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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 3 — Feb. 11, 2013
  • pp: 2832–2846

Theory of nonlinear pulse propagation in silicon-nanocrystal waveguides

Ivan D. Rukhlenko  »View Author Affiliations


Optics Express, Vol. 21, Issue 3, pp. 2832-2846 (2013)
http://dx.doi.org/10.1364/OE.21.002832


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Abstract

We develop a comprehensive theory of the nonlinear propagation of optical pulses through silica waveguides doped with highly nonlinear silicon nanocrystals. Our theory describes the dynamics of arbitrarily polarized pump and Stokes fields by a system of four generalized nonlinear Schrödinger equations for the slowly varying field amplitudes, coupled to the rate equation for the number density of free carriers. In deriving these equations, we use an analytic expression for the third-order effective susceptibility of the waveguide with randomly oriented nanocrystals, which takes into account both the weakening of the nonlinear optical response of silicon nanocrystals due to their embedment in fused silica and the change in the tensor properties of the response due to the modification of light interaction with electrons and phonons inside the silicon-nanocrystal waveguide. In order to facilitate the use of our theory by experimentalists, and for reasons of methodology, we provide a great deal of detail on the mathematical treatment throughout the paper, even though the derivation of the coupled-amplitude equations is quite straightforward. The developed theory can be applied for the solving of a wide variety of specific problems that require modeling of nonlinear optical phenomena in silicon-nanocrystal waveguides.

© 2013 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

History
Original Manuscript: December 14, 2012
Revised Manuscript: January 15, 2013
Manuscript Accepted: January 16, 2013
Published: January 29, 2013

Citation
Ivan D. Rukhlenko, "Theory of nonlinear pulse propagation in silicon-nanocrystal waveguides," Opt. Express 21, 2832-2846 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-3-2832


