Abstract

The interaction of terahertz waves with silicon is usually explained using a linear model of conduction in which free carriers respond to the oscillating electric field, leading to absorption. Here we employ a silicon dielectric waveguide to confine and concentrate terahertz pulses, and observe that the absorption saturates under strong terahertz fields. By comparing the response between lightly-doped and intrinsic silicon waveguides, we confirm the role of hot carriers in this saturable absorption. We introduce a nonlinear dynamical model of Drude conductivity that, when incorporated into a wave propagation equation, predicts a comparable field-induced transparency and elucidates the physical mechanism underlying this nonlinear effect: velocity saturation—an effect that fundamentally limits the speed of most semiconductor devices. The results are numerically confirmed by Monte Carlo simulations of the Boltzmann transport equation, coupled with split-step nonlinear wave propagation. The results reported here could have significance in understanding and designing a variety of emerging and future terahertz devices, such as waveguides, mixers, detectors, and oscillators.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2013 (2)

I. Al-Naib, G. Sharma, M. M. Dignam, H. Hafez, A. Ibrahim, D. G. Cooke, T. Ozaki, R. Morandotti, “Effect of local field enhancement on the nonlinear terahertz response of a silicon-based metamaterial,” Phys. Rev. B 88, 195203 (2013).
[Crossref]

Y.-G. Jeong, M. J. Paul, S.-H. Kim, K.-J. Yee, D.-S. Kim, Y.-S. Lee, “Large enhancement of nonlinear terahertz absorption in intrinsic GaAs by plasmonic nano antennas,” Appl. Phys. Lett. 103, 171109 (2013).
[Crossref]

2012 (3)

G. Sharma, I. Al-Naib, H. Hafez, R. Morandotti, D. G. Cooke, T. Ozaki, “Carrier density dependence of the nonlinear absorption of intense THz radiation in GaAs,” Opt. Express 20, 18016–18024 (2012).
[Crossref]

D. Turchinovich, J. M. Hvam, M. C. Hoffmann, “Self-phase modulation of a single-cycle terahertz pulse by nonlinear free-carrier response in a semiconductor,” Phys. Rev. B 85, 201304 (2012).
[Crossref]

F. Junginger, B. Mayer, C. Schmidt, O. Schubert, S. Mährlein, A. Leitenstorfer, R. Huber, A. Pashkin, “Nonperturbative interband response of a bulk InSb semiconductor driven off resonantly by terahertz electromagnetic few-cycle pulses,” Phys. Rev. Lett. 109, 147403 (2012).
[Crossref]

2011 (2)

P. Bowlan, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, C. Flytzanis, “High- field transport in an electron-hole plasma: transition from ballistic to drift motion,” Phys. Rev. Lett. 107, 256602 (2011).
[Crossref]

B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, W. M. J. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19, 20172–20181 (2011).
[Crossref]

2010 (4)

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “Observation of nonequilibrium carrier distribution in Ge, Si, and GaAs by terahertz pump terahertz probe measurements,” Phys. Rev. B 81, 035201 (2010).
[Crossref]

M. C. Hoffmann, D. Turchinovich, “Semiconductor saturable absorbers for ultrafast terahertz signals,” Appl. Phys. Lett. 96, 151110 (2010).
[Crossref]

B. Jalali, “Silicon photonics: Nonlinear optics in the midinfrared,” Nat. Photonics 4, 506–508 (2010).
[Crossref]

K. J. Willis, S. C. Hagness, I. Knezevic, “Terahertz conductivity of doped silicon calculated using the ensemble Monte Carlo/finite-difference time-domain simulation technique,” Appl. Phys. Lett. 96, 062106 (2010).
[Crossref]

2009 (3)

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “THz-pump/THz-probe spectroscopy of semiconductors at high field strengths,” J. Opt. Soc. Am. B 26, A29–A34 (2009).
[Crossref]

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “Impact ionization in InSb probed by terahertz pump/terahertz probe spectroscopy,” Phys. Rev. B 79, 161201 (2009).
[Crossref]

C. M. Yee, M. S. Sherwin, “High-Q terahertz microcavities in silicon photonic crystal slabs,” Appl. Phys. Lett. 94, 154104 (2009).
[Crossref]

2008 (3)

2007 (4)

K.-L. Yeh, M. C. Hoffmann, J. Hebling, K. A. Nelson, “Generation of 10  μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007).
[Crossref]

M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, S. C. Jeoung, Q. H. Park, P. C. M. Planken, D. S. Kim, “Fourier-transform terahertz near-field imaging of one-dimensional slit arrays: mapping of electric-field-, magnetic-field-, and Poynting vectors,” Opt. Express 15, 11781–11789 (2007).
[Crossref]

