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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 24 — Nov. 19, 2012
  • pp: 26275–26284

Effective third-order susceptibility of silicon-nanocrystal-doped silica

Ivan D. Rukhlenko, Weiren Zhu, Malin Premaratne, and Govind P. Agrawal  »View Author Affiliations

Optics Express, Vol. 20, Issue 24, pp. 26275-26284 (2012)

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We derive approximate analytic expressions for the effective susceptibility tensor of a nonlinear composite, consisting of silicon nanocrystals embedded in fused silica. Two types of composites are considered: by assuming that (i) the crystallographic axes of different crystallites are the same, or (ii) crystallites are oriented randomly. In the first case, the tensor properties of the effective third-order susceptibility are shown to coincide with those of the bulk silicon. In the second case, however, the tensor properties of the susceptibility of the composite material are found to be quite different due to drastic modification of light interaction with optical phonons inside the composite. The newly derived expressions should be useful for modeling nonlinear optical phenomena in silica fibers and waveguides doped with silicon nanocrystals.

© 2012 OSA

OCIS Codes
(160.4330) Materials : Nonlinear optical materials
(190.0190) Nonlinear optics : Nonlinear optics
(190.4400) Nonlinear optics : Nonlinear optics, materials
(260.2065) Physical optics : Effective medium theory

ToC Category:
Nonlinear Optics

Original Manuscript: October 1, 2012
Revised Manuscript: October 27, 2012
Manuscript Accepted: October 27, 2012
Published: November 6, 2012

Ivan D. Rukhlenko, Weiren Zhu, Malin Premaratne, and Govind P. Agrawal, "Effective third-order susceptibility of silicon-nanocrystal-doped silica," Opt. Express 20, 26275-26284 (2012)

