Abstract

Terahertz (THz) wave generation via four-wave mixing (FWM) in silicon membrane waveguides is theoretically investigated with mid-infrared laser pulses. Compared with the conventional parametric amplification or wavelength conversion based on FWM in silicon waveguides, which needs a pump wavelength located in the anomalous group-velocity dispersion (GVD) regime to realize broad phase matching, the pump wavelength located in the normal GVD regime is required to realize collinear phase matching for the THz-wave generation via FWM. The pump wavelength and rib height of the silicon membrane waveguide can be tuned to obtain a broadband phase matching. Moreover, the conversion efficiency of the THz-wave generation is studied with different pump wavelengths and rib heights of the silicon membrane waveguides, and broadband THz-wave can be obtained with high efficiency exceeding 1%.

© 2012 OSA

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2011 (4)

2010 (5)

2009 (1)

2008 (4)

2007 (4)

2006 (7)

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,” Nature 441(7096), 960–963 (2006).
[CrossRef] [PubMed]

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840 (2006).
[CrossRef]

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

T. Ikari, X. Zhang, H. Minamide, and H. Ito, “THz-wave parametric oscillator with a surface-emitted configuration,” Opt. Express 14(4), 1604–1610 (2006).
[CrossRef] [PubMed]

K. Suizu, Y. Suzuki, Y. Sasaki, H. Ito, and Y. Avetisyan, “Surface-emitted terahertz-wave generation by ridged periodically poled lithium niobate and enhancement by mixing of two terahertz waves,” Opt. Lett. 31(7), 957–959 (2006).
[CrossRef] [PubMed]

X. Xie, J. Xu, and X.-C. Zhang, “Terahertz wave generation and detection from a cdte crystal characterized by different excitation wavelengths,” Opt. Lett. 31(7), 978–980 (2006).
[CrossRef] [PubMed]

Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Ultrabroadband parametric generation and wavelength conversion in silicon waveguides,” Opt. Express 14(11), 4786–4799 (2006).
[CrossRef] [PubMed]

2005 (4)

2002 (1)

K. Kawase, H. Minamide, K. Imai, J. Shikata, and H. Ito, “Injection-seeded terahertz-wave parametric generator with wide tenability,” Appl. Phys. Lett. 80(2), 195–198 (2002).
[CrossRef]

Agrawal, G. P.

Andersen, K. N.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Avetisyan, Y.

Avetisyan, Y. H.

Bettiol, A. A.

G. Z. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Y. Yang, E. J. Teo, M. B. H. Breese, A. A. Bettiol, and G. T. Reed, “Silicon photonic waveguides for different wavelength regions,” Semicond. Sci. Technol. 23(6), 064002 (2008).
[CrossRef]

Bjarklev, A.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Bolten, J.

B. Chmielak, M. Waldow, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Nagel, F. Merget, and H. Kurz, “Pockels effect based fully integrated, strained silicon electro-optic modulator,” Opt. Express 19(18), 17212–17219 (2011).
[CrossRef] [PubMed]

M. Wächter, C. Matheisen, M. Waldow, T. Wahlbrink, J. Bolten, M. Nagel, and H. Kurz, “Optical generation of terahertz and second-harmonic light in plasma-activated silicon nanophotonic structures,” Appl. Phys. Lett. 97(16), 161107 (2010).
[CrossRef]

Borel, P. I.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Boyraz, O.

Breese, M. B. H.

G. Z. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Y. Yang, E. J. Teo, M. B. H. Breese, A. A. Bettiol, and G. T. Reed, “Silicon photonic waveguides for different wavelength regions,” Semicond. Sci. Technol. 23(6), 064002 (2008).
[CrossRef]

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[CrossRef]

Buchwald, W. R.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840 (2006).
[CrossRef]

Chen, X.

Chen, Y. H.

Chiang, A. C.

Chmielak, B.

Chung, Y. C.

Dadap, J. I.

Ding, Y. J.

Dulkeith, E.

Emelett, S. J.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840 (2006).
[CrossRef]

Espinola, R. L.

Fage-Pedersen, J.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Fauchet, P. M.

Foster, M. A.

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,” Nature 441(7096), 960–963 (2006).
[CrossRef] [PubMed]

Frandsen, L. H.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Fukuda, H.

Gaeta, A. L.

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,” Nature 441(7096), 960–963 (2006).
[CrossRef] [PubMed]

Gao, S.

Green, W. M. J.

Hansen, O.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Hon, N. K.

N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011).
[CrossRef]

Hsieh, I.

Hu, Y.