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References

  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. R. M. Osgood, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I.-W. Hsieh, E. Dulkeith, W. M. Green, and Y. A. Vlasov, “Engineering nonlinearities in nanoscale optical systems: Physics and applications in dispersion-engineered silicon nanophotonic wires,” Adv. Opt. Photonics1, 162–235 (2009). [CrossRef]
  4. 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]
  5. R. A. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron.12, 1678–1687 (2006). [CrossRef]
  6. G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (John Wiley, Hoboken, 2004). [CrossRef]
  7. L. Pavesi and D. Lockwood, eds., Silicon Photonics, vol. 94 of Topics in Applied Physics (Springer-Verlag, Berlin, 2004).
  8. M. Paniccia, “Integrating silicon photonics,” Nat. Photonics4, 498–499 (2010). [CrossRef]
  9. J. I. Dadap, N. C. Panoiu, X. Chen, I.-W. Hsieh, X. Liu, C.-Y. Chou, E. Dulkeith, S. J. McNab, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and J. R. M. Osgood, “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express16, 1280–1299 (2008). [CrossRef] [PubMed]
  10. C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express.15, 5976–5990 (2007). [CrossRef] [PubMed]
  11. X. Chen, N. C. Panoiu, I. Hsieh, J. I. Dadap, and R. M. Osgood, “Third-order dispersion and ultrafast-pulse propagation in silicon wire waveguides,” IEEE Photon. Technol. Lett.18, 2617–2619 (2006). [CrossRef]
  12. 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]
  13. C. Manolatou and M. Lipson, “All-optical silicon modulators based on carrier injection by two-photon absorption,” J. Lightwave Technol.24, 1433–1439 (2006). [CrossRef]
  14. R. Jones, A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Lossless optical modulation in a silicon waveguide using stimulated Raman scattering,” Opt. Express13, 1716–1723 (2005). [CrossRef] [PubMed]
  15. D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, “Ultrafast all-optical modulation via two-photon absorption in silicon-on-insulator waveguides,” Electron. Lett.41, 320–321 (2005). [CrossRef]
  16. I. D. Rukhlenko, M. Premaratne, I. L. Garanovich, A. A. Sukhorukov, and G. P. Agrawal, “Analytical study of pulse amplification in silicon Raman amplifiers,” Opt. Express18, 18324–18338 (2010). [CrossRef] [PubMed]
  17. M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman amplifiers with ring-resonator-enhanced pump power,” IEEE J. Sel. Top. Quantum Electron.16, 216–225 (2010). [CrossRef]
  18. 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]
  19. 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]
  20. M. Krause, H. Renner, S. Fathpour, B. Jalali, and E. Brinkmeyer, “Gain enhancement in cladding-pumped silicon Raman amplifiers,” IEEE J. Quantum Electron.44, 692–704 (2008). [CrossRef]
  21. 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,” Nature441, 960–963 (2006). [CrossRef] [PubMed]
  22. J. I. Dadap, R. L. Espinola, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Spontaneous Raman scattering in ultrasmall silicon waveguides,” Opt. Lett.29, 2755–2757 (2004). [CrossRef] [PubMed]
  23. D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics4, 511–517 (2010). [CrossRef]
  24. H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics2, 170–174 (2008). [CrossRef]
  25. M. Krause, H. Renner, and E. Brinkmeyer, “Analysis of Raman lasing characteristics in silicon-on-insulator waveguides,” Opt. Express12, 5703–5710 (2004). [CrossRef] [PubMed]
  26. O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express12, 5269–5273 (2004). [CrossRef] [PubMed]
  27. M. W. Geis, S. J. Spector, M. E. Grein, J. U. Yoon, D. M. Lennon, and T. M. Lyszczarz, “Silicon waveguide infrared photodiodes with > 35 GHz bandwidth and phototransistors with 50 AW-1 response,” Opt. Express17, 5193–5204 (2009). [CrossRef] [PubMed]
  28. W. Astar, J. B. Driscoll, X. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood, “Conversion of 10 Gb/s NRZ-OOK to RZ-OOK utilizing XPM in a Si nanowire,” Opt. Express17, 12987–12999 (2009). [CrossRef] [PubMed]
  29. 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]
  30. H. K. Tsang and Y. Liu, “Nonlinear optical properties of silicon waveguides,” Semicond. Sci. Technol.23, 064007 (2008). [CrossRef]