Q. Lin, O. J. Painter, G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007).
[Crossref]

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, P. M. Fauchet, “Anisotropic nonlinear response of silicon in the near-infrared region,” Appl. Phys. Lett. 91, 071113 (2007).
[Crossref]

2006 (2)

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref]

P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, K. H. Ploog, “Nonlinear terahertz response of n-type GaAs,” Phys. Rev. Lett. 96, 187402 (2006).
[Crossref]

2005 (1)

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[Crossref]

2004 (1)

2003 (1)

T. Grasser, T.-W. Tang, H. Kosina, S. Selberherr, “A review of hydrodynamic and energy-transport models for semiconductor device simulation,” Proc. IEEE 91, 251–274 (2003).
[Crossref]

2002 (1)

1990 (1)

1986 (1)

W. Hänsch, M. Miura-Mattausch, “The hot electron problem in small semiconductor devices,” J. Appl. Phys. 60, 650–656 (1986).
[Crossref]

1981 (1)

J. P. Nougier, J. C. Vaissiere, D. Gasquet, J. Zimmermann, E. Constant, “Determination of transient regime of hot carriers in semiconductors, using the relaxation time approximations,” J. Appl. Phys. 52, 825–832 (1981).
[Crossref]

Adam, A. J. L.

Agrawal, G. P.

Q. Lin, O. J. Painter, G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007).
[Crossref]

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, P. M. Fauchet, “Anisotropic nonlinear response of silicon in the near-infrared region,” Appl. Phys. Lett. 91, 071113 (2007).
[Crossref]

Almasi, G.

Al-Naib, I.

I. Al-Naib, G. Sharma, M. M. Dignam, H. Hafez, A. Ibrahim, D. G. Cooke, T. Ozaki, R. Morandotti, “Effect of local field enhancement on the nonlinear terahertz response of a silicon-based metamaterial,” Phys. Rev. B 88, 195203 (2013).
[Crossref]

G. Sharma, I. Al-Naib, H. Hafez, R. Morandotti, D. G. Cooke, T. Ozaki, “Carrier density dependence of the nonlinear absorption of intense THz radiation in GaAs,” Opt. Express 20, 18016–18024 (2012).
[Crossref]

Baets, R.

Bartal, B.

Bowlan, P.

P. Bowlan, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, C. Flytzanis, “High- field transport in an electron-hole plasma: transition from ballistic to drift motion,” Phys. Rev. Lett. 107, 256602 (2011).
[Crossref]

Boyd, R. W.

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, P. M. Fauchet, “Anisotropic nonlinear response of silicon in the near-infrared region,” Appl. Phys. Lett. 91, 071113 (2007).
[Crossref]

Chakkittakandy, R.

Cohen, O.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[Crossref]

Constant, E.

J. P. Nougier, J. C. Vaissiere, D. Gasquet, J. Zimmermann, E. Constant, “Determination of transient regime of hot carriers in semiconductors, using the relaxation time approximations,” J. Appl. Phys. 52, 825–832 (1981).
[Crossref]

Cooke, D. G.

I. Al-Naib, G. Sharma, M. M. Dignam, H. Hafez, A. Ibrahim, D. G. Cooke, T. Ozaki, R. Morandotti, “Effect of local field enhancement on the nonlinear terahertz response of a silicon-based metamaterial,” Phys. Rev. B 88, 195203 (2013).
[Crossref]

G. Sharma, I. Al-Naib, H. Hafez, R. Morandotti, D. G. Cooke, T. Ozaki, “Carrier density dependence of the nonlinear absorption of intense THz radiation in GaAs,” Opt. Express 20, 18016–18024 (2012).
[Crossref]

Corver, J. A.

Dai, J.

Dignam, M. M.

I. Al-Naib, G. Sharma, M. M. Dignam, H. Hafez, A. Ibrahim, D. G. Cooke, T. Ozaki, R. Morandotti, “Effect of local field enhancement on the nonlinear terahertz response of a silicon-based metamaterial,” Phys. Rev. B 88, 195203 (2013).
[Crossref]

Elsaesser, T.

P. Bowlan, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, C. Flytzanis, “High- field transport in an electron-hole plasma: transition from ballistic to drift motion,” Phys. Rev. Lett. 107, 256602 (2011).
[Crossref]

P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, K. H. Ploog, “Nonlinear terahertz response of n-type GaAs,” Phys. Rev. Lett. 96, 187402 (2006).
[Crossref]

Fang, A.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[Crossref]

Fattinger, C.

Fauchet, P. M.

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, P. M. Fauchet, “Anisotropic nonlinear response of silicon in the near-infrared region,” Appl. Phys. Lett. 91, 071113 (2007).
[Crossref]

Flytzanis, C.

P. Bowlan, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, C. Flytzanis, “High- field transport in an electron-hole plasma: transition from ballistic to drift motion,” Phys. Rev. Lett. 107, 256602 (2011).
[Crossref]

Foster, M. A.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref]

Gaal, P.

