OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 20 — Sep. 27, 2010
  • pp: 21024–21029

Theory of slow light enhanced four-wave mixing in photonic crystal waveguides

M. Santagiustina, C. G. Someda, G. Vadalà, S. Combrié, and A. De Rossi  »View Author Affiliations


Optics Express, Vol. 18, Issue 20, pp. 21024-21029 (2010)
http://dx.doi.org/10.1364/OE.18.021024


View Full Text Article

Enhanced HTML    Acrobat PDF (687 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The equations for Four-Wave-Mixing in a photonic crystal waveguide are derived accurately in the hypotesis of negligible nonlinear absorption. The dispersive nature of slow-light enhancement, the impact of Bloch mode reshaping in the nonlinear overlap integrals and the tensor nature of the third order polarization are therefore taken into account. Numerical calculations reveal substantial differences from simpler models, which increase with decreasing group velocity. We predict that the gain for a 1.3 mm long, un-optimized GaInP waveguide will exceed 10 dB if the pump power exceeds 1 W.

© 2010 Optical Society of America

OCIS Codes
(130.5990) Integrated optics : Semiconductors
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(130.5296) Integrated optics : Photonic crystal waveguides

ToC Category:
Nonlinear Optics

History
Original Manuscript: June 9, 2010
Revised Manuscript: July 22, 2010
Manuscript Accepted: July 27, 2010
Published: September 20, 2010

Citation
Marco Santagiustina, Carlo G. Someda, Giovanni Vadala', Sylvain Combrie', and Alfredo De Rossi, "Theory of Slow Light Enhanced Four-Wave Mixing in Photonic Crystal Waveguides," Opt. Express 18, 21024-21029 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-20-21024


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. . Slow Light: Science and Applications, J. B. Khurgin and R. S. Tucker, Eds., (CRC Press, Boca Raton, 2009).
  2. . M. Santagiustina, “Governing the speed of light: recent advances and future perspectives of slow and fast light in microwave-photonics”, in Proc. 2009 Intern. Top. Meet. on Microwave Photonics, (Valencia, Spain, 2009) Th3.1.
  3. . T. Baba, “Slow light in photonic crystals.” Nat. Phot. 2, 465–473 (2008). [CrossRef]
  4. . N. A. R. Bhat, and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals”. Phys. Rev. E 64, 056604 (2001). [CrossRef]
  5. . M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002). [CrossRef]
  6. . T. Kamalakis, and T. Sphicopoulos, “A new formulation of coupled propagation equations in periodic nanophotonic waveguides for the treatment of Kerr-induced nonlinearities,” IEEE J. Quantum Electron. 43, 923-933 (2007). [CrossRef]
  7. . T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D: Appl. Phys. 40, 2666-2670 (2007). [CrossRef]
  8. . B. Corcoran, C. Monat, C. Grillet, D. Moss, B. J. Eggleton, T. White, L. O’Faolain, and T. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Phot. 3, 206-210 (2009). [CrossRef]
  9. . B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640Gb/s using slow-light,” Opt. Express 18, 7770-7781 (2010). [CrossRef] [PubMed]
  10. . S. Combrié, Q. Vy Tran, C. Husko, P. Colman, and A. De Rossi, “High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95, 221108 (2009). [CrossRef]
  11. . C. Husko, S. Combrié, Q. Tran, F. Raineri, C. Wong, and A. De Rossi, “Non-trivial scaling of self-phase modulation and three-photon absorptionin III-V photonic crystal waveguides,” Opt. Express 17, 22442-22451 (2009). [CrossRef]
  12. . V. Eckhouse, I. Cestier, G. Eisenstein, S. Combrié, P. Colman, A. De Rossi, M. Santagiustina, C. G. Someda, and G. Vadalà, “Highly efficient four wave mixing in GaInP photonic crystal waveguides,” Opt. Lett. 35, 1440-1442 (2010). [CrossRef] [PubMed]
  13. . T. Hasegawa, T. Nagashima, and N. Sugimoto, “Determination of nonlinear coefficient and group-velocity dispersion of bismuth-based high nonlinear optical fiber by four-wave mixing,” Opt. Commun. 281, 782-787 (2008). [CrossRef]
  14. . M. D. Pelusi, F. Luan, E. Magi, M. R. E. Lamont, D. J. Moss, B. J. Eggleton, J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal, “High bit rate all-optical signal processing in a fiber photonic wire,” Opt. Express 16, 11506-11512 (2008). [CrossRef] [PubMed]
  15. . M. Ebnali-Heidari, C. Monat, C. Grillet, and M. K. Moravvej-Farshi, “A proposal for enhancing four-wave mixing in slow light engineered photonic crystal waveguides and its application to optical regeneration,” Opt. Express 17, 18340-18353 (2009). [CrossRef] [PubMed]
  16. . http://ab-initio.mit.edu/photons/
  17. . N. C. Panoiu, J. F. McMillan, and C. W. Wong, “Theoretical analysis of pulse dynamics in silicon photonic crystal wire waveguides,” IEEE J. Sel. T. Quantum Electron. 16, 257-266 (2010). [CrossRef]
  18. . D. Michaelis, U. Peschel, C. Wächter, and A. Braüer, “Reciprocity theorem and perturbation theory for photonic crystal waveguides,” Phys. Rev. E 68, 065601(R) (2003). [CrossRef]
  19. . R. Boyd, Nonlinear Optics Chapt. 4 (Academic Press, San Diego, 2003).
  20. . P. Yeh, “Electromagnetic propagation in birefringent layered media,” J. Opt. Soc. Am. 69, 742 (1979). [CrossRef]
  21. . K. Sakoda, Optical Properties of Photonic Crystals, Chapt. 2 (Springer, Berlin, 2005).
  22. . B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdre, “Bloch wave propagation in two-dimensional photonic crystals: Influence of the polarization,” Opt. Q. Electr. 37, 293-307 (2005). [CrossRef]
  23. . G. P. Agrawal, Nonlinear fiber optics, Chapt. 10 (Academic Press, San Diego, 2001).
  24. . D. C. Hutchings, and B. S. Wherrett, “Polarisation dichroism of nonlinear refraction in zinc-blende semiconductors,” Opt. Commun. 111, 507–512 (1994). [CrossRef]
  25. . J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16, 6227-6232 (2008). [CrossRef] [PubMed]

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.

Figures

Fig. 1 Fig. 2
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited