Abstract

The nonlinear response of nanoporous silicon optical waveguides is investigated using a novel pump-probe method. In this approach we use a two-frequency heterodyne technique to measure the pump-induced transient change in phase and intensity in a single measurement. We measure a 100 picosecond material response time and report behavior matching a physical model dominated by free-carrier effects significantly stronger than those observed in traditional silicon-based waveguides.

© 2014 Optical Society of America

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  1. M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photon. 4, 492–494 (2010).
    [CrossRef]
  2. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24, 4600–4615 (2006).
    [CrossRef]
  3. G. T. Reed and A. P. Knights, Silicon Photonics(Wiley, 2008).
    [CrossRef]
  4. D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
    [CrossRef]
  5. A. Agarwal, L. Liao, J. Foresi, M. R. Black, X. Duan, and L. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80, 6120–6123 (1996).
    [CrossRef]
  6. A. Harke, M. Krause, and J. Mueller, “Low-loss singlemode amorphous silicon waveguides,” Electron. Lett. 41, 1377–1379 (2005).
    [CrossRef]
  7. A. Cullis, L. T. Canham, and P. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82, 909–965 (1997).
    [CrossRef]
  8. G. Vincent, “Optical properties of porous silicon superlattices,” Appl. Phys. Lett. 64, 2367–2369 (1994).
    [CrossRef]
  9. P. Apiratikul, A. M. Rossi, and T. E. Murphy, “Nonlinearities in porous silicon opticalwaveguides at 1550 nm,” Opt. Express 17, 3396–3406 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. T. Matsumoto, M. Daimon, H. Mimura, Y. Kanemitsu, and N. Koshida, “Optically induced absorption in porous silicon and its application to logic gates,” J. Electrochem. Soc. 142, 3528–3533 (1995).
    [CrossRef]
  13. H. Foll, M. Christophersen, J. Carstensen, and G. Hasse, “Formation and application of porous silicon,” Mat. Sci. Eng. R 39, 93–141 (2002).
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  14. W. Theiß, “Optical properties of porous silicon,” Surf. Sci. Rep. 29, 91–192 (1997).
    [CrossRef]
  15. K. Kim and T. E. Murphy, “Porous silicon integrated mach-zehnder interferometer waveguide for biological and chemical sensing,” Opt. Express 21, 19488–19497 (2013).
    [CrossRef] [PubMed]
  16. R. Hui and M. O’Sullivan, Fiber Optic Measurement Techniques (Academic, 2009).
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  18. K. L. Hall, G. Lenz, E. P. Ippen, and G. Raybon, “Heterodyne pump–probe technique for time-domain studies of optical nonlinearities in waveguides,” Opt. Lett. 17, 874–876 (1992).
    [CrossRef]
  19. Y. Shoji, T. Ogasawara, T. Kamei, Y. Sakakibara, S. Suda, K. Kintaka, H. Kawashima, M. Okano, T. Hasama, H. Ishikawa, and M. Mori, “Ultrafast nonlinear effects in hydrogenated amorphous silicon wire waveguide,” Opt. Express 18, 5668–5673 (2010).
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  20. P. A. Elzinga, R. J. Kneisler, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump/probe method for fast analysis of visible spectral signatures utilizing asynchronous optical sampling,” Appl. Opt. 26, 4303–4309 (1987).
    [CrossRef] [PubMed]
  21. T. Matsumoto, T. Futagi, H. Mimura, and Y. Kanemitsu, “Ultrafast decay dynamics of luminescence in porous silicon,” Phys. Rev. B 47, 13876–13879 (1993).
    [CrossRef]
  22. R. Tsu, H. Shen, and M. Dutta, “Correlation of raman and photoluminescence spectra of porous silicon,” Appl. Phys. Lett. 60, 112–114 (1992).
    [CrossRef]
  23. R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
    [CrossRef]
  24. A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, “Silicon electro-optic modulator based on a three terminal device integrated in a low-loss single-mode soi waveguide,” J. Lightwave Technol. 15, 505–518 (1997).
    [CrossRef]
  25. X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
    [CrossRef]
  26. D. Lockwood, “Optical properties of porous silicon,” Solid State Commun. 92, 101–112 (1994).
    [CrossRef]
  27. O. E. DeLange, “Optical heterodyne detection,” IEEE Spectrum 5, 77–85 (1968).
    [CrossRef]
  28. R. H. Kingston, Optical Sources, Detectors, and Systems: Fundamentals and Applications (Academic, 1995).
  29. W. Hou and X. Zhao, “Drift of nonlinearity in the heterodyne interferometer,” Precis. Eng. 16, 25–35 (1994).
    [CrossRef]
  30. C.-K. Sun, B. Golubovic, J. Fujimoto, H. Choi, and C. Wang, “Heterodyne nondegenerate pump–probe measurement technique for guided-wave devices,” Opt. Lett. 20, 210–212 (1995).
    [CrossRef] [PubMed]
  31. A. R. Motamedi, A. H. Nejadmalayeri, A. Khilo, F. X. Kärtner, and E. P. Ippen, “Ultrafast nonlinear optical studies of silicon nanowaveguides,” Opt. Express 20, 4085–4101 (2012).
    [CrossRef] [PubMed]