P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, K. H. Ploog, “Nonlinear terahertz response of n-type GaAs,” Phys. Rev. Lett. 96, 187402 (2006).
[Crossref]

Gaeta, A. L.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref]

Gasquet, D.

J. P. Nougier, J. C. Vaissiere, D. Gasquet, J. Zimmermann, E. Constant, “Determination of transient regime of hot carriers in semiconductors, using the relaxation time approximations,” J. Appl. Phys. 52, 825–832 (1981).
[Crossref]

Grasser, T.

T. Grasser, T.-W. Tang, H. Kosina, S. Selberherr, “A review of hydrodynamic and energy-transport models for semiconductor device simulation,” Proc. IEEE 91, 251–274 (2003).
[Crossref]

Green, W. M. J.

Grischkowsky, D.

Hafez, H.

I. Al-Naib, G. Sharma, M. M. Dignam, H. Hafez, A. Ibrahim, D. G. Cooke, T. Ozaki, R. Morandotti, “Effect of local field enhancement on the nonlinear terahertz response of a silicon-based metamaterial,” Phys. Rev. B 88, 195203 (2013).
[Crossref]

G. Sharma, I. Al-Naib, H. Hafez, R. Morandotti, D. G. Cooke, T. Ozaki, “Carrier density dependence of the nonlinear absorption of intense THz radiation in GaAs,” Opt. Express 20, 18016–18024 (2012).
[Crossref]

Hagness, S. C.

K. J. Willis, S. C. Hagness, I. Knezevic, “Terahertz conductivity of doped silicon calculated using the ensemble Monte Carlo/finite-difference time-domain simulation technique,” Appl. Phys. Lett. 96, 062106 (2010).
[Crossref]

Hak, D.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[Crossref]

Han, P.

G. Kaur, P. Han, X.-C. Zhang, “Terahertz induced nonlinear effects in doped silicon observed by open-aperture Z-scan,” in 2010 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz) (IEEE, 2010).

Hänsch, W.

W. Hänsch, M. Miura-Mattausch, “The hot electron problem in small semiconductor devices,” J. Appl. Phys. 60, 650–656 (1986).
[Crossref]

Hebling, J.

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “Observation of nonequilibrium carrier distribution in Ge, Si, and GaAs by terahertz pump terahertz probe measurements,” Phys. Rev. B 81, 035201 (2010).
[Crossref]

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “Impact ionization in InSb probed by terahertz pump/terahertz probe spectroscopy,” Phys. Rev. B 79, 161201 (2009).
[Crossref]

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “THz-pump/THz-probe spectroscopy of semiconductors at high field strengths,” J. Opt. Soc. Am. B 26, A29–A34 (2009).
[Crossref]

J. Hebling, K.-L. Yeh, M. C. Hoffmann, B. Bartal, K. A. Nelson, “Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities,” J. Opt. Soc. Am. B 25, B6–B19 (2008).
[Crossref]

K.-L. Yeh, M. C. Hoffmann, J. Hebling, K. A. Nelson, “Generation of 10  μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007).
[Crossref]

J. Hebling, G. Almasi, I. Kozma, J. Kuhl, “Velocity matching by pulse front tilting for large area THz-pulse generation,” Opt. Express 10, 1161–1166 (2002).
[Crossref]

Hey, R.

P. Bowlan, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, C. Flytzanis, “High- field transport in an electron-hole plasma: transition from ballistic to drift motion,” Phys. Rev. Lett. 107, 256602 (2011).
[Crossref]

P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, K. H. Ploog, “Nonlinear terahertz response of n-type GaAs,” Phys. Rev. Lett. 96, 187402 (2006).
[Crossref]

Hoffmann, M. C.

D. Turchinovich, J. M. Hvam, M. C. Hoffmann, “Self-phase modulation of a single-cycle terahertz pulse by nonlinear free-carrier response in a semiconductor,” Phys. Rev. B 85, 201304 (2012).
[Crossref]

M. C. Hoffmann, D. Turchinovich, “Semiconductor saturable absorbers for ultrafast terahertz signals,” Appl. Phys. Lett. 96, 151110 (2010).
[Crossref]

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “Observation of nonequilibrium carrier distribution in Ge, Si, and GaAs by terahertz pump terahertz probe measurements,” Phys. Rev. B 81, 035201 (2010).
[Crossref]

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “Impact ionization in InSb probed by terahertz pump/terahertz probe spectroscopy,” Phys. Rev. B 79, 161201 (2009).
[Crossref]

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “THz-pump/THz-probe spectroscopy of semiconductors at high field strengths,” J. Opt. Soc. Am. B 26, A29–A34 (2009).
[Crossref]

J. Hebling, K.-L. Yeh, M. C. Hoffmann, B. Bartal, K. A. Nelson, “Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities,” J. Opt. Soc. Am. B 25, B6–B19 (2008).
[Crossref]

K.-L. Yeh, M. C. Hoffmann, J. Hebling, K. A. Nelson, “Generation of 10  μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007).
[Crossref]

Huber, R.

