Abstract

Using a self-diffraction experiment with 7ns pulses at 532nm we studied a silicon nitride film containing silicon nanoclusters (nc-Si) of 3.1±0.37 nm mean size. The sample was prepared by remote plasma-enhanced chemical vapor deposition (RPECVD), and we found that its nonlinearity consists of a combination of electronic and thermal contributions. By varying the repetition rate of the laser, we discriminated the responsible mechanisms for the nonlinear response. Using this procedure we determined a total |χ (3)1111|=3.3×10-10esu, n2=2.7×10-16 m2/W, β=1×10-9 m/W and dn/dT=1×10-4 oC-1 for our sample. We also show results for the optical Kerr effect using 80 fs pulses at 820 nm. The purely electronic nonlinearity measured is characterized by |χ (3)1111|=9.5×10-11 esu.

© 2008 Optical Society of America

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  1. L. Domash, M. Wu, N. Nemchuk, E. Ma, "Tunable and Switchable Multiple Cavity Thin Film Filters," J. Lightwave Technol. 22, 126-135 (2004).
    [CrossRef]
  2. M. W. Pruessner, T. H. Stievater, M. S. Ferraro, W. S. Rabinovich, "Thermo-optic tuning and switching in SOI waveguide Fabry-Perot microcavities," Opt. Express,  15, 7557-7563 (2007).
    [CrossRef] [PubMed]
  3. Y.  Li, J.  Yu, and S.  Chen, "Rearrangeable nonblocking SOI waveguide thermo optic 4×4 switch matrix with low insertion loss and fast response," IEEE Photon. Technol. Lett.  17, 1641-1643 (2005).
    [CrossRef]
  4. R. W. Boyd, Nonlinear Optics, (Academic Press, San Diego, 1992).
  5. M. von Allmen and A. BlatterLaser-beam interaction with materials, (Berlin,Springer,1995) Chap. 3.
    [CrossRef]
  6. C. Torres-Torres, A. V. Khomenko, J. C. Cheang-Wong, L. Rodríguez-Fernández, A. Crespo-Sosa, A. Oliver, "Absorptive and refractive nonlinearities by four-wave mixing for Au nanoparticles in ion-implanted silica," Opt. Express,  15, 9248-9253 (2007).
    [CrossRef] [PubMed]
  7. G. Santana, B. M. Monroy, A. Ortiz. L. Huerta, J.C. Alonso, "Influence of the surrounding host in obtaining tunable and strong visible photoluminescence from silicon nanoparticles," Appl. Phys. Lett. 88, 041916(1) - 041916(3) (2006).
    [CrossRef]
  8. T. Y. Kim, Nae-Man Park, Kyung-Hyun Kim, G. Y. Sung, Young-Woo Ok, Tae-Yeon Sung, Cheol-Jong Choi,"Quantum confinement effect of silicon nanocrystals in situ grown in silicon nitride films," Appl. Phys. Lett. 85, 5355-5357 (2004).
    [CrossRef]
  9. A. Benami, G. Santana, A. Ortiz, A. Poce, D. Romeu, J. Aguilar-Hernández, G. Contreras-Puente, J. C. Alonso, "Strong white and blue photoluminescence from silicon nancrystals in SiNx grown by remote PECVD using SiCl4/NH3," Nanotechnology 18, 155704-155709 (2007).
    [CrossRef]
  10. G. Heng-Qun and W. Qi-Ming, "Nonlinear optical response of nc-Si-SiO2 films studied with femtosecond four-wave mixing technique," Chin. Phys. Lett. 23, 2989-2992 (2006).
    [CrossRef]
  11. M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
    [CrossRef]
  12. P. Cheng, H. Zhu, Y. Bai, Y. Zhang, T. He, Y. Mo, "Third-order nonlinear optical response of silicon nanostructures dispersed in organic solvent under 1064 nm and 532 nm laser excitations," Opt. Commun.,  270, 391-395 (2007).
    [CrossRef]
  13. I. Umezu, T. Yamaguchi, K. Kohno, M. Inada, and A. Sugimura, "Preparation of SiNx film by pulsed laser ablation in nitrogen gas ambient," Appl. Surf. Sci. 197, 376-378 (2002).
    [CrossRef]
  14. C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, "Optical third order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica," J. of Appl. Phys. 104, 014306 (2008).
    [CrossRef]