2013 (2)

K. Kim and T. E. Murphy, “Porous silicon integrated mach-zehnder interferometer waveguide for biological and chemical sensing,” Opt. Express 21, 19488–19497 (2013).
[CrossRef] [PubMed]

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[CrossRef]

2012 (1)

2010 (2)

2009 (1)

2006 (1)

2005 (2)

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[CrossRef]

A. Harke, M. Krause, and J. Mueller, “Low-loss singlemode amorphous silicon waveguides,” Electron. Lett. 41, 1377–1379 (2005).
[CrossRef]

2002 (1)

H. Foll, M. Christophersen, J. Carstensen, and G. Hasse, “Formation and application of porous silicon,” Mat. Sci. Eng. R 39, 93–141 (2002).
[CrossRef]

1997 (3)

W. Theiß, “Optical properties of porous silicon,” Surf. Sci. Rep. 29, 91–192 (1997).
[CrossRef]

A. Cullis, L. T. Canham, and P. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82, 909–965 (1997).
[CrossRef]

A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, “Silicon electro-optic modulator based on a three terminal device integrated in a low-loss single-mode soi waveguide,” J. Lightwave Technol. 15, 505–518 (1997).
[CrossRef]

1996 (1)

A. Agarwal, L. Liao, J. Foresi, M. R. Black, X. Duan, and L. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80, 6120–6123 (1996).
[CrossRef]

1995 (3)

F. Z. Henari, K. Morgenstern, W. J. Blau, V. A. Karavanskii, and V. S. Dneprovskii, “Third-order optical nonlinearity and all-optical switching in porous silicon,” Appl. Phys. Lett. 67, 323–325 (1995).
[CrossRef]

T. Matsumoto, M. Daimon, H. Mimura, Y. Kanemitsu, and N. Koshida, “Optically induced absorption in porous silicon and its application to logic gates,” J. Electrochem. Soc. 142, 3528–3533 (1995).
[CrossRef]

C.-K. Sun, B. Golubovic, J. Fujimoto, H. Choi, and C. Wang, “Heterodyne nondegenerate pump–probe measurement technique for guided-wave devices,” Opt. Lett. 20, 210–212 (1995).
[CrossRef] [PubMed]

1994 (3)

W. Hou and X. Zhao, “Drift of nonlinearity in the heterodyne interferometer,” Precis. Eng. 16, 25–35 (1994).
[CrossRef]

D. Lockwood, “Optical properties of porous silicon,” Solid State Commun. 92, 101–112 (1994).
[CrossRef]

G. Vincent, “Optical properties of porous silicon superlattices,” Appl. Phys. Lett. 64, 2367–2369 (1994).
[CrossRef]

1993 (1)

T. Matsumoto, T. Futagi, H. Mimura, and Y. Kanemitsu, “Ultrafast decay dynamics of luminescence in porous silicon,” Phys. Rev. B 47, 13876–13879 (1993).
[CrossRef]

1992 (2)

R. Tsu, H. Shen, and M. Dutta, “Correlation of raman and photoluminescence spectra of porous silicon,” Appl. Phys. Lett. 60, 112–114 (1992).
[CrossRef]

K. L. Hall, G. Lenz, E. P. Ippen, and G. Raybon, “Heterodyne pump–probe technique for time-domain studies of optical nonlinearities in waveguides,” Opt. Lett. 17, 874–876 (1992).
[CrossRef]

1987 (2)

1968 (1)

O. E. DeLange, “Optical heterodyne detection,” IEEE Spectrum 5, 77–85 (1968).
[CrossRef]

Agarwal, A.