Huang, N.

Huang, Y.

Huang, Y. C.

Ikari, T.

Imai, K.

K. Kawase, H. Minamide, K. Imai, J. Shikata, and H. Ito, “Injection-seeded terahertz-wave parametric generator with wide tenability,” Appl. Phys. Lett. 80(2), 195–198 (2002).
[CrossRef]

Itabashi, S.

Ito, H.

Jacobsen, R. S.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Jalali, B.

N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011).
[CrossRef]

Johnson, T. J.

Kalyoncu, S. K.

Kawase, K.

K. Suizu and K. Kawase, “Terahertz-wave generation in a conventional optical fiber,” Opt. Lett. 32(20), 2990–2992 (2007).
[CrossRef] [PubMed]

K. Kawase, H. Minamide, K. Imai, J. Shikata, and H. Ito, “Injection-seeded terahertz-wave parametric generator with wide tenability,” Appl. Phys. Lett. 80(2), 195–198 (2002).
[CrossRef]

Kristensen, M.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Kurz, H.

B. Chmielak, M. Waldow, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Nagel, F. Merget, and H. Kurz, “Pockels effect based fully integrated, strained silicon electro-optic modulator,” Opt. Express 19(18), 17212–17219 (2011).
[CrossRef] [PubMed]

M. Wächter, C. Matheisen, M. Waldow, T. Wahlbrink, J. Bolten, M. Nagel, and H. Kurz, “Optical generation of terahertz and second-harmonic light in plasma-activated silicon nanophotonic structures,” Appl. Phys. Lett. 97(16), 161107 (2010).
[CrossRef]

Lavrinenko, A. V.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Lee, H. H.

Lin, Q.

Lin, S. T.

Lin, Y. Y.

Lipson, M.

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,” Nature 441(7096), 960–963 (2006).
[CrossRef] [PubMed]

Liu, H.

Liu, X.

Mashanovich, G. Z.

G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express 19(8), 7112–7119 (2011).
[CrossRef] [PubMed]

G. Z. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Y. Yang, E. J. Teo, M. B. H. Breese, A. A. Bettiol, and G. T. Reed, “Silicon photonic waveguides for different wavelength regions,” Semicond. Sci. Technol. 23(6), 064002 (2008).
[CrossRef]

Matavulj, P.

G. Z. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Y. Yang, E. J. Teo, M. B. H. Breese, A. A. Bettiol, and G. T. Reed, “Silicon photonic waveguides for different wavelength regions,” Semicond. Sci. Technol. 23(6), 064002 (2008).
[CrossRef]

Matheisen, C.

B. Chmielak, M. Waldow, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Nagel, F. Merget, and H. Kurz, “Pockels effect based fully integrated, strained silicon electro-optic modulator,” Opt. Express 19(18), 17212–17219 (2011).
[CrossRef] [PubMed]

M. Wächter, C. Matheisen, M. Waldow, T. Wahlbrink, J. Bolten, M. Nagel, and H. Kurz, “Optical generation of terahertz and second-harmonic light in plasma-activated silicon nanophotonic structures,” Appl. Phys. Lett. 97(16), 161107 (2010).
[CrossRef]

McNab, S. J.

Merget, F.

Michael, C. P.

Milosevic, M.

G. Z. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Y. Yang, E. J. Teo, M. B. H. Breese, A. A. Bettiol, and G. T. Reed, “Silicon photonic waveguides for different wavelength regions,” Semicond. Sci. Technol. 23(6), 064002 (2008).
[CrossRef]

Miloševic, M. M.

Minamide, H.

T. Ikari, X. Zhang, H. Minamide, and H. Ito, “THz-wave parametric oscillator with a surface-emitted configuration,” Opt. Express 14(4), 1604–1610 (2006).
[CrossRef] [PubMed]

K. Kawase, H. Minamide, K. Imai, J. Shikata, and H. Ito, “Injection-seeded terahertz-wave parametric generator with wide tenability,” Appl. Phys. Lett. 80(2), 195–198 (2002).
[CrossRef]

Moulin, G.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Nagel, M.

B. Chmielak, M. Waldow, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Nagel, F. Merget, and H. Kurz, “Pockels effect based fully integrated, strained silicon electro-optic modulator,” Opt. Express 19(18), 17212–17219 (2011).
[CrossRef] [PubMed]

M. Wächter, C. Matheisen, M. Waldow, T. Wahlbrink, J. Bolten, M. Nagel, and H. Kurz, “Optical generation of terahertz and second-harmonic light in plasma-activated silicon nanophotonic structures,” Appl. Phys. Lett. 97(16), 161107 (2010).
[CrossRef]

Nedeljkovic, M.

