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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)
http://dx.doi.org/10.1364/OE.16.010596


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Abstract

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

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

Citation
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)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-14-10596


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References

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  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.
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  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.
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  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]
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  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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