2008

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, "Optical third order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica," J. of Appl. Phys. 104, 014306 (2008).
[CrossRef]

2007

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, W. S. Rabinovich, "Thermo-optic tuning and switching in SOI waveguide Fabry-Perot microcavities," Opt. Express,  15, 7557-7563 (2007).
[CrossRef] [PubMed]

C. Torres-Torres, A. V. Khomenko, J. C. Cheang-Wong, L. Rodríguez-Fernández, A. Crespo-Sosa, A. Oliver, "Absorptive and refractive nonlinearities by four-wave mixing for Au nanoparticles in ion-implanted silica," Opt. Express,  15, 9248-9253 (2007).
[CrossRef] [PubMed]

A. Benami, G. Santana, A. Ortiz, A. Poce, D. Romeu, J. Aguilar-Hernández, G. Contreras-Puente, J. C. Alonso, "Strong white and blue photoluminescence from silicon nancrystals in SiNx grown by remote PECVD using SiCl4/NH3," Nanotechnology 18, 155704-155709 (2007).
[CrossRef]

P. Cheng, H. Zhu, Y. Bai, Y. Zhang, T. He, Y. Mo, "Third-order nonlinear optical response of silicon nanostructures dispersed in organic solvent under 1064 nm and 532 nm laser excitations," Opt. Commun.,  270, 391-395 (2007).
[CrossRef]

2006

G. Heng-Qun and W. Qi-Ming, "Nonlinear optical response of nc-Si-SiO2 films studied with femtosecond four-wave mixing technique," Chin. Phys. Lett. 23, 2989-2992 (2006).
[CrossRef]

2005

Y.  Li, J.  Yu, and S.  Chen, "Rearrangeable nonblocking SOI waveguide thermo optic 4×4 switch matrix with low insertion loss and fast response," IEEE Photon. Technol. Lett.  17, 1641-1643 (2005).
[CrossRef]

2004

T. Y. Kim, Nae-Man Park, Kyung-Hyun Kim, G. Y. Sung, Young-Woo Ok, Tae-Yeon Sung, Cheol-Jong Choi,"Quantum confinement effect of silicon nanocrystals in situ grown in silicon nitride films," Appl. Phys. Lett. 85, 5355-5357 (2004).
[CrossRef]

L. Domash, M. Wu, N. Nemchuk, E. Ma, "Tunable and Switchable Multiple Cavity Thin Film Filters," J. Lightwave Technol. 22, 126-135 (2004).
[CrossRef]

2003

M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

2002

I. Umezu, T. Yamaguchi, K. Kohno, M. Inada, and A. Sugimura, "Preparation of SiNx film by pulsed laser ablation in nitrogen gas ambient," Appl. Surf. Sci. 197, 376-378 (2002).
[CrossRef]

Aguilar-Hernández, J.

A. Benami, G. Santana, A. Ortiz, A. Poce, D. Romeu, J. Aguilar-Hernández, G. Contreras-Puente, J. C. Alonso, "Strong white and blue photoluminescence from silicon nancrystals in SiNx grown by remote PECVD using SiCl4/NH3," Nanotechnology 18, 155704-155709 (2007).
[CrossRef]

Alonso, J. C.

A. Benami, G. Santana, A. Ortiz, A. Poce, D. Romeu, J. Aguilar-Hernández, G. Contreras-Puente, J. C. Alonso, "Strong white and blue photoluminescence from silicon nancrystals in SiNx grown by remote PECVD using SiCl4/NH3," Nanotechnology 18, 155704-155709 (2007).
[CrossRef]

Bai, Y.

P. Cheng, H. Zhu, Y. Bai, Y. Zhang, T. He, Y. Mo, "Third-order nonlinear optical response of silicon nanostructures dispersed in organic solvent under 1064 nm and 532 nm laser excitations," Opt. Commun.,  270, 391-395 (2007).
[CrossRef]

Benami, A.