F. Junginger, B. Mayer, C. Schmidt, O. Schubert, S. Mährlein, A. Leitenstorfer, R. Huber, A. Pashkin, “Nonperturbative interband response of a bulk InSb semiconductor driven off resonantly by terahertz electromagnetic few-cycle pulses,” Phys. Rev. Lett. 109, 147403 (2012).
[Crossref]

Hvam, J. M.

D. Turchinovich, J. M. Hvam, M. C. Hoffmann, “Self-phase modulation of a single-cycle terahertz pulse by nonlinear free-carrier response in a semiconductor,” Phys. Rev. B 85, 201304 (2012).
[Crossref]

Hwang, H. Y.

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “Observation of nonequilibrium carrier distribution in Ge, Si, and GaAs by terahertz pump terahertz probe measurements,” Phys. Rev. B 81, 035201 (2010).
[Crossref]

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “Impact ionization in InSb probed by terahertz pump/terahertz probe spectroscopy,” Phys. Rev. B 79, 161201 (2009).
[Crossref]

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “THz-pump/THz-probe spectroscopy of semiconductors at high field strengths,” J. Opt. Soc. Am. B 26, A29–A34 (2009).
[Crossref]

Ibrahim, A.

I. Al-Naib, G. Sharma, M. M. Dignam, H. Hafez, A. Ibrahim, D. G. Cooke, T. Ozaki, R. Morandotti, “Effect of local field enhancement on the nonlinear terahertz response of a silicon-based metamaterial,” Phys. Rev. B 88, 195203 (2013).
[Crossref]

Jalali, B.

B. Jalali, “Silicon photonics: Nonlinear optics in the midinfrared,” Nat. Photonics 4, 506–508 (2010).
[Crossref]

Jeong, Y.-G.

Y.-G. Jeong, M. J. Paul, S.-H. Kim, K.-J. Yee, D.-S. Kim, Y.-S. Lee, “Large enhancement of nonlinear terahertz absorption in intrinsic GaAs by plasmonic nano antennas,” Appl. Phys. Lett. 103, 171109 (2013).
[Crossref]

Jeoung, S. C.

Jones, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[Crossref]

Junginger, F.

F. Junginger, B. Mayer, C. Schmidt, O. Schubert, S. Mährlein, A. Leitenstorfer, R. Huber, A. Pashkin, “Nonperturbative interband response of a bulk InSb semiconductor driven off resonantly by terahertz electromagnetic few-cycle pulses,” Phys. Rev. Lett. 109, 147403 (2012).
[Crossref]

Kang, J. H.

Kaur, G.

G. Kaur, P. Han, X.-C. Zhang, “Terahertz induced nonlinear effects in doped silicon observed by open-aperture Z-scan,” in 2010 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz) (IEEE, 2010).

Keiding, S.

Kim, D. S.

Kim, D.-S.

Y.-G. Jeong, M. J. Paul, S.-H. Kim, K.-J. Yee, D.-S. Kim, Y.-S. Lee, “Large enhancement of nonlinear terahertz absorption in intrinsic GaAs by plasmonic nano antennas,” Appl. Phys. Lett. 103, 171109 (2013).
[Crossref]

Kim, S.-H.

Y.-G. Jeong, M. J. Paul, S.-H. Kim, K.-J. Yee, D.-S. Kim, Y.-S. Lee, “Large enhancement of nonlinear terahertz absorption in intrinsic GaAs by plasmonic nano antennas,” Appl. Phys. Lett. 103, 171109 (2013).
[Crossref]

Knezevic, I.

K. J. Willis, S. C. Hagness, I. Knezevic, “Terahertz conductivity of doped silicon calculated using the ensemble Monte Carlo/finite-difference time-domain simulation technique,” Appl. Phys. Lett. 96, 062106 (2010).
[Crossref]

Kosina, H.

T. Grasser, T.-W. Tang, H. Kosina, S. Selberherr, “A review of hydrodynamic and energy-transport models for semiconductor device simulation,” Proc. IEEE 91, 251–274 (2003).
[Crossref]

Kozma, I.

Kuehn, W.

P. Bowlan, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, C. Flytzanis, “High- field transport in an electron-hole plasma: transition from ballistic to drift motion,” Phys. Rev. Lett. 107, 256602 (2011).
[Crossref]

Kuhl, J.

Kuyken, B.

Lee, J. W.

Lee, Y.-S.

