processes
  • (230.4320) Optical devices : Nonlinear optical devices
  • (190.4223) Nonlinear optics : Nonlinear wave mixing
ToC Category:
Nonlinear Optics

Citation
Ian B. Burgess, Alejandro W. Rodriguez, Murray W. McCutcheon, Jorge Bravo-Abad, Yinan Zhang, Steven G. Johnson, and Marko Lončar, "Difference-frequency generation with quantum-limited efficiency in triply-resonant nonlinear cavities," Opt. Express 17, 9241-9251 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-11-9241

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Abstract

We present a comprehensive study of second-order nonlinear difference frequency generation in triply resonant cavities using a theoretical framework based on coupled-mode theory. We show that optimal “quantum-limited” conversion efficiency can be achieved at any pump power when the powers at the pump and idler frequencies satisfy a critical relationship. We demonstrate the existence of a broad parameter range in which all triply-resonant DFG processes exhibit monostable conversion. We also demonstrate the existence of a geometry-dependent bistable region.

© 2009 OSA

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History
Original Manuscript: March 24, 2009
Manuscript Accepted: May 11, 2009
Revised Manuscript: May 8, 2009
Published: May 18, 2009

References

  1. R. W. Boyd, Nonlinear Optics, (Academic Press, CA, 1992).
  2. H. M. Gibbs, G. Khitrova, and N. Peyghambarian, Nonlinear Photonics, (Springer-Verlag, 1990).
  3. R. A. Baumgartner and R. L. Byer, “Optical Parametric Amplification,” IEEE J. Quantum Electron. 15, 432–444 (1979). [CrossRef]
  4. J. A. Giordmaine and R. C. Miller, “Tunable Coherent Parametric Oscillation in LiNbO3 at Optical Frequencies,” Phys. Rev. Lett. 14(24), 973–976 (1965). [CrossRef]
  5. A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant Optical Second Harmonic Generation and Mixing,” IEEE J. Quantum Electron. 2(6), 109–124 (1966). [CrossRef]
  6. 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(11), 2631–2654 (1992). [CrossRef]
  7. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-Phase Matched Optical Parametric Oscillators in Bulk Periodically Poled LiNbO3,” J. Opt. Soc. Am. B 12(11), 2102–2116 (1995). [CrossRef]
  8. M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004). [CrossRef]
  9. M. Bieler, “THz generation from resonant excitation of semiconductor nanostructures: Investigation of second-order nonlinear optical effects,” IEEE J. Sel. Top. Quantum Electron. 14(2), 458–469 (2008). [CrossRef]
  10. A. Andronico, J. Claudon, J. M. Gérard, V. Berger, and G. Leo, “Integrated terahertz source based on three-wave mixing of whispering-gallery modes,” Opt. Lett. 33(21), 2416–2418 (2008). [CrossRef]
  11. R. E. Hamam, M. Ibanescu, E. J. Reed, P. Bermel, S. G. Johnson, E. Ippen, J. D. Joannopoulos, and M. Soljacic, “Purcell effect in nonlinear photonic structures: a coupled mode theory analysis,” Opt. Express 16(17), 12523–12537 (2008). [CrossRef]
  12. M. W. McCutcheon, J. F. Young, G. W. Rieger, D. Dalacu, S. Frederick, P. J. Poole, and R. L. Williams, “Experimental demonstration of second-order processes in photonic crystal microcavities at submilliwatt excitation powers,” Phys. Rev. B 76(24), 245104 (2007). [CrossRef]
  13. L.-A. Wu, M. Xiao, and H. J. Kimble, “Squeezed states of light from an optical parametric oscillator,” J. Opt. Soc. Am. B 4(10), 1465–1476 (1987). [CrossRef]
  14. Z. Y. Ou and H. J. Kimble, “Enhanced conversion efficiency for harmonic generation with double resonance,” Opt. Lett. 18(13), 1053–1055 (1993). [CrossRef]
  15. R. Paschotta, K. Fiedler, P. Kurz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. B 58, 117–122 (1994). [CrossRef]
  16. V. Berger, “Second harmonic generation in monolithic cavities,” J. Opt. Soc. Am. B 14(6), 1351–1360 (1997). [CrossRef]
  17. A. B. Matsko, D. V. Strekalov, and N. Yu, “Sensitivity of terahertz photonic receivers,” Phys. Rev. A 77(4), 043812 (2008). [CrossRef]
  18. B. Maes, P. Bienstman, and R. Baets, “Modeling second-harmonic generation by use of mode expansion,” J. Opt. Soc. Am. B 22(7), 1378–1383 (2005). [CrossRef]
  19. M. Liscidini and L. Claudio Andreani, “Second-harmonic generation in doubly resonant microcavities with periodic dielectric mirrors,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(1), 016613 (2006). [CrossRef]