Osgood, R. M.

Ou, H.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Owens, N.

Painter, O. J.

Panoiu, N. C.

Perahia, R.

Peucheret, C.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Qian, F.

Reed, G. T.

G. Z. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Y. Yang, E. J. Teo, M. B. H. Breese, A. A. Bettiol, and G. T. Reed, “Silicon photonic waveguides for different wavelength regions,” Semicond. Sci. Technol. 23(6), 064002 (2008).
[CrossRef]

Ripperda, C.

Rotenberg, N.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[CrossRef]

Sasaki, Y.

Schmidt, B. S.

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,” Nature 441(7096), 960–963 (2006).
[CrossRef] [PubMed]

Sharping, J. E.

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,” Nature 441(7096), 960–963 (2006).
[CrossRef] [PubMed]

Shikata, J.

K. Kawase, H. Minamide, K. Imai, J. Shikata, and H. Ito, “Injection-seeded terahertz-wave parametric generator with wide tenability,” Appl. Phys. Lett. 80(2), 195–198 (2002).
[CrossRef]

Shin, S. Y.

Shoji, T.

Song, Q.

Soref, R.

N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011).
[CrossRef]

Soref, R. A.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840 (2006).
[CrossRef]

Stankovic, S.

G. Z. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Y. Yang, E. J. Teo, M. B. H. Breese, A. A. Bettiol, and G. T. Reed, “Silicon photonic waveguides for different wavelength regions,” Semicond. Sci. Technol. 23(6), 064002 (2008).
[CrossRef]

Suizu, K.

Sun, Q.

Suzuki, Y.

Takahashi, J.

Takahashi, M.

Takushima, Y.

Teo, E. J.

G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express 19(8), 7112–7119 (2011).
[CrossRef] [PubMed]

G. Z. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Y. Yang, E. J. Teo, M. B. H. Breese, A. A. Bettiol, and G. T. Reed, “Silicon photonic waveguides for different wavelength regions,” Semicond. Sci. Technol. 23(6), 064002 (2008).
[CrossRef]

Tien, E. K.

Timotijevic, B.

G. Z. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Y. Yang, E. J. Teo, M. B. H. Breese, A. A. Bettiol, and G. T. Reed, “Silicon photonic waveguides for different wavelength regions,” Semicond. Sci. Technol. 23(6), 064002 (2008).
[CrossRef]

Tsuchizawa, T.

Turner, A. C.

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,” Nature 441(7096), 960–963 (2006).
[CrossRef] [PubMed]

van Driel, H. M.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[CrossRef]

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Vodopyanov, K. L.

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M. Wächter, C. Matheisen, M. Waldow, T. Wahlbrink, J. Bolten, M. Nagel, and H. Kurz, “Optical generation of terahertz and second-harmonic light in plasma-activated silicon nanophotonic structures,” Appl. Phys. Lett. 97(16), 161107 (2010).
[CrossRef]

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B. Chmielak, M. Waldow, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Nagel, F. Merget, and H. Kurz, “Pockels effect based fully integrated, strained silicon electro-optic modulator,” Opt. Express 19(18), 17212–17219 (2011).
[CrossRef] [PubMed]

M. Wächter, C. Matheisen, M. Waldow, T. Wahlbrink, J. Bolten, M. Nagel, and H. Kurz, “Optical generation of terahertz and second-harmonic light in plasma-activated silicon nanophotonic structures,” Appl. Phys. Lett. 97(16), 161107 (2010).
[CrossRef]

Waldow, M.

B. Chmielak, M. Waldow, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Nagel, F. Merget, and H. Kurz, “Pockels effect based fully integrated, strained silicon electro-optic modulator,” Opt. Express 19(18), 17212–17219 (2011).
[CrossRef] [PubMed]

M. Wächter, C. Matheisen, M. Waldow, T. Wahlbrink, J. Bolten, M. Nagel, and H. Kurz, “Optical generation of terahertz and second-harmonic light in plasma-activated silicon nanophotonic structures,” Appl. Phys. Lett. 97(16), 161107 (2010).
[CrossRef]

Wang, T. D.

Wang, Z.

Watanabe, T.

Wen, J.

Xie, X.

Xiong, B.

Xu, J.

Yamada, K.

Yang, P. Y.

G. Z. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Y. Yang, E. J. Teo, M. B. H. Breese, A. A. Bettiol, and G. T. Reed, “Silicon photonic waveguides for different wavelength regions,” Semicond. Sci. Technol. 23(6), 064002 (2008).
[CrossRef]

Yin, L.