Y.-G. Jeong, M. J. Paul, S.-H. Kim, K.-J. Yee, D.-S. Kim, Y.-S. Lee, “Large enhancement of nonlinear terahertz absorption in intrinsic GaAs by plasmonic nano antennas,” Appl. Phys. Lett. 103, 171109 (2013).
[Crossref]

Leitenstorfer, A.

F. Junginger, B. Mayer, C. Schmidt, O. Schubert, S. Mährlein, A. Leitenstorfer, R. Huber, A. Pashkin, “Nonperturbative interband response of a bulk InSb semiconductor driven off resonantly by terahertz electromagnetic few-cycle pulses,” Phys. Rev. Lett. 109, 147403 (2012).
[Crossref]

Lin, Q.

Q. Lin, O. J. Painter, G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007).
[Crossref]

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, P. M. Fauchet, “Anisotropic nonlinear response of silicon in the near-infrared region,” Appl. Phys. Lett. 91, 071113 (2007).
[Crossref]

Lindenberg, A. M.

H. Wen, M. Wiczer, A. M. Lindenberg, “Ultrafast electron cascades in semiconductors driven by intense femtosecond terahertz pulses,” Phys. Rev. B 78, 125203 (2008).
[Crossref]

Lipson, M.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref]

Liu, A.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[Crossref]

Liu, X.

Lundstrom, M.

M. Lundstrom, Fundamentals of Carrier Transport, 2nd ed. (Cambridge University, 2000).

Mährlein, S.

F. Junginger, B. Mayer, C. Schmidt, O. Schubert, S. Mährlein, A. Leitenstorfer, R. Huber, A. Pashkin, “Nonperturbative interband response of a bulk InSb semiconductor driven off resonantly by terahertz electromagnetic few-cycle pulses,” Phys. Rev. Lett. 109, 147403 (2012).
[Crossref]

Mayer, B.

F. Junginger, B. Mayer, C. Schmidt, O. Schubert, S. Mährlein, A. Leitenstorfer, R. Huber, A. Pashkin, “Nonperturbative interband response of a bulk InSb semiconductor driven off resonantly by terahertz electromagnetic few-cycle pulses,” Phys. Rev. Lett. 109, 147403 (2012).
[Crossref]

Miura-Mattausch, M.

W. Hänsch, M. Miura-Mattausch, “The hot electron problem in small semiconductor devices,” J. Appl. Phys. 60, 650–656 (1986).
[Crossref]

Morandotti, R.

I. Al-Naib, G. Sharma, M. M. Dignam, H. Hafez, A. Ibrahim, D. G. Cooke, T. Ozaki, R. Morandotti, “Effect of local field enhancement on the nonlinear terahertz response of a silicon-based metamaterial,” Phys. Rev. B 88, 195203 (2013).
[Crossref]

G. Sharma, I. Al-Naib, H. Hafez, R. Morandotti, D. G. Cooke, T. Ozaki, “Carrier density dependence of the nonlinear absorption of intense THz radiation in GaAs,” Opt. Express 20, 18016–18024 (2012).
[Crossref]

Nelson, K. A.

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “Observation of nonequilibrium carrier distribution in Ge, Si, and GaAs by terahertz pump terahertz probe measurements,” Phys. Rev. B 81, 035201 (2010).
[Crossref]

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “Impact ionization in InSb probed by terahertz pump/terahertz probe spectroscopy,” Phys. Rev. B 79, 161201 (2009).
[Crossref]

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “THz-pump/THz-probe spectroscopy of semiconductors at high field strengths,” J. Opt. Soc. Am. B 26, A29–A34 (2009).
[Crossref]

J. Hebling, K.-L. Yeh, M. C. Hoffmann, B. Bartal, K. A. Nelson, “Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities,” J. Opt. Soc. Am. B 25, B6–B19 (2008).
[Crossref]

K.-L. Yeh, M. C. Hoffmann, J. Hebling, K. A. Nelson, “Generation of 10  μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007).
[Crossref]

Nicolaescu, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[Crossref]

Nougier, J. P.

J. P. Nougier, J. C. Vaissiere, D. Gasquet, J. Zimmermann, E. Constant, “Determination of transient regime of hot carriers in semiconductors, using the relaxation time approximations,” J. Appl. Phys. 52, 825–832 (1981).
[Crossref]

Osgood, R. M.

Ozaki, T.

I. Al-Naib, G. Sharma, M. M. Dignam, H. Hafez, A. Ibrahim, D. G. Cooke, T. Ozaki, R. Morandotti, “Effect of local field enhancement on the nonlinear terahertz response of a silicon-based metamaterial,” Phys. Rev. B 88, 195203 (2013).
[Crossref]

G. Sharma, I. Al-Naib, H. Hafez, R. Morandotti, D. G. Cooke, T. Ozaki, “Carrier density dependence of the nonlinear absorption of intense THz radiation in GaAs,” Opt. Express 20, 18016–18024 (2012).
[Crossref]

Painter, O. J.