A. Benami, G. Santana, A. Ortiz, A. Poce, D. Romeu, J. Aguilar-Hernández, G. Contreras-Puente, J. C. Alonso, "Strong white and blue photoluminescence from silicon nancrystals in SiNx grown by remote PECVD using SiCl4/NH3," Nanotechnology 18, 155704-155709 (2007).
[CrossRef]

Cheang-Wong, J. C.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, "Optical third order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica," J. of Appl. Phys. 104, 014306 (2008).
[CrossRef]

C. Torres-Torres, A. V. Khomenko, J. C. Cheang-Wong, L. Rodríguez-Fernández, A. Crespo-Sosa, A. Oliver, "Absorptive and refractive nonlinearities by four-wave mixing for Au nanoparticles in ion-implanted silica," Opt. Express,  15, 9248-9253 (2007).
[CrossRef] [PubMed]

Chen, S.

Y.  Li, J.  Yu, and S.  Chen, "Rearrangeable nonblocking SOI waveguide thermo optic 4×4 switch matrix with low insertion loss and fast response," IEEE Photon. Technol. Lett.  17, 1641-1643 (2005).
[CrossRef]

Cheng, P.

P. Cheng, H. Zhu, Y. Bai, Y. Zhang, T. He, Y. Mo, "Third-order nonlinear optical response of silicon nanostructures dispersed in organic solvent under 1064 nm and 532 nm laser excitations," Opt. Commun.,  270, 391-395 (2007).
[CrossRef]

Contreras-Puente, G.

A. Benami, G. Santana, A. Ortiz, A. Poce, D. Romeu, J. Aguilar-Hernández, G. Contreras-Puente, J. C. Alonso, "Strong white and blue photoluminescence from silicon nancrystals in SiNx grown by remote PECVD using SiCl4/NH3," Nanotechnology 18, 155704-155709 (2007).
[CrossRef]

Crespo-Sosa, A.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, "Optical third order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica," J. of Appl. Phys. 104, 014306 (2008).
[CrossRef]

C. Torres-Torres, A. V. Khomenko, J. C. Cheang-Wong, L. Rodríguez-Fernández, A. Crespo-Sosa, A. Oliver, "Absorptive and refractive nonlinearities by four-wave mixing for Au nanoparticles in ion-implanted silica," Opt. Express,  15, 9248-9253 (2007).
[CrossRef] [PubMed]

Dinu, M.

M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

Domash, L.

Ferraro, M. S.

Garcia, H.

M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

He, T.

P. Cheng, H. Zhu, Y. Bai, Y. Zhang, T. He, Y. Mo, "Third-order nonlinear optical response of silicon nanostructures dispersed in organic solvent under 1064 nm and 532 nm laser excitations," Opt. Commun.,  270, 391-395 (2007).
[CrossRef]

Heng-Qun, G.

G. Heng-Qun and W. Qi-Ming, "Nonlinear optical response of nc-Si-SiO2 films studied with femtosecond four-wave mixing technique," Chin. Phys. Lett. 23, 2989-2992 (2006).
[CrossRef]

Inada, M.

I. Umezu, T. Yamaguchi, K. Kohno, M. Inada, and A. Sugimura, "Preparation of SiNx film by pulsed laser ablation in nitrogen gas ambient," Appl. Surf. Sci. 197, 376-378 (2002).
[CrossRef]

Khomenko, A. V.

Kim, T. Y.

T. Y. Kim, Nae-Man Park, Kyung-Hyun Kim, G. Y. Sung, Young-Woo Ok, Tae-Yeon Sung, Cheol-Jong Choi,"Quantum confinement effect of silicon nanocrystals in situ grown in silicon nitride films," Appl. Phys. Lett. 85, 5355-5357 (2004).
[CrossRef]

Kohno, K.