A. Agarwal, L. Liao, J. Foresi, M. R. Black, X. Duan, and L. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80, 6120–6123 (1996).
[CrossRef]

Apiratikul, P.

P. Apiratikul, A. M. Rossi, and T. E. Murphy, “Nonlinearities in porous silicon opticalwaveguides at 1550 nm,” Opt. Express 17, 3396–3406 (2009).
[CrossRef] [PubMed]

P. Apiratikul, “Semiconductor waveguides for nonlinear optical signal processing,” Ph.D. thesis, University of Maryland, College Park (2009).

Baehr-Jones, T.

M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photon. 4, 492–494 (2010).
[CrossRef]

Baets, R.

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[CrossRef]

Bennett, B.

R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
[CrossRef]

Black, M. R.

A. Agarwal, L. Liao, J. Foresi, M. R. Black, X. Duan, and L. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80, 6120–6123 (1996).
[CrossRef]

Blau, W. J.

F. Z. Henari, K. Morgenstern, W. J. Blau, V. A. Karavanskii, and V. S. Dneprovskii, “Third-order optical nonlinearity and all-optical switching in porous silicon,” Appl. Phys. Lett. 67, 323–325 (1995).
[CrossRef]

Calcott, P.

A. Cullis, L. T. Canham, and P. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82, 909–965 (1997).
[CrossRef]

Campenhout, J.

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[CrossRef]

Canham, L. T.

A. Cullis, L. T. Canham, and P. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82, 909–965 (1997).
[CrossRef]

Carstensen, J.

H. Foll, M. Christophersen, J. Carstensen, and G. Hasse, “Formation and application of porous silicon,” Mat. Sci. Eng. R 39, 93–141 (2002).
[CrossRef]

Choi, H.

Christophersen, M.

H. Foll, M. Christophersen, J. Carstensen, and G. Hasse, “Formation and application of porous silicon,” Mat. Sci. Eng. R 39, 93–141 (2002).
[CrossRef]

Claps, R.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[CrossRef]

Cullis, A.

A. Cullis, L. T. Canham, and P. Calcott, “The structural and luminescence properties of porous silicon,” J. Appl. Phys. 82, 909–965 (1997).
[CrossRef]

Cutolo, A.

A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, “Silicon electro-optic modulator based on a three terminal device integrated in a low-loss single-mode soi waveguide,” J. Lightwave Technol. 15, 505–518 (1997).
[CrossRef]

Daimon, M.

T. Matsumoto, M. Daimon, H. Mimura, Y. Kanemitsu, and N. Koshida, “Optically induced absorption in porous silicon and its application to logic gates,” J. Electrochem. Soc. 142, 3528–3533 (1995).
[CrossRef]

DeLange, O. E.

O. E. DeLange, “Optical heterodyne detection,” IEEE Spectrum 5, 77–85 (1968).
[CrossRef]

Dimitropoulos, D.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[CrossRef]

Dneprovskii, V. S.

F. Z. Henari, K. Morgenstern, W. J. Blau, V. A. Karavanskii, and V. S. Dneprovskii, “Third-order optical nonlinearity and all-optical switching in porous silicon,” Appl. Phys. Lett. 67, 323–325 (1995).
[CrossRef]

Duan, X.

A. Agarwal, L. Liao, J. Foresi, M. R. Black, X. Duan, and L. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80, 6120–6123 (1996).
[CrossRef]

Dutta, M.

R. Tsu, H. Shen, and M. Dutta, “Correlation of raman and photoluminescence spectra of porous silicon,” Appl. Phys. Lett. 60, 112–114 (1992).
[CrossRef]

Elzinga, P. A.

Fathpour, S.

Foll, H.

H. Foll, M. Christophersen, J. Carstensen, and G. Hasse, “Formation and application of porous silicon,” Mat. Sci. Eng. R 39, 93–141 (2002).
[CrossRef]

Foresi, J.

