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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 14 — Jul. 7, 2008
  • pp: 10596–10610

A proposal for highly tunable optical parametric oscillation in silicon micro-resonators

Q. Lin, T. J. Johnson, R. Perahia, C. P. Michael, and O. J. Painter  »View Author Affiliations

Optics Express, Vol. 16, Issue 14, pp. 10596-10610 (2008)

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We propose a novel scheme for continuous-wave pumped optical parametric oscillation (OPO) inside silicon micro-resonators. The proposed scheme not only requires a relative low lasing threshold, but also exhibits extremely broad tunability extending from the telecom band to mid infrared.

© 2008 Optical Society of America

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(190.4970) Nonlinear optics : Parametric oscillators and amplifiers
(130.3990) Integrated optics : Micro-optical devices

ToC Category:
Nonlinear Optics

Original Manuscript: April 22, 2008
Revised Manuscript: June 18, 2008
Manuscript Accepted: June 28, 2008
Published: July 1, 2008

Q. Lin, T. J. Johnson, R. Perahia, C. P. Michael, and O. J. Painter, "A proposal for highly tunable optical parametric oscillation in silicon micro-resonators," Opt. Express 16, 10596-10610 (2008)

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  1. R. Soref, "The Past, Present, and Future of Silicon Photonics," IEEE J. Sel. Top. Quantum Electron. 12, 1678-1687 (2006), and references therein. [CrossRef]
  2. Q. Lin, O. J. Painter, and G. P. Agrawal, "Nonlinear optical phenomena in silicon waveguides: Modeling and applications," Opt. Express 15, 16604-16644 (2007). [CrossRef] [PubMed]
  3. V. Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, "Parametric Raman wavelength conversion in scaled silicon waveguides," J. Lightwave Technol. 23, 2094-2102 (2005). [CrossRef]
  4. H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, "Four-wave mixing in silicon wire waveguides," Opt. Express 13, 4629-4637 (2005). [CrossRef] [PubMed]
  5. H. Rong, Y. Kuo, A. Liu, M. Paniccia, and O. Cohen, "High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides," Opt. Express 14, 1182-1188 (2006). [CrossRef] [PubMed]
  6. M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, "Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides," Opt. Express 15, 12949-12958 (2007). [CrossRef] [PubMed]
  7. I-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, Jr., S. J. McNab, and Y. A. Vlasov, "Crossphase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires," Opt. Express 15, 1135-1146 (2007). [CrossRef] [PubMed]
  8. A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, "Ultra-low power parametric frequency conversion in a silicon microring resonator," Opt. Express 16, 4881-4887 (2008). [CrossRef] [PubMed]
  9. Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, "Ultrabroadband parametric generation and wavelength conversion in silicon waveguides," Opt. Express 14, 4786-4799 (2006). [CrossRef] [PubMed]
  10. M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003). [CrossRef]
  11. A. D. Bristow, N. Rotenberg, and H. M. van Driel, "Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm," Appl. Phys. Lett. 90, 191104 (2007). [CrossRef]
  12. Q. Lin, J. Zhang, G. Piredda, R.W. Boyd, P. M. Fauchet, and G. P. Agrawal, "Dispersion of silicon nonlinearities in the near-infrared region," Appl. Phys. Lett. 90, 021111 (2007). [CrossRef]
  13. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, Boston, 2007).
  14. Although the waveguide shown in Fig. 1 is multimoded over a broad spectral range, higher-order modes have quite different mode profiles and dispersion properties compared with the fundamental quasi-TE mode. They are not likely to participate in the FWM process if the pump and signal waves propagate predominantly in the fundamental quasi-TE mode.