I. Umezu, T. Yamaguchi, K. Kohno, M. Inada, and A. Sugimura, "Preparation of SiNx film by pulsed laser ablation in nitrogen gas ambient," Appl. Surf. Sci. 197, 376-378 (2002).
[CrossRef]

Li, Y.

Y.  Li, J.  Yu, and S.  Chen, "Rearrangeable nonblocking SOI waveguide thermo optic 4×4 switch matrix with low insertion loss and fast response," IEEE Photon. Technol. Lett.  17, 1641-1643 (2005).
[CrossRef]

Ma, E.

Mo, Y.

P. Cheng, H. Zhu, Y. Bai, Y. Zhang, T. He, Y. Mo, "Third-order nonlinear optical response of silicon nanostructures dispersed in organic solvent under 1064 nm and 532 nm laser excitations," Opt. Commun.,  270, 391-395 (2007).
[CrossRef]

Monroy, B. M.

G. Santana, B. M. Monroy, A. Ortiz. L. Huerta, J.C. Alonso, "Influence of the surrounding host in obtaining tunable and strong visible photoluminescence from silicon nanoparticles," Appl. Phys. Lett. 88, 041916(1) - 041916(3) (2006).
[CrossRef]

Nemchuk, N.

Oliver, A.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, "Optical third order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica," J. of Appl. Phys. 104, 014306 (2008).
[CrossRef]

C. Torres-Torres, A. V. Khomenko, J. C. Cheang-Wong, L. Rodríguez-Fernández, A. Crespo-Sosa, A. Oliver, "Absorptive and refractive nonlinearities by four-wave mixing for Au nanoparticles in ion-implanted silica," Opt. Express,  15, 9248-9253 (2007).
[CrossRef] [PubMed]

Ortiz, A.

A. Benami, G. Santana, A. Ortiz, A. Poce, D. Romeu, J. Aguilar-Hernández, G. Contreras-Puente, J. C. Alonso, "Strong white and blue photoluminescence from silicon nancrystals in SiNx grown by remote PECVD using SiCl4/NH3," Nanotechnology 18, 155704-155709 (2007).
[CrossRef]

G. Santana, B. M. Monroy, A. Ortiz. L. Huerta, J.C. Alonso, "Influence of the surrounding host in obtaining tunable and strong visible photoluminescence from silicon nanoparticles," Appl. Phys. Lett. 88, 041916(1) - 041916(3) (2006).
[CrossRef]

Poce, A.

A. Benami, G. Santana, A. Ortiz, A. Poce, D. Romeu, J. Aguilar-Hernández, G. Contreras-Puente, J. C. Alonso, "Strong white and blue photoluminescence from silicon nancrystals in SiNx grown by remote PECVD using SiCl4/NH3," Nanotechnology 18, 155704-155709 (2007).
[CrossRef]

Pruessner, M. W.

Qi-Ming, W.

G. Heng-Qun and W. Qi-Ming, "Nonlinear optical response of nc-Si-SiO2 films studied with femtosecond four-wave mixing technique," Chin. Phys. Lett. 23, 2989-2992 (2006).
[CrossRef]

Quochi, F.

M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

Rabinovich, W. S.

Reyes-Esqueda, J. A.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, "Optical third order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica," J. of Appl. Phys. 104, 014306 (2008).
[CrossRef]

Rodríguez-Fernández, L.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, "Optical third order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica," J. of Appl. Phys. 104, 014306 (2008).
[CrossRef]

C. Torres-Torres, A. V. Khomenko, J. C. Cheang-Wong, L. Rodríguez-Fernández, A. Crespo-Sosa, A. Oliver, "Absorptive and refractive nonlinearities by four-wave mixing for Au nanoparticles in ion-implanted silica," Opt. Express,  15, 9248-9253 (2007).
[CrossRef] [PubMed]

Romeu, D.

A. Benami, G. Santana, A. Ortiz, A. Poce, D. Romeu, J. Aguilar-Hernández, G. Contreras-Puente, J. C. Alonso, "Strong white and blue photoluminescence from silicon nancrystals in SiNx grown by remote PECVD using SiCl4/NH3," Nanotechnology 18, 155704-155709 (2007).
[CrossRef]

Santana, G.