  31. M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express16, 1300–1320 (2008). [CrossRef] [PubMed]
  32. I.-W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C.-Y. Chou, F. Xia, W. M. Green, Y. A. Vlasov, and R. M. Osgood, “Supercontinuum generation in silicon photonic wires,” Opt. Express15, 15242–15249 (2007). [CrossRef] [PubMed]
  33. R. Espinola, J. Dadap, R. Osgood, S. McNab, and Y. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express13, 4341–4349 (2005). [CrossRef] [PubMed]
  34. M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, “Submicrosecond submilliwatt silicon-on-insulator thermooptic switch,” IEEE Photon. Technol. Lett.16, 2514–2516 (2004). [CrossRef]
  35. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82, 2954–2956 (2003). [CrossRef]
  36. I. D. Rukhlenko, W. Zhu, M. Premaratne, and G. P. Agrawal, “Effective third-order susceptibility of silicon-nanocrystal-doped silica,” Opt. Express20, 26275–26284 (2012). [CrossRef] [PubMed]
  37. L. Pavesi and R. Turan, eds., Silicon Nanocrystals: Fundamentals, Synthesis and Applications (WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2010).
  38. L. Khriachtchev, ed., Silicon Nanophotonics: Basic Principles, Present Status and Perspectives (Pan Stanford, Singapore, 2009).
  39. 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).
  40. F. Iori, E. Degoli, R. Magri, I. Marri, G. Cantele, D. Ninno, F. Trani, O. Pulci, and S. Ossicini, “Engineering silicon nanocrystals: Theoretical study of the effect of codoping with boron and phosphorus,” Phys. Rev. B76, 085302 (2007). [CrossRef]
  41. I. D. Rukhlenko and M. Premaratne, “Optimization of nonlinear performance of silicon-nanocrystal cylindrical nanowires,” IEEE Photonics J.4, 952–959 (2012). [CrossRef]
  42. F. D. Leonardis and V. M. N. Passaro, “Dispersion engineered silicon nanocrystal slot waveguides for soliton ultrafast optical processing,” Adv. OptoElectron.2011, 751498 (2011).
  43. L. Sirleto, M. A. Ferrara, T. Nikitin, S. Novikov, and L. Khriachtchev, “Giant Raman gain in silicon nanocrystals,” Nat. Commun.3, 1220 (2012). [CrossRef] [PubMed]
  44. K. Imakita, M. Ito, R. Naruiwa, M. Fujii, and S. Hayashi, “Enhancement of ultrafast nonlinear optical response of silicon nanocrystals by boron-doping,” Opt. Lett.37, 1877–1879 (2012). [CrossRef] [PubMed]
  45. R. J. Kashtiban, U. Bangert, I. F. Crowe, M. Halsall, A. J. Harvey, and M. Gass, “Study of erbium-doped silicon nanocrystals in silica,” J. Phys.: Conference Series241, 012097 (2010). [CrossRef]
  46. R. J. Walters, G. I. Bourianoff, and H. A. Atwater, “Field-effect electroluminescence in silicon nanocrystals,” Nat. Mater.4, 143–146 (2005). [CrossRef] [PubMed]
  47. T. Nikitin, R. Velagapudi, J. Sainio, J. Lahtinen, M. Räsänen, S. Novikov, and L. Khriachtchev, “Optical and structural properties of SiOx films grown by molecular beam deposition: Effect of the Si concentration and annealing temperature,” J. Appl. Phys.112, 094316–094316 (2012). [CrossRef]
  48. J. Wei, J. Price, T. Wang, C. Hessel, and M. C. Downer, “Size-dependent optical properties of Si nanocrystals embedded in amorphous SiO2 measured by spectroscopic ellipsometry,” J. Vac. Sci. Technol. B29, 04D112 (2011). [CrossRef]
  49. T. Nikitin, K. Aitola, S. Novikov, M. Räsänen, R. Velagapudi, J. Sainio, J. Lahtinen, K. Mizohata, T. Ahlgren, and L. Khriachtchev, “Optical and structural properties of silicon-rich silicon oxide films: Comparison of ion implantation and molecular beam deposition methods,” Phys. Status Solidi (a)208, 2176–2181 (2011). [CrossRef]
  50. L. Ding, T. P. Chen, Y. Liu, C. Y. Ng, and S. Fung, “Optical properties of silicon nanocrystals embedded in a SiO2 matrix,” Phys. Rev. B72, 125419 (2005). [CrossRef]
  51. 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]
  52. F. Trani, D. Ninno, and G. Iadonisi, “Role of local fields in the optical properties of silicon nanocrystals using the tight binding approach,” Phys. Rev. B75, 033312 (2007). [CrossRef]
  53. C. M. Dissanayake, I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Raman-mediated nonlinear interactions in silicon waveguides: Copropagating and counterpropagating pulses,” IEEE Photonics Technol. Lett.21, 1372–1374 (2009). [CrossRef]
