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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 20 — Sep. 26, 2011
  • pp: 18810–18826

Optimized wavelength conversion in silicon waveguides based on “off-Raman-resonance” operation: extending the phase mismatch formalism

Yannick Lefevre, Nathalie Vermeulen, Christof Debaes, and Hugo Thienpont  »View Author Affiliations

Optics Express, Vol. 19, Issue 20, pp. 18810-18826 (2011)

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We present a generic approach to determine the phase mismatch for any optical nonlinear process. When applying this approach, which is based on the evaluation of local phase changes, to Raman- and Kerr-based four-wave mixing in silicon waveguides, we obtain an expression for the phase mismatch which is more accurate as compared to the conventional definition; and which contains additional contributions due to the dispersion of the four-wave-mixing processes. Furthermore, starting from the general propagation equations for the involved pump, Stokes and anti-Stokes waves, we investigate the impact of this four-wave-mixing dispersion in silicon waveguides and examine how it is influenced by changing the frequency difference between the pump and Stokes input waves. We show by means of numerical simulations that, by detuning this frequency difference slightly away from Raman resonance, the four-wave-mixing conversion efficiency can be more than doubled, but can also lead to a decrease in efficiency of more than 10 dB. We also discuss how the pump-Stokes frequency difference that is optimal for wavelength conversion varies with the length of the silicon waveguides and with their dispersion characteristics. Finally, starting from the newly introduced phase mismatch formula we simplify the set of propagation equations such that they are less computationally intensive to solve while still giving accurate estimates of the optimal pump-Stokes frequency difference and the corresponding wavelength conversion efficiency.

© 2011 OSA

OCIS Codes
(130.4310) Integrated optics : Nonlinear
(160.4330) Materials : Nonlinear optical materials
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.5650) Nonlinear optics : Raman effect

ToC Category:
Nonlinear Optics

Original Manuscript: June 6, 2011
Revised Manuscript: August 7, 2011
Manuscript Accepted: August 11, 2011
Published: September 13, 2011

Yannick Lefevre, Nathalie Vermeulen, Christof Debaes, and Hugo Thienpont, "Optimized wavelength conversion in silicon waveguides based on “off-Raman-resonance” operation: extending the phase mismatch formalism," Opt. Express 19, 18810-18826 (2011)

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  1. R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, “Anti-Stokes Raman conversion in silicon waveguides,” Opt. Express 11, 2862–2872 (2003). [CrossRef] [PubMed]
  2. D. Dimitropoulos, V. Raghunathan, R. Claps, and B. Jalali, “Phase-matching and nonlinear optical processes in silicon waveguides,” Opt. Express 12, 149–160 (2004). [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. R. Espinola, J. Dadap, J. Osgood, S. McNab, and Y. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express 13, 4341–4349 (2005). [CrossRef] [PubMed]
  6. 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]
  7. Y. Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia, and O. Cohen, “Demonstration of wavelength conversion at 40 Gb/s data rate in silicon waveguides,” Opt. Express 14, 11721–11726 (2006). [CrossRef] [PubMed]
  8. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006). [CrossRef] [PubMed]
  9. 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]
  10. W. Mathlouthi, H. Rong, and M. Paniccia, “Characterization of efficient wavelength conversion by four-wave mixing in sub-micron silicon waveguides,” Opt. Express 16, 16735–16745 (2008). [CrossRef] [PubMed]
  11. P. Koonath, D. R. Solli, and B. Jalali, “High efficiency CARS conversion in silicon,” in Conference on Lasers and Electro-Optics and on Quantum Electronics and Laser Science, (2008), pp. 1–2.
  12. N. Vermeulen, C. Debaes, and H. Thienpont, “The behavior of CARS in anti-Stokes Raman converters operating at exact Raman resonance,” IEEE J. Quantum Electron. 44, 1248–1255 (2008). [CrossRef]
  13. A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18, 1904–1908 (2010). [CrossRef] [PubMed]
  14. S. Gao, E. Tien, Q. Song, Y. Huang, and O. Boyraz, “Ultra-broadband one-to-two wavelength conversion using low-phase-mismatching four-wave mixing in silicon waveguides,” Opt. Express 18, 11898–11903 (2010). [CrossRef] [PubMed]
  15. N. Vermeulen, J. E. Sipe, Y. Lefevre, C. Debaes, and H. Thienpont, “Wavelength conversion based on Raman-and non-resonant four-wave mixing in silicon nanowire rings without dispersion engineering,” IEEE J. Sel. Top. Quantum Electron. 17, 1078–1091 (2011). [CrossRef]
  16. G. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, 2001).
  17. E. Golovchenko, P. Mamyshev, A. Pilipetskii, and E. Dianov, “Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990). [CrossRef]
  18. B. Jalali, V. Raghunathan, D. Dimitropoulos, and O. Boyraz, “Raman-based silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 412–421 (2006). [CrossRef]
  19. 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]
  20. Y. Chen, “Combined processes of stimulated Raman scattering and four-wave mixing in optical fibers,” J. Opt. Soc. Am. B 7, 43–52 (1990). [CrossRef]
  21. G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B 8, 824–838 (1991). [CrossRef]
  22. Y. Chen and A.W. Snyder, “Four-photon parametric mixing in optical fibers: effect of pump depletion,” Opt. Lett. 14, 87–89 (1989). [CrossRef] [PubMed]
  23. T. Sylvestre, H. Maillotte, E. Lantz, and P. Tchofo Dinda, “Raman-assisted parametric frequency conversion in a normally dispersive single-mode fiber,” Opt. Lett. 24, 1561–1563 (1999). [CrossRef]
  24. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguides,” Opt. Express 11, 1731–1739 (2003). [CrossRef] [PubMed]
  25. ITU-T Rec. G.694.1, “Spectral grids for WDM applications: DWDM frequency grid” (2002).

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