Paniccia, M.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[Crossref]

Park, Q. H.

Pashkin, A.

F. Junginger, B. Mayer, C. Schmidt, O. Schubert, S. Mährlein, A. Leitenstorfer, R. Huber, A. Pashkin, “Nonperturbative interband response of a bulk InSb semiconductor driven off resonantly by terahertz electromagnetic few-cycle pulses,” Phys. Rev. Lett. 109, 147403 (2012).
[Crossref]

Paul, M. J.

Y.-G. Jeong, M. J. Paul, S.-H. Kim, K.-J. Yee, D.-S. Kim, Y.-S. Lee, “Large enhancement of nonlinear terahertz absorption in intrinsic GaAs by plasmonic nano antennas,” Appl. Phys. Lett. 103, 171109 (2013).
[Crossref]

Piredda, G.

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, P. M. Fauchet, “Anisotropic nonlinear response of silicon in the near-infrared region,” Appl. Phys. Lett. 91, 071113 (2007).
[Crossref]

Planken, P. C.

Planken, P. C. M.

Ploog, K. H.

P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, K. H. Ploog, “Nonlinear terahertz response of n-type GaAs,” Phys. Rev. Lett. 96, 187402 (2006).
[Crossref]

Reimann, K.

P. Bowlan, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, C. Flytzanis, “High- field transport in an electron-hole plasma: transition from ballistic to drift motion,” Phys. Rev. Lett. 107, 256602 (2011).
[Crossref]

P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, K. H. Ploog, “Nonlinear terahertz response of n-type GaAs,” Phys. Rev. Lett. 96, 187402 (2006).
[Crossref]

Roelkens, G.

Rong, H.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[Crossref]

Schmidt, B. S.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref]

Schmidt, C.

F. Junginger, B. Mayer, C. Schmidt, O. Schubert, S. Mährlein, A. Leitenstorfer, R. Huber, A. Pashkin, “Nonperturbative interband response of a bulk InSb semiconductor driven off resonantly by terahertz electromagnetic few-cycle pulses,” Phys. Rev. Lett. 109, 147403 (2012).
[Crossref]

Schubert, O.

F. Junginger, B. Mayer, C. Schmidt, O. Schubert, S. Mährlein, A. Leitenstorfer, R. Huber, A. Pashkin, “Nonperturbative interband response of a bulk InSb semiconductor driven off resonantly by terahertz electromagnetic few-cycle pulses,” Phys. Rev. Lett. 109, 147403 (2012).
[Crossref]

Selberherr, S.

T. Grasser, T.-W. Tang, H. Kosina, S. Selberherr, “A review of hydrodynamic and energy-transport models for semiconductor device simulation,” Proc. IEEE 91, 251–274 (2003).
[Crossref]

Seo, M. A.

Sharma, G.

I. Al-Naib, G. Sharma, M. M. Dignam, H. Hafez, A. Ibrahim, D. G. Cooke, T. Ozaki, R. Morandotti, “Effect of local field enhancement on the nonlinear terahertz response of a silicon-based metamaterial,” Phys. Rev. B 88, 195203 (2013).
[Crossref]

G. Sharma, I. Al-Naib, H. Hafez, R. Morandotti, D. G. Cooke, T. Ozaki, “Carrier density dependence of the nonlinear absorption of intense THz radiation in GaAs,” Opt. Express 20, 18016–18024 (2012).
[Crossref]

Sharping, J. E.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref]

Sherwin, M. S.

C. M. Yee, M. S. Sherwin, “High-Q terahertz microcavities in silicon photonic crystal slabs,” Appl. Phys. Lett. 94, 154104 (2009).
[Crossref]

Tang, T.-W.

T. Grasser, T.-W. Tang, H. Kosina, S. Selberherr, “A review of hydrodynamic and energy-transport models for semiconductor device simulation,” Proc. IEEE 91, 251–274 (2003).
[Crossref]

Turchinovich, D.

D. Turchinovich, J. M. Hvam, M. C. Hoffmann, “Self-phase modulation of a single-cycle terahertz pulse by nonlinear free-carrier response in a semiconductor,” Phys. Rev. B 85, 201304 (2012).
[Crossref]

M. C. Hoffmann, D. Turchinovich, “Semiconductor saturable absorbers for ultrafast terahertz signals,” Appl. Phys. Lett. 96, 151110 (2010).
[Crossref]

Turner, A. C.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref]

Vaissiere, J. C.

J. P. Nougier, J. C. Vaissiere, D. Gasquet, J. Zimmermann, E. Constant, “Determination of transient regime of hot carriers in semiconductors, using the relaxation time approximations,” J. Appl. Phys. 52, 825–832 (1981).
[Crossref]

van Exter, M.

Wen, H.