  54. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear propagation in silicon-based plasmonic waveguides from the standpoint of applications,” Opt. Express19, 206–217 (2011). [CrossRef] [PubMed]
  55. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Analytical study of optical bistability in silicon ring resonators,” Opt. Lett.35, 55–57 (2010). [CrossRef] [PubMed]
  56. B. A. Daniel and G. P. Agrawal, “Vectorial nonlinear propagation in silicon nanowire waveguides: Polarization effects,” J. Opt. Soc. Am. B27, 956–965 (2010). [CrossRef]
  57. I. D. Rukhlenko, C. Dissanayake, M. Premaratne, and G. P. Agrawal, “Optimization of Raman amplification in silicon waveguides with finite facet reflectivities,” IEEE J. Sel. Top. Quantum Electron.16, 226–233 (2010). [CrossRef]
  58. I. D. Rukhlenko, I. Udagedara, M. Premaratne, and G. P. Agrawal, “Effect of free carriers on pump-to-signal noise transfer in silicon Raman amplifiers,” Opt. Lett.35, 2343–2345 (2010). [CrossRef] [PubMed]
  59. M. D. Turner, T. M. Monro, and S. Afshar V., “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part II: Stimulated Raman scattering,” Opt. Express17, 11565–11581 (2009). [CrossRef] [PubMed]
  60. 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]
  61. I. D. Rukhlenko, M. Premaratne, C. Dissanayake, and G. P. Agrawal, “Nonlinear pulse evolution in silicon waveguides: An approximate analytic approach,” J. Lightwave Technol.27, 3241–3248 (2009). [CrossRef]
  62. D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, “Coupled-mode theory of Raman effect in silicon-on-insulator waveguides,” Opt. Lett.28, 1954–1956 (2003). [CrossRef] [PubMed]
  63. S. Afshar V. and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express17, 2298–2318 (2009). [CrossRef] [PubMed]
  64. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, San Diego, 2008).
  65. X. Chen, N. C. Panoiu, and R. M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron.42, 160–170 (2006). [CrossRef]
  66. 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]
  67. 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]
  68. W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, New York, 2010).
  69. C. M. Dissanayake, M. Premaratne, I. D. Rukhlenko, and G. P. Agrawal, “FDTD modeling of anisotropic nonlinear optical phenomena in silicon waveguides,” Opt. Express18, 21427–21448 (2010). [CrossRef] [PubMed]
  70. F. Trojanek, K. Neudert, K. Zidek, K. Dohnalova, I. Pelant, and P. Maly, “Femtosecond photoluminescence spectroscopy of silicon nanocrystals,” Physica Status Solidi (c)3, 3873–3876 (2006). [CrossRef]
  71. R. Spano, N. Daldosso, M. Cazzanelli, L. Ferraioli, L. Tartara, J. Yu, V. Degiorgio, E. Giordana, J. M. Fedeli, and L. Pavesi, “Bound electronic and free carrier nonlinearities in silicon nanocrystals at 1550 nm,” Opt. Express17, 3941–3950 (2009). [CrossRef] [PubMed]
  72. M. A. Ferrara, I. Rendina, S. N. Basu, L. D. Negro, and L. Sirleto, “Raman amplifier based on amorphous silicon nanoparticles,” Int. J. Photoenergy2012, 254946 (2012). [CrossRef]
  73. M. A. Ferrara, I. Rendina, and L. Sirleto, “Stimulated Raman scattering in quantum dots and nanocomposite silicon based materials,” in “Nonlinear Optics,” N. Kamanina, ed. (InTech, Rijeka, 2012), pp. 53–70.
  74. H. Richter, Z. P. Wang, and L. Ley, “The one phonon Raman spectrum in microcrystalline silicon,” Solid State Commun.39, 625–629 (1981). [CrossRef]
  75. I. H. Campbell and P. M. Fauchet, “The effects of microcrystal size and shape on the one phonon Raman spectra of crystalline semiconductors,” Solid State Commun.58, 739–741 (1986). [CrossRef]
  76. L. Cao, B. Nabet, and J. E. Spanier, “Enhanced Raman scattering from individual semiconductor nanocones and nanowires,” Phys. Rev. Lett.96, 157402 (2006). [CrossRef] [PubMed]
  77. R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light-matter interaction at the nanometre scale,” Nature418, 159–162 (2002). [CrossRef] [PubMed]
  78. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2007).
  79. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: Analytical tools,” IEEE J. Sel. Top. Quantum Electron.16, 200–215 (2010). [CrossRef]
  80. 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 Photonics J.2, 423–435 (2010). [CrossRef]

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