A. Benami, G. Santana, A. Ortiz, A. Poce, D. Romeu, J. Aguilar-Hernández, G. Contreras-Puente, J. C. Alonso, "Strong white and blue photoluminescence from silicon nancrystals in SiNx grown by remote PECVD using SiCl4/NH3," Nanotechnology 18, 155704-155709 (2007).
[CrossRef]

G. Santana, B. M. Monroy, A. Ortiz. L. Huerta, J.C. Alonso, "Influence of the surrounding host in obtaining tunable and strong visible photoluminescence from silicon nanoparticles," Appl. Phys. Lett. 88, 041916(1) - 041916(3) (2006).
[CrossRef]

Stievater, T. H.

Sugimura, A.

I. Umezu, T. Yamaguchi, K. Kohno, M. Inada, and A. Sugimura, "Preparation of SiNx film by pulsed laser ablation in nitrogen gas ambient," Appl. Surf. Sci. 197, 376-378 (2002).
[CrossRef]

Torres-Torres, C.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, "Optical third order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica," J. of Appl. Phys. 104, 014306 (2008).
[CrossRef]

C. Torres-Torres, A. V. Khomenko, J. C. Cheang-Wong, L. Rodríguez-Fernández, A. Crespo-Sosa, A. Oliver, "Absorptive and refractive nonlinearities by four-wave mixing for Au nanoparticles in ion-implanted silica," Opt. Express,  15, 9248-9253 (2007).
[CrossRef] [PubMed]

Umezu, I.

I. Umezu, T. Yamaguchi, K. Kohno, M. Inada, and A. Sugimura, "Preparation of SiNx film by pulsed laser ablation in nitrogen gas ambient," Appl. Surf. Sci. 197, 376-378 (2002).
[CrossRef]

Wu, M.

Yamaguchi, T.

I. Umezu, T. Yamaguchi, K. Kohno, M. Inada, and A. Sugimura, "Preparation of SiNx film by pulsed laser ablation in nitrogen gas ambient," Appl. Surf. Sci. 197, 376-378 (2002).
[CrossRef]

Yu, J.

Y.  Li, J.  Yu, and S.  Chen, "Rearrangeable nonblocking SOI waveguide thermo optic 4×4 switch matrix with low insertion loss and fast response," IEEE Photon. Technol. Lett.  17, 1641-1643 (2005).
[CrossRef]

Zhang, Y.

P. Cheng, H. Zhu, Y. Bai, Y. Zhang, T. He, Y. Mo, "Third-order nonlinear optical response of silicon nanostructures dispersed in organic solvent under 1064 nm and 532 nm laser excitations," Opt. Commun.,  270, 391-395 (2007).
[CrossRef]

Zhu, H.

P. Cheng, H. Zhu, Y. Bai, Y. Zhang, T. He, Y. Mo, "Third-order nonlinear optical response of silicon nanostructures dispersed in organic solvent under 1064 nm and 532 nm laser excitations," Opt. Commun.,  270, 391-395 (2007).
[CrossRef]

Appl. Phys. Lett.

T. Y. Kim, Nae-Man Park, Kyung-Hyun Kim, G. Y. Sung, Young-Woo Ok, Tae-Yeon Sung, Cheol-Jong Choi,"Quantum confinement effect of silicon nanocrystals in situ grown in silicon nitride films," Appl. Phys. Lett. 85, 5355-5357 (2004).
[CrossRef]

M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

Appl. Surf. Sci.

I. Umezu, T. Yamaguchi, K. Kohno, M. Inada, and A. Sugimura, "Preparation of SiNx film by pulsed laser ablation in nitrogen gas ambient," Appl. Surf. Sci. 197, 376-378 (2002).
[CrossRef]

Chin. Phys. Lett.

G. Heng-Qun and W. Qi-Ming, "Nonlinear optical response of nc-Si-SiO2 films studied with femtosecond four-wave mixing technique," Chin. Phys. Lett. 23, 2989-2992 (2006).
[CrossRef]

IEEE Photon. Technol. Lett.

