Abstract

The strength of the nonlinear optical effects in silicon–nanocrystal waveguides can be varied as required for applications by altering the geometry of the waveguide and the composition of its nonlinear core. By studying theoretically the geometric and composition dependencies of the mode overlap factors responsible for the nonlinear interaction between the pump and Stokes optical fields, which are separated by the Raman shift in silicon, we demonstrate that this strength can be varied in a wide range, thus offering broad opportunities for engineering optical nonlinearities in silicon–nanocrystal waveguides. The numerically calculated mode overlap factors are useful in modeling light propagation through nonlinear silicon–nanocrystal waveguides governed by the recently derived generalized nonlinear Schrödinger equations.

© 2013 Optical Society of America

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  26. B. A. Daniel and G. P. Agrawal, “Vectorial nonlinear propagation in silicon nanowire waveguides: polarization effects,” J. Opt. Soc. Am. B 27, 956–965 (2010).
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  27. 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]
  28. 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]
  29. 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]
  30. C. M. Dissanayake, I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Raman-mediated nonlinear interactions in silicon waveguides: copropagating and counterpropagating pulses,” IEEE Photon. Technol. Lett. 21, 1372–1374 (2009).
    [CrossRef]
  31. 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. Express 17, 11565–11581 (2009).
    [CrossRef]
  32. 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]
  33. 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]
  34. 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]
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  38. 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]
  39. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Maximization of gain in slow-light silicon Raman amplifiers,” Int. J. Opt. 2011, 581810 (2011).
    [CrossRef]
  40. I. D. Rukhlenko, C. Dissanayake, M. Premaratne, and G. P. Agrawal, “Maximization of net optical gain in silicon-waveguide Raman amplifiers,” Opt. Express 17, 5807–5814 (2009).
    [CrossRef]
  41. 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]

2013 (1)

2012 (7)

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]

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]

I. D. Rukhlenko, W. Zhu, M. Premaratne, and G. P. Agrawal, “Effective third-order susceptibility of silicon–nanocrystal-doped silica,” Opt. Express 20, 26275–26284 (2012).
[CrossRef]

L. Sirleto, M. A. Ferrara, T. Nikitin, S. Novikov, and L. Khriachtchev, “Giant Raman gain in silicon nanocrystals,” Nat. Commun. 3, 1220 (2012).
[CrossRef]

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]

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 (2012).
[CrossRef]

I. D. Rukhlenko and M. Premaratne, “Optimization of nonlinear performance of silicon–nanocrystal cylindrical nanowires,” IEEE Photon. J. 4, 952–959 (2012).
[CrossRef]

2011 (5)

F. D. Leonardis and V. M. N. Passaro, “Dispersion engineered silicon nanocrystal slot waveguides for soliton ultrafast optical processing,” Adv. Optoelectron. 2011, 751498 (2011).
[CrossRef]

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. B 29, 04D112 (2011).
[CrossRef]

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,” Physica Status Solidi A 208, 2176–2181 (2011).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Maximization of gain in slow-light silicon Raman amplifiers,” Int. J. Opt. 2011, 581810 (2011).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear propagation in silicon-based plasmonic waveguides from the standpoint of applications,” Opt. Express 19, 206–217 (2011).
[CrossRef]

2010 (11)

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]

B. A. Daniel and G. P. Agrawal, “Vectorial nonlinear propagation in silicon nanowire waveguides: polarization effects,” J. Opt. Soc. Am. B 27, 956–965 (2010).
[CrossRef]

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]

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]

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]

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]

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. Conf. Ser. 241, 012097 (2010).
[CrossRef]

M. Paniccia, “Integrating silicon photonics,” Nat. Photonics 4, 498–499 (2010).
[CrossRef]

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4, 511–517 (2010).
[CrossRef]

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. Express 18, 18324–18338 (2010).
[CrossRef]

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[CrossRef]

2009 (7)

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. Photon. 1, 162–235 (2009).
[CrossRef]

C. M. Dissanayake, I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Raman-mediated nonlinear interactions in silicon waveguides: copropagating and counterpropagating pulses,” IEEE Photon. Technol. Lett. 21, 1372–1374 (2009).
[CrossRef]

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. Express 17, 11565–11581 (2009).
[CrossRef]

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]

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]

I. D. Rukhlenko, C. Dissanayake, M. Premaratne, and G. P. Agrawal, “Maximization of net optical gain in silicon-waveguide Raman amplifiers,” Opt. Express 17, 5807–5814 (2009).
[CrossRef]

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]

2008 (1)

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).
[CrossRef]

2007 (2)

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. B 76, 085302 (2007).
[CrossRef]

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]

2006 (1)

R. A. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006).
[CrossRef]

2005 (1)

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. B 72, 125419 (2005).
[CrossRef]

Afshar V., S.

Agrawal, G. P.