Yokoyama, H.

Zhang, J.

Zhang, X.

Zhang, X.-C.

Zsigri, B.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (3)

K. Kawase, H. Minamide, K. Imai, J. Shikata, and H. Ito, “Injection-seeded terahertz-wave parametric generator with wide tenability,” Appl. Phys. Lett. 80(2), 195–198 (2002).
[CrossRef]

M. Wächter, C. Matheisen, M. Waldow, T. Wahlbrink, J. Bolten, M. Nagel, and H. Kurz, “Optical generation of terahertz and second-harmonic light in plasma-activated silicon nanophotonic structures,” Appl. Phys. Lett. 97(16), 161107 (2010).
[CrossRef]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[CrossRef]

J. Appl. Phys. (1)

N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840 (2006).
[CrossRef]

Nat. Photonics (1)

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophtonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[CrossRef]

Nature (2)

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

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,” Nature 441(7096), 960–963 (2006).
[CrossRef] [PubMed]

Opt. Express (11)

R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express 13(11), 4341–4349 (2005).
[CrossRef]

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005).
[CrossRef] [PubMed]

T. Ikari, X. Zhang, H. Minamide, and H. Ito, “THz-wave parametric oscillator with a surface-emitted configuration,” Opt. Express 14(4), 1604–1610 (2006).
[CrossRef] [PubMed]

Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Ultrabroadband parametric generation and wavelength conversion in silicon waveguides,” Opt. Express 14(11), 4786–4799 (2006).
[CrossRef] [PubMed]

Y. Takushima, S. Y. Shin, and Y. C. Chung, “Design of a LiNbO(3) ribbon waveguide for efficient difference-frequency generation of terahertz wave in the collinear configuration,” Opt. Express 15(22), 14783–14792 (2007).
[CrossRef] [PubMed]

T. D. Wang, S. T. Lin, Y. Y. Lin, A. C. Chiang, and Y. C. Huang, “Forward and backward terahertz-wave difference-frequency generations from periodically poled lithium niobate,” Opt. Express 16(9), 6471–6478 (2008).
[CrossRef] [PubMed]

Q. Lin, T. J. Johnson, R. Perahia, C. P. Michael, and O. J. Painter, “A proposal for highly tunable optical parametric oscillation in silicon micro-resonators,” Opt. Express 16(14), 10596–10610 (2008).
[CrossRef] [PubMed]

E. K. Tien, Y. Huang, S. Gao, Q. Song, F. Qian, S. K. Kalyoncu, and O. Boyraz, “Discrete parametric band conversion in silicon for mid-infrared applications,” Opt. Express 18(21), 21981–21989 (2010).
[CrossRef] [PubMed]

G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express 19(8), 7112–7119 (2011).
[CrossRef] [PubMed]

B. Chmielak, M. Waldow, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Nagel, F. Merget, and H. Kurz, “Pockels effect based fully integrated, strained silicon electro-optic modulator,” Opt. Express 19(18), 17212–17219 (2011).
[CrossRef] [PubMed]

Z. Wang, H. Liu, N. Huang, Q. Sun, and J. Wen, “Impact of dispersion profiles of silicon waveguides on optical parametric amplification in the femtosecond regime,” Opt. Express 19(24), 24730–24737 (2011).
[CrossRef] [PubMed]

Opt. Lett. (9)

K. L. Vodopyanov and Y. H. Avetisyan, “Optical terahertz wave generation in a planar GaAs waveguide,” Opt. Lett. 33(20), 2314–2316 (2008).
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Y. J. Ding, “Efficient generation of high-frequency terahertz waves from highly lossy second-order nonlinear medium at polariton resonance under transverse-pumping geometry,” Opt. Lett. 35(2), 262–264 (2010).
[CrossRef] [PubMed]

Y. H. Avetisyan, “Terahertz-wave surface-emitted difference-frequency generation without quasi-phase-matching technique,” Opt. Lett. 35(15), 2508–2510 (2010).
[CrossRef] [PubMed]

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32(4), 391–393 (2007).
[CrossRef] [PubMed]

K. Suizu and K. Kawase, “Terahertz-wave generation in a conventional optical fiber,” Opt. Lett. 32(20), 2990–2992 (2007).
[CrossRef] [PubMed]

K. Suizu, Y. Suzuki, Y. Sasaki, H. Ito, and Y. Avetisyan, “Surface-emitted terahertz-wave generation by ridged periodically poled lithium niobate and enhancement by mixing of two terahertz waves,” Opt. Lett. 31(7), 957–959 (2006).
[CrossRef] [PubMed]