  20. Y. Dumeige and P. Feron, “Whispering-gallery mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74(6), 063804 (2006). [CrossRef]
  21. A. Rodriguez, M. Soljacic, J. Joannopoulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in homogeneous doubly resonant microcavities,” Opt. Express 15(12), 7303–7318 (2007). [CrossRef]
  22. 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). [CrossRef]
  23. J. Bravo-Abad, A. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Enhanced nonlinear optics in photonic-crystal microcavities,” Opt. Express 15(24), 16161–16176 (2007). [CrossRef]
  24. 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. A 79(1), 013812 (2009). [CrossRef]
  25. Y. A. Morozov, I. S. Nefedov, V. Y. Aleshkin, and I. V. Krasnikova, “Terahertz Oscillator Based on Nonlinear Frequency Conversion in a Double Vertical Cavity,” Semiconductors 39(1), 113 (2005). [CrossRef]
  26. Y. H. Avetisyan, “Cavity-enhanced terahertz region difference frequency generation in surface-emitting geometry,” Proc. SPIE 3795, 501 (1999).
  27. P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High Quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009). [CrossRef]
  28. S. S. Jha and N. Bloembergen, “Nonlinear optical susceptibilities in group-4 and 3-5 semiconductors,” Phys. Rev. 171(3), 891–898 (1968). [CrossRef]
  29. S. Saltiel and Y. S. Kivshar, “Phase matching in nonlinear χ((2)) photonic crystals,” Opt. Lett. 25(16), 1204–1206 (2000). [CrossRef]
  30. K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89(14), 141119 (2006). [CrossRef]
  31. G. Imeshev, M. E. Fermann, K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, D. Bliss, and C. Lynch, “High-power source of THz radiation based on orientation-patterned GaAs pumped by a fiber laser,” Opt. Express 14(10), 4439–4444 (2006). [CrossRef]
  32. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “N. loembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962). [CrossRef]
  33. F. S. Felber and J. H. Marburger, “Theory of nonresonant multistable optical devices,” Appl. Phys. Lett. 28(12), 731–733 (1976). [CrossRef]
  34. S. Schiller, Principles and Applications of Optical Monolithic Total-Internal-Reflection Resonators. PhD thesis, Stanford University, Stanford, CA (1993).
  35. E. Abraham, W. J. Firth, and J. Carr, “Self-oscillation and chaos in nonlinear Fabry-Perot resonators with finite response time,” Phys. Lett. A 91(2), 47–51 (1982). [CrossRef]
  36. A. Parini, G. Bellanca, S. Trillo, M. Conforti, A. Locatelli, and C. D. Angelis, “Self-pulsing and bistability in nonlinear Bragg gratings,” J. Opt. Soc. Am. B 24(9), 2229–2237 (2007). [CrossRef]
  37. 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). [CrossRef]
  38. J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).
  39. H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984).
  40. Note that there is a typographical error in the corresponding equation for the degenerate case in [21], where ε is written instead of ε0 in the numerator.
  41. S. Singh, “Nonlinear Optical Materials” in M.J. Weber Ed., Handbook of laser science and technology, Vol. III: Optical Materials, Part I, CRC Press 1986.
  42. I. B. Burgess, M. W. McCutcheon, Y. Zhang, A. W. Rodriguez, J. Bravo-Abad, S. G. Johnson, and M. Loncar, “Efficient terahertz generation in triply resonant nonlinear photonic crystal microcavities” manuscript in preparation (2009).
  43. B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, 2007).
  44. M. W. McCutcheon, D. E. Chang, Y. Zhang, M. D. Lukin, and M. Loncar, “Broad-band spectral control of single photon sources using a nonlinear photonic crystal cavity” arXiv:0903.4706 (2009).
  45. M. Tabor, Chaos and Integrability in Nonlinear Dynamics: An Introduction (Wiley, New York, 1989).
  46. A. Hurwitz, “On the Conditions Under Which an Equation Has Only Roots with Negative Real Parts,” Mathematicsche Annalen 46, 273–284 (1895). Also in selected papers on Mathematical Trends in Control Theory, Dover, New York, 70–82 (1964).

Author Affiliations

Steven G. Johnson

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139.

Alejandro W. Rodriguez, Jorge Bravo-Abad

Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139.

Ian B. Burgess, Murray W. McCutcheon, Yinan Zhang, Marko Lončar

School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138.

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