A. Agarwal, L. Liao, J. Foresi, M. R. Black, X. Duan, and L. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80, 6120–6123 (1996).
[CrossRef]

Fujimoto, J.

Futagi, T.

T. Matsumoto, T. Futagi, H. Mimura, and Y. Kanemitsu, “Ultrafast decay dynamics of luminescence in porous silicon,” Phys. Rev. B 47, 13876–13879 (1993).
[CrossRef]

Gai, X.

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[CrossRef]

Golubovic, B.

Hall, K. L.

Harke, A.

A. Harke, M. Krause, and J. Mueller, “Low-loss singlemode amorphous silicon waveguides,” Electron. Lett. 41, 1377–1379 (2005).
[CrossRef]

Hasama, T.

Hasse, G.

H. Foll, M. Christophersen, J. Carstensen, and G. Hasse, “Formation and application of porous silicon,” Mat. Sci. Eng. R 39, 93–141 (2002).
[CrossRef]

Henari, F. Z.

F. Z. Henari, K. Morgenstern, W. J. Blau, V. A. Karavanskii, and V. S. Dneprovskii, “Third-order optical nonlinearity and all-optical switching in porous silicon,” Appl. Phys. Lett. 67, 323–325 (1995).
[CrossRef]

Hochberg, M.

M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photon. 4, 492–494 (2010).
[CrossRef]

Hou, W.

W. Hou and X. Zhao, “Drift of nonlinearity in the heterodyne interferometer,” Precis. Eng. 16, 25–35 (1994).
[CrossRef]

Hui, R.

R. Hui and M. O’Sullivan, Fiber Optic Measurement Techniques (Academic, 2009).

Iodice, M.

A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, “Silicon electro-optic modulator based on a three terminal device integrated in a low-loss single-mode soi waveguide,” J. Lightwave Technol. 15, 505–518 (1997).
[CrossRef]

Ippen, E. P.

Ishikawa, H.

Jalali, B.

B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24, 4600–4615 (2006).
[CrossRef]

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[CrossRef]

Jhaveri, R.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[CrossRef]

Jiang, Y.

Kamei, T.

Kanemitsu, Y.

T. Matsumoto, M. Daimon, H. Mimura, Y. Kanemitsu, and N. Koshida, “Optically induced absorption in porous silicon and its application to logic gates,” J. Electrochem. Soc. 142, 3528–3533 (1995).
[CrossRef]

T. Matsumoto, T. Futagi, H. Mimura, and Y. Kanemitsu, “Ultrafast decay dynamics of luminescence in porous silicon,” Phys. Rev. B 47, 13876–13879 (1993).
[CrossRef]

Karavanskii, V. A.

F. Z. Henari, K. Morgenstern, W. J. Blau, V. A. Karavanskii, and V. S. Dneprovskii, “Third-order optical nonlinearity and all-optical switching in porous silicon,” Appl. Phys. Lett. 67, 323–325 (1995).
[CrossRef]

Kärtner, F. X.

Kawashima, H.

Khilo, A.

Kim, K.

Kimerling, L.

A. Agarwal, L. Liao, J. Foresi, M. R. Black, X. Duan, and L. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80, 6120–6123 (1996).
[CrossRef]

King, G. B.

Kingston, R. H.

R. H. Kingston, Optical Sources, Detectors, and Systems: Fundamentals and Applications (Academic, 1995).

Kintaka, K.

Kneisler, R. J.

Knights, A. P.

G. T. Reed and A. P. Knights, Silicon Photonics(Wiley, 2008).
[CrossRef]

Koshida, N.

T. Matsumoto, M. Daimon, H. Mimura, Y. Kanemitsu, and N. Koshida, “Optically induced absorption in porous silicon and its application to logic gates,” J. Electrochem. Soc. 142, 3528–3533 (1995).
[CrossRef]

Krause, M.

A. Harke, M. Krause, and J. Mueller, “Low-loss singlemode amorphous silicon waveguides,” Electron. Lett. 41, 1377–1379 (2005).
[CrossRef]

Kuyken, B.

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[CrossRef]

Laurendeau, N. M.

Lenz, G.

Liao, L.