X. Xie, J. Xu, and X.-C. Zhang, “Terahertz wave generation and detection from a cdte crystal characterized by different excitation wavelengths,” Opt. Lett. 31(7), 978–980 (2006).
[CrossRef] [PubMed]

Y. Sasaki, Y. Avetisyan, H. Yokoyama, and H. Ito, “Surface-emitted terahertz-wave difference-frequency generation in two-dimensional periodically poled lithium niobate,” Opt. Lett. 30(21), 2927–2929 (2005).
[CrossRef] [PubMed]

A. C. Chiang, T. D. Wang, Y. Y. Lin, S. T. Lin, H. H. Lee, Y. C. Huang, and Y. H. Chen, “Enhanced terahertz-wave parametric generation and oscillation in lithium niobate waveguides at terahertz frequencies,” Opt. Lett. 30(24), 3392–3394 (2005).
[CrossRef] [PubMed]

Semicond. Sci. Technol. (1)

G. Z. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Y. Yang, E. J. Teo, M. B. H. Breese, A. A. Bettiol, and G. T. Reed, “Silicon photonic waveguides for different wavelength regions,” Semicond. Sci. Technol. 23(6), 064002 (2008).
[CrossRef]

Other (3)

T. E. Murphy, software available at http://www.photonics.umd.edu .

http://www.nature.com/nphoton/journal/v4/n8/full/nphoton.2010.173.html .

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

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Figures (11)

Fig. 1
Fig. 1

Schematic of (a) energy-conservation diagram and (b) the phase-matching condition for collinear phase matching.

Fig. 2
Fig. 2

Left: rib silicon membrane waveguide dimension; Right: the TM mode profiles of the silicon membrane waveguide at the wavelength of 35 μm for different rib heights.

Fig. 3
Fig. 3

Plots of computed effective index of refraction (a), and (b) GVD dispersion (c) forth order dispersion (d) sixth order dispersion as a function of pump wavelength for different rib heights.

Fig. 4
Fig. 4

The fundamental TM mode profiles of the waveguides with different rib heights.

Fig. 5
Fig. 5

Linear phase mismatch as a function of THz wavelength for different pump wavelengths when the rib height is 15 μm.

Fig. 6
Fig. 6

(a) Linear phase mismatch as a function of THz wavelength for different pump wavelengths, and (b) signal wavelength and related THz-wavelength depend on pump wavelength for collinear phase-matched THz-wave generation when the rib height is 15 μm.

Fig. 7
Fig. 7

(a) Linear phase mismatch as a function of THz wavelength for different rib heights, and (b) signal wavelength and related THz-wavelength depend on rib heights for collinear phase-matched THz-wave generation when the pump wavelength is 4.3 μm.

Fig. 8
Fig. 8

(a) The THz-wave peak power depends on distance for different pump peak powers; (b) The output spectra of THz-wave with different pump peak powers when the distance is 6 mm.

Fig. 9
Fig. 9

The conversion efficiency as a function of THz-wavelength when the signal wavelength is tuned from 2299.8 nm to 2304.9 nm for a fixed pump located at 4.3 μm.

Fig. 10
Fig. 10

(a) The peak power and related wavelength of THz-wave as a function of pump wavelength and (b) the corresponding output spectra of THz-wave when the rib height is 15 μm.

Fig. 11
Fig. 11

(a) The THz-wave peak power and related THz-wavelength as a function of rib height and (b) the corresponding output spectra of THz-wave when the pump wavelength is 4.3 μm.

Equations (8)

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

2 ω p ω s ω THz =0,
k s + k THz 2 k p + k NL =0,
k L = β 2p Ω sp 2 +2 m=2 β 2mp (2m)! Ω sp 2m ,
W H 0.3+ r 1 r 2 ,
d A p dz = α p 2 A p +i γ p | A p | 2 A p +2i γ ps | A s | 2 A p +2i γ pt | A t | 2 A p +2i γ p A s A t A p * exp( i k L z ),
d A s dz = α s 2 A s +i γ s | A s | 2 A s +2i γ sp | A p | 2 A s +2i γ st | A t | 2 A s +i γ s A p 2 A t * exp( i k L z ),
d A t dz = α t 2 A t +i γ t | A t | 2 A t +2i γ tp | A p | 2 A t +2i γ ts | A s | 2 A t +i γ t A p 2 A s * exp( i k L z ),
η= P THz out / P pump in

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