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]

I. D. Rukhlenko, W. Zhu, M. Premaratne, and G. P. Agrawal, “Effective third-order susceptibility of silicon–nanocrystal-doped silica,” Opt. Express 20, 26275–26284 (2012).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear propagation in silicon-based plasmonic waveguides from the standpoint of applications,” Opt. Express 19, 206–217 (2011).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Maximization of gain in slow-light silicon Raman amplifiers,” Int. J. Opt. 2011, 581810 (2011).
[CrossRef]

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]

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]

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]

B. A. Daniel and G. P. Agrawal, “Vectorial nonlinear propagation in silicon nanowire waveguides: polarization effects,” J. Opt. Soc. Am. B 27, 956–965 (2010).
[CrossRef]

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]

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. Express 18, 18324–18338 (2010).
[CrossRef]

I. D. Rukhlenko, C. Dissanayake, M. Premaratne, and G. P. Agrawal, “Maximization of net optical gain in silicon-waveguide Raman amplifiers,” Opt. Express 17, 5807–5814 (2009).
[CrossRef]

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]

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]

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]

C. M. Dissanayake, I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Raman-mediated nonlinear interactions in silicon waveguides: copropagating and counterpropagating pulses,” IEEE Photon. Technol. Lett. 21, 1372–1374 (2009).
[CrossRef]

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]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

Ahlgren, T.

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,” Physica Status Solidi A 208, 2176–2181 (2011).
[CrossRef]

Aitola, K.

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,” Physica Status Solidi A 208, 2176–2181 (2011).
[CrossRef]

Bangert, U.

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. Conf. Ser. 241, 012097 (2010).
[CrossRef]

Belyakov, V. A.

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).
[CrossRef]

Blasco, J.

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]

Bowers, J. E.

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4, 511–517 (2010).
[CrossRef]

Burdov, V. A.

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).
[CrossRef]

Cai, W.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).

Cantele, G.

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. B 76, 085302 (2007).
[CrossRef]

Chen, T. P.

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. B 72, 125419 (2005).
[CrossRef]

Chen, X.

Crowe, I. F.

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. Conf. Ser. 241, 012097 (2010).
[CrossRef]

Dadap, J. I.

Daldosso, N.

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]

Daniel, B. A.

Degoli, E.

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. B 76, 085302 (2007).
[CrossRef]

Ding, L.

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. B 72, 125419 (2005).
[CrossRef]

Dissanayake, C.

Dissanayake, C. M.

C. M. Dissanayake, I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Raman-mediated nonlinear interactions in silicon waveguides: copropagating and counterpropagating pulses,” IEEE Photon. Technol. Lett. 21, 1372–1374 (2009).
[CrossRef]

Downer, M. C.

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. B 29, 04D112 (2011).
[CrossRef]

Dulkeith, E.

Fauchet, P. M.

Fedeli, J. M.

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]

Ferrara, M. A.

L. Sirleto, M. A. Ferrara, T. Nikitin, S. Novikov, and L. Khriachtchev, “Giant Raman gain in silicon nanocrystals,” Nat. Commun. 3, 1220 (2012).
[CrossRef]

Freude, W.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[CrossRef]

Fujii, M.

Fung, S.

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. B 72, 125419 (2005).
[CrossRef]

Galan, J. V.

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]

Garanovich, I. L.

Garcia-Ruperez, J.

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]

Garrido, B.

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]

Gass, M.

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. Conf. Ser. 241, 012097 (2010).
[CrossRef]

Gautier, P.

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]

Green, W. M.

Guider, R.

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]

Halsall, M.

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. Conf. Ser. 241, 012097 (2010).
[CrossRef]

Harvey, A. J.

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. Conf. Ser. 241, 012097 (2010).
[CrossRef]

Hayashi, S.

Hernandez, S.

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]

Hessel, C.

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. B 29, 04D112 (2011).
[CrossRef]

Hsieh, I.-W.

Imakita, K.

Iori, F.

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. B 76, 085302 (2007).
[CrossRef]

Ito, M.

Jordana, E.

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]

Kashtiban, R. J.

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. Conf. Ser. 241, 012097 (2010).
[CrossRef]

Khriachtchev, L.

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 (2012).
[CrossRef]

L. Sirleto, M. A. Ferrara, T. Nikitin, S. Novikov, and L. Khriachtchev, “Giant Raman gain in silicon nanocrystals,” Nat. Commun. 3, 1220 (2012).
[CrossRef]

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,” Physica Status Solidi A 208, 2176–2181 (2011).
[CrossRef]

Knights, A. P.

G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (Wiley, 2004).

Koos, C.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[CrossRef]

Lahtinen, J.

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 (2012).
[CrossRef]

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,” Physica Status Solidi A 208, 2176–2181 (2011).
[CrossRef]

Lebour, Y.

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]

Leonardis, F. D.