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  1. R. Soref and J. Lorenzo, “All-silicon active and passive guided-wave components for λ = 1.3 and 1.6 μm,” IEEE J. Quantum Electron.22, 873–879 (1986). [CrossRef]
  2. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics4, 535–544 (2010). [CrossRef]
  3. L. Pavesi and D. Lockwood, eds., Silicon Photonics, vol. 94 of Topics in Applied Physics (Springer-Verlag, Berlin, 2004).
  4. D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics4, 511–517 (2010). [CrossRef]
  5. I. D. Rukhlenko, C. Dissanayake, M. Premaratne, and G. P. Agrawal, “Maximization of net optical gain in silicon-waveguide Raman amplifiers,” Opt. Express17, 5807–5814 (2009). [CrossRef] [PubMed]
  6. A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, “Ultrafast all-optical switching in a silicon-nanocrystal-based silicon slot waveguide at telecom wavelengths,” Nano Lett.10, 1506–1511 (2010). [CrossRef] [PubMed]
  7. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Analytical study of optical bistability in silicon-waveguide resonators,” Opt. Express17, 22124–22137 (2009). [CrossRef] [PubMed]
  8. M. Paniccia, “Integrating silicon photonics,” Nat. Photonics4, 498–499 (2010). [CrossRef]
  9. L. Pavesi and R. Turan, eds., Silicon Nanocrystals: Fundamentals, Synthesis and Applications (WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2010).
  10. L. Khriachtchev, ed., Silicon Nanophotonics: Basic Principles, Present Status and Perspectives (Pan Stanford, Singapore, 2009).
  11. I. D. Rukhlenko and M. Premaratne, “Optimization of nonlinear performance of silicon-nanocrystal cylindrical nanowires,” IEEE Photon. J.4, 952–959 (2012). [CrossRef]
  12. F. D. Leonardis and V. M. N. Passaro, “Dispersion engineered silicon nanocrystal slot waveguides for soliton ultrafast optical processing,” Adv. OptoElectron.2011, 751498 (2011).
  13. P. Sanchis, J. Blasco, A. Martinez, and J. Marti, “Design of silicon-based slot waveguide configurations for optimum nonlinear performance,” J. Lightwave Technol.25, 1298–1305 (2007). [CrossRef]
  14. V. A. Belyakov, V. A. Burdov, R. Lockwood, and A. Meldrum, “Silicon nanocrystals: Fundamental theory and implications for stimulated emission,” Adv. Opt. Technol.2008, 279502 (2008).
  15. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Effective mode area and its optimization in silicon-nanocrystal waveguides,” Opt. Lett.37, 2295–2297 (2012). [CrossRef] [PubMed]
  16. D. Stroud and P. M. Hui, “Nonlinear susceptibilities of granular matter,” Phys. Rev. B37, 8719–8724 (1988). [CrossRef]
  17. X. C. Zeng, D. J. Bergman, P. M. Hui, and D. Stroud, “Effective-medium theory for weakly nonlinear composites,” Phys. Rev. B38, 10970–10973 (1988). [CrossRef]
  18. D. J. Bergman, “The dielectric constant of a composite material – a problem in classical physics,” Phys. Rep.43, 377–407 (1978). [CrossRef]
  19. S. N. Volkov, J. J. Saarinen, and J. E. Sipe, “Effective medium theory for 2D disordered structures: A comparison to numerical simulations,” J. Mod. Opt.59, 954–961 (2012). [CrossRef]
  20. W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, New York, 2010).
  21. R. W. Boyd, R. J. Gehr, G. L. Fischer, and J. E. Sipe, “Nonlinear optical properties of nanocomposite materials,” Pure Appl. Opt.5, 505–512 (1996). [CrossRef]
  22. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1998).
  23. P. M. Hui, P. Cheung, and D. Stroud, “Theory of third harmonic generation in random composites of nonlinear dielectrics,” J. Appl. Phys.84, 3451–3458 (1998). [CrossRef]
  24. D. Stroud, “Generalized effective-medium approach to the conductivity of an inhomogeneous material,” Phys. Rev. B12, 3368–3373 (1975). [CrossRef]
  25. J. Sipe and R. Boyd, “Nanocomposite materials for nonlinear optics based on local field effects,” in “Optical Properties of Nanostructured Random Media,”, vol. 82 of Topics Appl. Phys., V. M. Shalaev, ed. (Springer-Verlag, BerlinHeidelberg, 2002), pp. 1–19. [CrossRef]
  26. G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett.74, 1871–1874 (1995). [CrossRef] [PubMed]
  27. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, San Diego, 2008).
  28. J. Wei, A. Wirth, M. C. Downer, and B. S. Mendoza, “Second-harmonic and linear optical spectroscopic study of silicon nanocrystals embedded in SiO2,” Phys. Rev. B84, 165316 (2011). [CrossRef]
  29. Y. Jiang, P. T. Wilson, M. C. Downer, C. W. White, and S. P. Withrow, “Second-harmonic generation from silicon nanocrystals embedded in SiO2,” Appl. Phys. Lett.78, 766 (2001). [CrossRef]
  30. W. L. Mochan, J. A. Maytorena, B. S. Mendoza, and V. L. Brudny, “Second-harmonic generation in arrays of spherical particles,” Phys. Rev. B68, 085318 (2003). [CrossRef]
  31. J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett.83, 4045–4048 (1999). [CrossRef]
  32. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express15, 16604–16644 (2007). [CrossRef] [PubMed]
  33. M. Premaratne and G. P. Agrawal, Light Propagation in Gain Media (Cambridge Univ. Press, Cambridge, 2011).
  34. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2007).
  35. R. M. Murray, Z. Li, and S. S. Sastry, A Mathematical Introduction to Robotic Manipulation (CRC Press, Boca Raton, FL, 1994).
  36. W. Grieshaber, E. Belorizky, and M. L. Berre, “A general method for tensor averaging and an application to polycrystalline materials,” Solid State Commun.93, 805–809 (1995). [CrossRef]
  37. I. D. Rukhlenko, M. Premaratne, C. Dissanayake, and G. P. Agrawal, “Continuous-wave Raman amplification in silicon waveguides: Beyond the undepleted pump approximation,” Opt. Lett.34, 536–538 (2009). [CrossRef] [PubMed]
  38. L. Yin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Optical switching using nonlinear polarization rotation inside silicon waveguides,” Opt. Lett.34, 476–478 (2009). [CrossRef] [PubMed]
  39. I. D. Rukhlenko, I. L. Garanovich, M. Premaratne, A. A. Sukhorukov, G. P. Agrawal, and Y. S. Kivshar, “Polarization rotation in silicon waveguides: Analytical modeling and applications,” IEEE Photon. J.2, 423–435 (2010). [CrossRef]
  40. C. Torres-Torres, A. López-Suárez, R. Torres-Martínez, A. Rodriguez, J. A. Reyes-Esqueda, L. Castaneda, J. C. Alonso, and A. Oliver, “Modulation of the propagation speed of mechanical waves in silicon quantum dots embedded in a silicon-nitride film,” Opt. Express20, 4784–4789 (2012). [CrossRef] [PubMed]

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