A. Agarwal, L. Liao, J. Foresi, M. R. Black, X. Duan, and L. Kimerling, “Low-loss polycrystalline silicon waveguides for silicon photonics,” J. Appl. Phys. 80, 6120–6123 (1996).
[CrossRef]

Lockwood, D.

D. Lockwood, “Optical properties of porous silicon,” Solid State Commun. 92, 101–112 (1994).
[CrossRef]

Luther-Davies, B.

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[CrossRef]

Lytle, F. E.

Ma, P.

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[CrossRef]

Madden, S. J.

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[CrossRef]

Matsumoto, T.

T. Matsumoto, M. Daimon, H. Mimura, Y. Kanemitsu, and N. Koshida, “Optically induced absorption in porous silicon and its application to logic gates,” J. Electrochem. Soc. 142, 3528–3533 (1995).
[CrossRef]

T. Matsumoto, T. Futagi, H. Mimura, and Y. Kanemitsu, “Ultrafast decay dynamics of luminescence in porous silicon,” Phys. Rev. B 47, 13876–13879 (1993).
[CrossRef]

Mimura, H.

T. Matsumoto, M. Daimon, H. Mimura, Y. Kanemitsu, and N. Koshida, “Optically induced absorption in porous silicon and its application to logic gates,” J. Electrochem. Soc. 142, 3528–3533 (1995).
[CrossRef]

T. Matsumoto, T. Futagi, H. Mimura, and Y. Kanemitsu, “Ultrafast decay dynamics of luminescence in porous silicon,” Phys. Rev. B 47, 13876–13879 (1993).
[CrossRef]

Morgenstern, K.

F. Z. Henari, K. Morgenstern, W. J. Blau, V. A. Karavanskii, and V. S. Dneprovskii, “Third-order optical nonlinearity and all-optical switching in porous silicon,” Appl. Phys. Lett. 67, 323–325 (1995).
[CrossRef]

Mori, M.

Motamedi, A. R.

Mueller, J.

A. Harke, M. Krause, and J. Mueller, “Low-loss singlemode amorphous silicon waveguides,” Electron. Lett. 41, 1377–1379 (2005).
[CrossRef]

Murphy, T. E.

Nejadmalayeri, A. H.

O’Sullivan, M.

R. Hui and M. O’Sullivan, Fiber Optic Measurement Techniques (Academic, 2009).

Ogasawara, T.

Okano, M.

Raybon, G.

Reed, G. T.

G. T. Reed and A. P. Knights, Silicon Photonics(Wiley, 2008).
[CrossRef]

Roelkens, G.

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photon. Rev. 7, 1054–1064 (2013).
[CrossRef]

Rossi, A. M.

Sakakibara, Y.

Shen, H.

R. Tsu, H. Shen, and M. Dutta, “Correlation of raman and photoluminescence spectra of porous silicon,” Appl. Phys. Lett. 60, 112–114 (1992).
[CrossRef]

Shoji, Y.

Soref, R.

R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
[CrossRef]

Spirito, P.

A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, “Silicon electro-optic modulator based on a three terminal device integrated in a low-loss single-mode soi waveguide,” J. Lightwave Technol. 15, 505–518 (1997).
[CrossRef]

Suda, S.

Suess, R. J.

R. J. Suess and T. E. Murphy, “Third-order optical nonlinearity in bulk nanoporous silicon at telecom wavelengths,” in “CLEO: Applications and Technology” (Optical Society of America, 2012).

Sun, C.-K.

Theiß, W.

W. Theiß, “Optical properties of porous silicon,” Surf. Sci. Rep. 29, 91–192 (1997).
[CrossRef]

Tsu, R.

R. Tsu, H. Shen, and M. Dutta, “Correlation of raman and photoluminescence spectra of porous silicon,” Appl. Phys. Lett. 60, 112–114 (1992).
[CrossRef]

Verheyen, P.

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Figures (5)

Fig. 1
Fig. 1

Scanning electron micrographs showing nanoporous silicon structure (a) and the waveguide end facet of the type characterized in this study (b). The dashed circle shows the approximate mode dimension as estimated by a diffraction technique described in the text. The polymer cover layer (appearing as the topmost material in (b)) was not present during device characterization.