F. D. Leonardis and V. M. N. Passaro, “Dispersion engineered silicon nanocrystal slot waveguides for soliton ultrafast optical processing,” Adv. Optoelectron. 2011, 751498 (2011).
[CrossRef]

Leuthold, J.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[CrossRef]

Liang, D.

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4, 511–517 (2010).
[CrossRef]

Lin, Q.

Liu, X.

Liu, Y.

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. B 72, 125419 (2005).
[CrossRef]

Lockwood, R.

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).
[CrossRef]

Magri, R.

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. B 76, 085302 (2007).
[CrossRef]

Marri, I.

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. B 76, 085302 (2007).
[CrossRef]

Marti, J.

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]

Martinez, A.

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]

Meldrum, A.

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).
[CrossRef]

Mizohata, K.

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,” Physica Status Solidi A 208, 2176–2181 (2011).
[CrossRef]

Monro, T. M.

Naruiwa, R.

Ng, C. Y.

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. B 72, 125419 (2005).
[CrossRef]

Nikitin, T.

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 (2012).
[CrossRef]

L. Sirleto, M. A. Ferrara, T. Nikitin, S. Novikov, and L. Khriachtchev, “Giant Raman gain in silicon nanocrystals,” Nat. Commun. 3, 1220 (2012).
[CrossRef]

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,” Physica Status Solidi A 208, 2176–2181 (2011).
[CrossRef]

Ninno, D.

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. B 76, 085302 (2007).
[CrossRef]

Novikov, S.

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 (2012).
[CrossRef]

L. Sirleto, M. A. Ferrara, T. Nikitin, S. Novikov, and L. Khriachtchev, “Giant Raman gain in silicon nanocrystals,” Nat. Commun. 3, 1220 (2012).
[CrossRef]

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,” Physica Status Solidi A 208, 2176–2181 (2011).
[CrossRef]

Osgood, R. M.

Ossicini, S.

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. B 76, 085302 (2007).
[CrossRef]

Painter, O. J.

Paniccia, M.

M. Paniccia, “Integrating silicon photonics,” Nat. Photonics 4, 498–499 (2010).
[CrossRef]

Panoiu, N. C.

Passaro, V. M. N.

F. D. Leonardis and V. M. N. Passaro, “Dispersion engineered silicon nanocrystal slot waveguides for soliton ultrafast optical processing,” Adv. Optoelectron. 2011, 751498 (2011).
[CrossRef]

Pavesi, L.

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]

Premaratne, M.

I. D. Rukhlenko and M. Premaratne, “Optimization of nonlinear performance of silicon–nanocrystal cylindrical nanowires,” IEEE Photon. J. 4, 952–959 (2012).
[CrossRef]

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]

I. D. Rukhlenko, W. Zhu, M. Premaratne, and G. P. Agrawal, “Effective third-order susceptibility of silicon–nanocrystal-doped silica,” Opt. Express 20, 26275–26284 (2012).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear propagation in silicon-based plasmonic waveguides from the standpoint of applications,” Opt. Express 19, 206–217 (2011).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Maximization of gain in slow-light silicon Raman amplifiers,” Int. J. Opt. 2011, 581810 (2011).
[CrossRef]

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]

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]

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]

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]

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. Express 18, 18324–18338 (2010).
[CrossRef]

C. M. Dissanayake, I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Raman-mediated nonlinear interactions in silicon waveguides: copropagating and counterpropagating pulses,” IEEE Photon. Technol. Lett. 21, 1372–1374 (2009).
[CrossRef]

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]

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]

I. D. Rukhlenko, C. Dissanayake, M. Premaratne, and G. P. Agrawal, “Maximization of net optical gain in silicon-waveguide Raman amplifiers,” Opt. Express 17, 5807–5814 (2009).
[CrossRef]

Price, J.

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. B 29, 04D112 (2011).
[CrossRef]

Pulci, O.

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. B 76, 085302 (2007).
[CrossRef]

Räsänen, M.

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 (2012).
[CrossRef]

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,” Physica Status Solidi A 208, 2176–2181 (2011).
[CrossRef]

Reed, G. T.

G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (Wiley, 2004).

Rukhlenko, I. D.