H. Wen, M. Wiczer, A. M. Lindenberg, “Ultrafast electron cascades in semiconductors driven by intense femtosecond terahertz pulses,” Phys. Rev. B 78, 125203 (2008).
[Crossref]

Wiczer, M.

H. Wen, M. Wiczer, A. M. Lindenberg, “Ultrafast electron cascades in semiconductors driven by intense femtosecond terahertz pulses,” Phys. Rev. B 78, 125203 (2008).
[Crossref]

Willis, K. J.

K. J. Willis, S. C. Hagness, I. Knezevic, “Terahertz conductivity of doped silicon calculated using the ensemble Monte Carlo/finite-difference time-domain simulation technique,” Appl. Phys. Lett. 96, 062106 (2010).
[Crossref]

Woerner, M.

P. Bowlan, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, C. Flytzanis, “High- field transport in an electron-hole plasma: transition from ballistic to drift motion,” Phys. Rev. Lett. 107, 256602 (2011).
[Crossref]

P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, K. H. Ploog, “Nonlinear terahertz response of n-type GaAs,” Phys. Rev. Lett. 96, 187402 (2006).
[Crossref]

Yee, C. M.

C. M. Yee, M. S. Sherwin, “High-Q terahertz microcavities in silicon photonic crystal slabs,” Appl. Phys. Lett. 94, 154104 (2009).
[Crossref]

Yee, K.-J.

Y.-G. Jeong, M. J. Paul, S.-H. Kim, K.-J. Yee, D.-S. Kim, Y.-S. Lee, “Large enhancement of nonlinear terahertz absorption in intrinsic GaAs by plasmonic nano antennas,” Appl. Phys. Lett. 103, 171109 (2013).
[Crossref]

Yeh, K.-L.

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “Observation of nonequilibrium carrier distribution in Ge, Si, and GaAs by terahertz pump terahertz probe measurements,” Phys. Rev. B 81, 035201 (2010).
[Crossref]

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “Impact ionization in InSb probed by terahertz pump/terahertz probe spectroscopy,” Phys. Rev. B 79, 161201 (2009).
[Crossref]

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “THz-pump/THz-probe spectroscopy of semiconductors at high field strengths,” J. Opt. Soc. Am. B 26, A29–A34 (2009).
[Crossref]

J. Hebling, K.-L. Yeh, M. C. Hoffmann, B. Bartal, K. A. Nelson, “Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities,” J. Opt. Soc. Am. B 25, B6–B19 (2008).
[Crossref]

K.-L. Yeh, M. C. Hoffmann, J. Hebling, K. A. Nelson, “Generation of 10  μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007).
[Crossref]

Zhang, J.

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, P. M. Fauchet, “Anisotropic nonlinear response of silicon in the near-infrared region,” Appl. Phys. Lett. 91, 071113 (2007).
[Crossref]

J. Dai, J. Zhang, W. Zhang, D. Grischkowsky, “Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon,” J. Opt. Soc. Am. B 21, 1379–1386 (2004).
[Crossref]

Zhang, W.

Zhang, X.-C.

G. Kaur, P. Han, X.-C. Zhang, “Terahertz induced nonlinear effects in doped silicon observed by open-aperture Z-scan,” in 2010 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz) (IEEE, 2010).

Zimmermann, J.

J. P. Nougier, J. C. Vaissiere, D. Gasquet, J. Zimmermann, E. Constant, “Determination of transient regime of hot carriers in semiconductors, using the relaxation time approximations,” J. Appl. Phys. 52, 825–832 (1981).
[Crossref]

Appl. Phys. Lett. (6)

C. M. Yee, M. S. Sherwin, “High-Q terahertz microcavities in silicon photonic crystal slabs,” Appl. Phys. Lett. 94, 154104 (2009).
[Crossref]

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, P. M. Fauchet, “Anisotropic nonlinear response of silicon in the near-infrared region,” Appl. Phys. Lett. 91, 071113 (2007).
[Crossref]

Y.-G. Jeong, M. J. Paul, S.-H. Kim, K.-J. Yee, D.-S. Kim, Y.-S. Lee, “Large enhancement of nonlinear terahertz absorption in intrinsic GaAs by plasmonic nano antennas,” Appl. Phys. Lett. 103, 171109 (2013).
[Crossref]

M. C. Hoffmann, D. Turchinovich, “Semiconductor saturable absorbers for ultrafast terahertz signals,” Appl. Phys. Lett. 96, 151110 (2010).
[Crossref]

K.-L. Yeh, M. C. Hoffmann, J. Hebling, K. A. Nelson, “Generation of 10  μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007).
[Crossref]

K. J. Willis, S. C. Hagness, I. Knezevic, “Terahertz conductivity of doped silicon calculated using the ensemble Monte Carlo/finite-difference time-domain simulation technique,” Appl. Phys. Lett. 96, 062106 (2010).
[Crossref]