  15. The real and imaginary parts of χ(3) are related to Kerr nonlinearity and TPA, respectively [2]. An accurate description of SPM, XPM, TPA, and FWM requires complete information about χ(3)(-ωi;ωj, -ωk,ωl). However, current experimental knowledge is only available for χ(3)(-ωiωi,-ωi,ωi) [11, 12]. As cross-TPA involves the simultaneous absorption of two photons at ωi and ωj, we approximate χ(3)(-ωi;ωj, -ωj, ωi) ≈χ(3)(-ω- ;ω-, -ω-, ω-) where ω- = (ωi+ωj)/2. Similarly, FWM involves the annihilation of two pump photons tocreate a signal and idler photon, and we approximate χ(3)(-ωs;ωp,-ωi,ωp) ≈ χ(3)(-ωp;ωp,-ωp,ωp). Note also χ(3)(-ωi;ωp,-ωs,ωp)=χ(3)(-ωs;ωp,-ωi,ωp) = [χ(3)(-ωp;ωs,-ωp,ωi)]* because of the time-reversal symmetry.
  16. We fit each set of experimental data (1.2-2.2 µm) in Refs. [11, 12] with a fifth-order polynomial, and average them to obtain the silicon nonlinearity. TPA is zero and the Kerr nonlinearity is assumed to be constant for wavelength longer than 2.2 µm.
  17. R. A. Soref and B. R. Bennett, "Electrooptical effects in silicon," IEEE J. Quantum Electron. 23, 123-129 (1987). [CrossRef]
  18. For completeness, we have included all possible self- and cross-TPA and induced free carriers from all the three waves and their combinations in the numerical results of this paper.
  19. A. Y. H. Chen, G. K. L. Wong, S. G. Murdoch, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Widely tunable optical parametric generation in a photonic crystal fiber," Opt. Lett. 30, 762-764 (2005). [CrossRef] [PubMed]
  20. Y. Deng, Q. Lin, F. Lu, G. P. Agrawal, and W. H. Knox, "Broadly tunable femtosecond parametric oscillator using a photonic crystal fiber," Opt. Lett. 30, 1234-1236 (2005). [CrossRef] [PubMed]
  21. T. V. Andersen, K. M. Hilligsøe, C. K. Nielsen, J. Thøgersen, K. P. Hansen, S. R. Keiding, and J. J. Larsen, "Continuous-wave wavelength conversion in a photonic crystal fiber with two zero-dispersion wavelengths," Opt. Express 12, 4113-4122 (2004). [CrossRef] [PubMed]
  22. M. Borselli, T. J. Johnson, and O. J. Painter, "Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment", Opt. Express 13, 1515-1529 (2005). [CrossRef] [PubMed]
  23. T. J. Kippenberg, S.M. Spillane, and K. J. Vahala, "Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity," Phys. Rev. Lett. 93, 083904 (2004). [CrossRef] [PubMed]
  24. C. P. Michael, M. Borselli, T. J. Johnson, C. Chrystal, and O. Painter, "An optical fiber-taper probe for wafer-scale microphotonic device characterization," Opt. Express 15, 4745-4752 (2007). [CrossRef] [PubMed]
  25. In practice, a critical coupling over such a broad spectral region is difficult for a straight bus waveguide, but is possible by using a curved bus waveguide with a curvature similar to the resonator. SeeT . Carmon, S. Y. T. Wang, E. P . Ostby, and K. J. Vahala, "Wavelength-independent coupler from fiber to an on-chip cavity, demonstrated over an 850nm span," Opt. Express 15, 7677-7681 (2007). [CrossRef] [PubMed]
  26. I. T. Sorokina and K. L. Vodopyanov, eds., Solid-State Mid-Infrared Laser Sources, Top. Appl. Phys. 89 (2003). [CrossRef]
  27. B. Jalali, V. Raghunathan, R. Shori, S. Fathpour,D. Dimitropoulos, and O. Strafsudd, "Propests for silicon mid-IR Raman lasers," IEEE J. Sel. Top. Quantum Electron. 12, 1618-1627 (2006). [CrossRef]
  28. M. Krause, R. Draheim, H. Renner, and E. Brinkmeyer, "Cascaded silicon Raman lasers as mid-infrared sources," Electron. Lett. 42, 1224-1225 (2006). [CrossRef]
  29. H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, "A cascaded silicon Raman laser," Nat. Photonics 2, 170 (2008). [CrossRef]
  30. 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]

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