Y.  Li, J.  Yu, and S.  Chen, "Rearrangeable nonblocking SOI waveguide thermo optic 4×4 switch matrix with low insertion loss and fast response," IEEE Photon. Technol. Lett.  17, 1641-1643 (2005).
[CrossRef]

J. Lightwave Technol.

J. of Appl. Phys.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, "Optical third order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica," J. of Appl. Phys. 104, 014306 (2008).
[CrossRef]

Nanotechnology

A. Benami, G. Santana, A. Ortiz, A. Poce, D. Romeu, J. Aguilar-Hernández, G. Contreras-Puente, J. C. Alonso, "Strong white and blue photoluminescence from silicon nancrystals in SiNx grown by remote PECVD using SiCl4/NH3," Nanotechnology 18, 155704-155709 (2007).
[CrossRef]

Opt. Commun.

P. Cheng, H. Zhu, Y. Bai, Y. Zhang, T. He, Y. Mo, "Third-order nonlinear optical response of silicon nanostructures dispersed in organic solvent under 1064 nm and 532 nm laser excitations," Opt. Commun.,  270, 391-395 (2007).
[CrossRef]

Opt. Express

Other

R. W. Boyd, Nonlinear Optics, (Academic Press, San Diego, 1992).

M. von Allmen and A. BlatterLaser-beam interaction with materials, (Berlin,Springer,1995) Chap. 3.
[CrossRef]

G. Santana, B. M. Monroy, A. Ortiz. L. Huerta, J.C. Alonso, "Influence of the surrounding host in obtaining tunable and strong visible photoluminescence from silicon nanoparticles," Appl. Phys. Lett. 88, 041916(1) - 041916(3) (2006).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Optical set up for (a) self-diffraction experiment, (b) Kerr gate experiment.

Fig. 2.
Fig. 2.

(a) PL spectrum (b) Linear optical absorption spectrum.

Fig. 3.
Fig. 3.

HRTEM images of nc-Si embedded in a silicon nitride matrix.

Fig. 4.
Fig. 4.

(a). Self-diffraction intensity obtained at different repetition rate of ns pulses, (b) Kerr Transmittance versus probe delay in the fs experiment.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

T t = z [ κ ρ C T z ] + α ρ C I ( t , z ) ,
Ψ ± ( x ) = Ψ ± ( 0 ) + Ψ ± ( 1 ) cos 2 π x Λ ,
Ψ ± ( 0 ) = 4 π 2 z ( n 0 + d n d T Δ T ) λ [ A ( E 1 ± 2 + E 2 ± 2 ) + ( A + B ) ( E 1 2 + E 2 2 ) ] ,
Ψ ± ( 1 ) = 4 π 2 z ( n 0 + d n d T Δ T ) λ [ A E 1 ± E 2 ± * + ( A + B ) E 1 E 2 * ] + 2 π z λ d n d T Δ T .
E 1 ± ( z ) = [ J 0 ( Ψ ± ( 1 ) ) E 1 + 0 + i J 1 ( Ψ ± ( 1 ) ) E 2 + 0 ] exp ( i Ψ ± ( 0 ) α ( I ) z 2 ) ,
E 2 ± ( z ) = [ J 0 ( Ψ ± ( 1 ) ) E 2 + 0 i J 1 ( Ψ ± ( 1 ) ) E 1 + 0 ] exp ( i Ψ ± ( 0 ) α ( I ) z 2 ) ,
E 3 ± ( z ) = [ i J 1 ( Ψ ± ( 1 ) ) E 1 + 0 J 2 ( Ψ ± ( 1 ) ) E 2 + 0 ] exp ( i Ψ ± ( 0 ) α ( I ) z 2 ) ,
E 4 ± ( z ) = [ i J 1 ( Ψ ± ( 1 ) ) E 2 + 0 J 2 ( Ψ ± ( 1 ) ) E 1 + 0 ] exp ( i Ψ ± ( 0 ) α ( I ) z 2 ) ,

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