Fig. 2
Fig. 2

Diagram of pump-probe experiment used in this study. The inset shows the relative timing of pulses incident on the device under test (DUT). A dual-phase lock-in amplifier measures the in-phase and quadrature components (x and y respectively) at two different frequencies fH and fH + fC. AOFS: acousto-optic frequency shifter; HWP: half waveplate; PBS: polarizing beam splitter.

Fig. 3
Fig. 3

(a) Transient normalized change in probe intensity for coupled pump intensity of 2.4 GW/cm2. The inset shows a zoomed view of transient near zero delay for different coupled pump intensities (1.4, 2.4, 3.3 GW/cm2 top to bottom). An effective time constant for the initial recovery is also indicated on the inset. (b) Relative change in probe intensity for delays τ = 0 ps (top curve) and τ = 7 ps (bottom curve) for varying coupled pump intensity. The theoretical curve (dotted line) is an approximate solution valid at low intensities.

Fig. 4
Fig. 4

(a) Change in phase for coupled pump intensity of 2.4 GW/cm2. The inset shows a zoomed view of transient change in phase near zero delay for different intensities (1.4, 2.4, 3.3 GW/cm2 bottom to top). (b) Change in phase for delays τ = 0 ps (top curve) and τ = 7 ps (bottom curve) for varying coupled pump intensity. The theoretical curve (dotted line) is an approximate solution valid at low intensities.

Fig. 5
Fig. 5

(a) Notional time series data showing the function s(t) over one chopping period as described by Eq. (6). The chopper wheel blocks or passes the pump beam in time intervals of length 1 2 f c with the sinusoidally varying signal in each interval being described by {X0, Y0} or {X1, Y1} respectively. (b) Component representation of the notional time series is shown in the first quadrant of the in-phase and quadrature-phase plane. (c) Measured frequency spectrum of s(t) with relevant harmonics indicated. Harmonics of the collinear pump, which occur at even integer multiples of the 0.5 kHz lock-in amplifier reference frequency, are suppressed through the use of balanced detection.

Equations (21)

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z u ( z , t ) = [ α 2 + ( i ω c n 2 β 2 PA 2 ) | u ( z , t ) | 2 A eff ( i ω c Δ n FCD ( z , t ) + 1 2 Δ α FCA ( z , t ) ) ] u ( z , t )
Δ α FCA ( z , t ) = σ FCA Δ N ( z , t )
Δ n FCD ( z , t ) = k FCD Δ N ( z , t )
t Δ N ( z , t ) = β 2 PA 2 h ¯ ω [ | u ( z , t ) | 2 A eff ] 2 Δ N ( z , t ) τ c
u probe ( t ) = u 0 , probe ( t τ ) exp ( α 2 L ) exp { ( 1 2 σ FCA + i ω c k FCD ) × [ β 2 PA 2 h ¯ ω 0 L τ I pump 2 ( z , t ; I 0 , pump ) d t d z ] e t / τ c }
s ( t ) = { X 1 cos ( N t ) + Y 1 sin ( N t ) π < t π 2 X 0 cos ( N t ) + Y 0 sin ( N t ) π 2 < t 0 X 1 cos ( N t ) + Y 1 sin ( N t ) 0 < t π 2 X 0 cos ( N t ) + Y 0 sin ( N t ) π 2 < t π
s ( t ) = x 0 2 + n = 1 x n cos ( n t ) + y n sin ( n t )
x n = 1 π π π s ( t ) cos ( n t ) d t , n = 0 , 1 , 2 ,
y n = 1 π π π s ( t ) sin ( n t ) d t , n = 1 , 2 ,
x N = X 0 + X 1 2 + Y 1 Y 0 π N
y N = Y 0 + Y 1 2 + X 1 X 0 π N
x M = Y 0 Y 1 π
y M = X 1 X 0 π
X 0 = x N + 1 N x M π 2 y M
Y 0 = y N 1 N y M + π 2 x M
X 1 = X 0 + π y M
Y 1 = Y 0 π x M
( Δ I I ) = X 1 2 + Y 1 2 X 0 2 + Y 0 2 1
Δ ϕ = tan 1 ( Y 1 X 1 ) tan 1 ( Y 0 X 0 )
( Δ I I ) = 2 π ( x N y M y N x M x N 2 + y N 2 )
Δ ϕ = π ( x N x M + y N y M x N 2 + y N 2 )

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