I. D. Rukhlenko, “Theory of nonlinear pulse propagation in silicon–nanocrystal waveguides,” Opt. Express 21, 2832–2846 (2013).
[CrossRef]

I. D. Rukhlenko, W. Zhu, M. Premaratne, and G. P. Agrawal, “Effective third-order susceptibility of silicon–nanocrystal-doped silica,” Opt. Express 20, 26275–26284 (2012).
[CrossRef]

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]

I. D. Rukhlenko and M. Premaratne, “Optimization of nonlinear performance of silicon–nanocrystal cylindrical nanowires,” IEEE Photon. J. 4, 952–959 (2012).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Maximization of gain in slow-light silicon Raman amplifiers,” Int. J. Opt. 2011, 581810 (2011).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear propagation in silicon-based plasmonic waveguides from the standpoint of applications,” Opt. Express 19, 206–217 (2011).
[CrossRef]

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]

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]

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]

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. Express 18, 18324–18338 (2010).
[CrossRef]

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]

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]

I. D. Rukhlenko, C. Dissanayake, M. Premaratne, and G. P. Agrawal, “Maximization of net optical gain in silicon-waveguide Raman amplifiers,” Opt. Express 17, 5807–5814 (2009).
[CrossRef]

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]

C. M. Dissanayake, I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Raman-mediated nonlinear interactions in silicon waveguides: copropagating and counterpropagating pulses,” IEEE Photon. Technol. Lett. 21, 1372–1374 (2009).
[CrossRef]

Saarinen, J. J.

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).
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Sainio, J.

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 (2012).
[CrossRef]

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,” Physica Status Solidi A 208, 2176–2181 (2011).
[CrossRef]

Sanchis, P.

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).
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Shalaev, V.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).

Sipe, J. E.

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]

Sirleto, L.

L. Sirleto, M. A. Ferrara, T. Nikitin, S. Novikov, and L. Khriachtchev, “Giant Raman gain in silicon nanocrystals,” Nat. Commun. 3, 1220 (2012).
[CrossRef]

Soref, R. A.

R. A. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006).
[CrossRef]

Spano, R.

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]

Sukhorukov, A. A.

Trani, F.

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. B 76, 085302 (2007).
[CrossRef]

Turner, M. D.

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Figures (5)

Fig. 1.
Fig. 1.

Cross-sections of two types of silicon–nanocrystal waveguides considered in the paper. In both cases, the nonlinear core of the waveguide has a rectangular cross section of height h and width w, and is made of fused silica (SiO2) doped with highly nonlinear silicon nanocrystals (Si NCs). The core is (a) surrounded by air and (b) embedded in silicon slab of thickness w.

Fig. 2.
Fig. 2.

Snapshots of electric and magnetic fields of (a), (b) x-polarized and (c)–(f) y-polarized propagating modes inside silicon–nanocrystal waveguides shown in (a)–(d) Fig. 1(a) and (e), (f) Fig. 1(b). The geometric parameters are w=2h in (a)–(d) and w=6h in (e), (f); w=600nm, λs=1.55μm, and f=0.1 (neff1.596) in all cases.

Fig. 3.
Fig. 3.

(a) Mode overlap factors and (b) the corresponding effective mode areas (left scale, solid curves) and effective refractive indices (right scale, dashed curves) as functions of width of silicon–nanocrystal waveguide [shown in Fig. 1(b)] for h=100nm and f=10%. For other parameters, refer to the text.

Fig. 4.
Fig. 4.

(a) Mode overlap factors and (b) the corresponding effective mode areas (left scale, solid curves) and effective refractive indices (right scale, dashed curves) as functions of height of silicon–nanocrystal waveguide [shown in Fig. 1(b)] for w=300nm and f=10%. For other parameters, refer to the text.

Fig. 5.
Fig. 5.

(a) Mode overlap factors and (b) the corresponding effective mode areas (left scale, solid curves) and effective refractive indices (right scale, dashed curves) as functions of volume fraction of silicon nanocrystals for w=3h=300nm [see Fig. 1(b)]. For other parameters, refer to the text.

Equations (8)

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Eμ(0)(r,t)=eμν(x,y,ωμ)Nμνexp[i(βμνzωμt)]
Hμ(0)(r,t)=hμν(x,y,ωμ)Nμνexp[i(βμνzωμt)],
γννμμ=neff2nμνnμνANL|eμν|2|eμν|2dxdy×(|eμν|2dxdyNL|eμν|2dxdy)1,
Aeffμν=ANL|eμν|2dxdy/NL|eμν|2dxdy.
Γ=(γxxssγxyssγyxssγyyssγxxspγxyspγyxspγyyspγxxpsγxypsγyxpsγyypsγxxppγxyppγyxppγyypp).
neff2=14(u+u2+8ε1ε2),
1ξ(lnapz+αp2)=q(βTPA2in2kp)(γyyppIp+2γyypsIs)6445gRγyypsIsqζτcneffnpy(ωsωp)2(σα2+iσ¯nkp)×[βTPA2ωp(γyyppIp+2γyypsIs)Ip+βTPA2ωs(γyyssIs+2γyyspIp)Is]
1ξ(lnasz+αs2)=q(βTPA2in2ks)(γyyssIs+2γyyspIp)+6445gRγyyspIpqζτcneffnsy(σα2+iσ¯nks)×[βTPA2ωp(γyyppIp+2γyypsIs)Ip+βTPA2ωs(γyyssIs+2γyyspIp)Is],

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