J. Appl. Phys. (2)

J. P. Nougier, J. C. Vaissiere, D. Gasquet, J. Zimmermann, E. Constant, “Determination of transient regime of hot carriers in semiconductors, using the relaxation time approximations,” J. Appl. Phys. 52, 825–832 (1981).
[Crossref]

W. Hänsch, M. Miura-Mattausch, “The hot electron problem in small semiconductor devices,” J. Appl. Phys. 60, 650–656 (1986).
[Crossref]

J. Opt. Soc. Am. B (4)

Nat. Photonics (1)

B. Jalali, “Silicon photonics: Nonlinear optics in the midinfrared,” Nat. Photonics 4, 506–508 (2010).
[Crossref]

Nature (2)

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[Crossref]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref]

Opt. Express (6)

Phys. Rev. B (5)

H. Wen, M. Wiczer, A. M. Lindenberg, “Ultrafast electron cascades in semiconductors driven by intense femtosecond terahertz pulses,” Phys. Rev. B 78, 125203 (2008).
[Crossref]

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “Impact ionization in InSb probed by terahertz pump/terahertz probe spectroscopy,” Phys. Rev. B 79, 161201 (2009).
[Crossref]

D. Turchinovich, J. M. Hvam, M. C. Hoffmann, “Self-phase modulation of a single-cycle terahertz pulse by nonlinear free-carrier response in a semiconductor,” Phys. Rev. B 85, 201304 (2012).
[Crossref]

I. Al-Naib, G. Sharma, M. M. Dignam, H. Hafez, A. Ibrahim, D. G. Cooke, T. Ozaki, R. Morandotti, “Effect of local field enhancement on the nonlinear terahertz response of a silicon-based metamaterial,” Phys. Rev. B 88, 195203 (2013).
[Crossref]

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, K. A. Nelson, “Observation of nonequilibrium carrier distribution in Ge, Si, and GaAs by terahertz pump terahertz probe measurements,” Phys. Rev. B 81, 035201 (2010).
[Crossref]

Phys. Rev. Lett. (3)

P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, K. H. Ploog, “Nonlinear terahertz response of n-type GaAs,” Phys. Rev. Lett. 96, 187402 (2006).
[Crossref]

P. Bowlan, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, C. Flytzanis, “High- field transport in an electron-hole plasma: transition from ballistic to drift motion,” Phys. Rev. Lett. 107, 256602 (2011).
[Crossref]

F. Junginger, B. Mayer, C. Schmidt, O. Schubert, S. Mährlein, A. Leitenstorfer, R. Huber, A. Pashkin, “Nonperturbative interband response of a bulk InSb semiconductor driven off resonantly by terahertz electromagnetic few-cycle pulses,” Phys. Rev. Lett. 109, 147403 (2012).
[Crossref]

Proc. IEEE (1)

T. Grasser, T.-W. Tang, H. Kosina, S. Selberherr, “A review of hydrodynamic and energy-transport models for semiconductor device simulation,” Proc. IEEE 91, 251–274 (2003).
[Crossref]

Other (2)

M. Lundstrom, Fundamentals of Carrier Transport, 2nd ed. (Cambridge University, 2000).

G. Kaur, P. Han, X.-C. Zhang, “Terahertz induced nonlinear effects in doped silicon observed by open-aperture Z-scan,” in 2010 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz) (IEEE, 2010).

Supplementary Material (1)

» Media 1: MP4 (986 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

(a) Cross-sectional micrograph of fabricated silicon ridge waveguide and (b) calculated TE eigenmode at 0.5 THz.

Fig. 2.
Fig. 2.

Experimental setup used to measure the terahertz nonlinear transmission through the silicon waveguide.

Fig. 3.
Fig. 3.

Normalized power transmission for semi-insulating (circle) and doped (square) waveguides, and corresponding calculated (dashed lines) pulse energy transmission.

Fig. 4.
Fig. 4.

Evolution of the temporal profile of a terahertz pulse along the p-doped waveguide obtained from (a) the conventional Drude model and (b) nonlinear split-step simulation.

Fig. 5.
Fig. 5.

(a) Transmitted terahertz waveform, calculated using Monte Carlo simulation of carrier dynamics together with the split-step Fourier method. The linear (green) output curve was calculated using the conventional linear Drude model and waveguide dispersion, and shows lower transmission. Inset: the simulated input pulse, with a peak–peak field of 100 kV/cm. Media 1 provides an animation showing how the field and nonlinearity evolve with distance. (b) Transmitted power spectrum, calculated with (blue) and without (green) nonlinearity. (c) Experimentally measured transmitted terahertz waveform for 75 nJ (blue) and 0.75 nJ (green) incident pulse energy. The green field was scaled by 10× to account for the 100× lower energy. (d) Experimentally measured power spectra for 75 nJ (blue) and 0.75 nJ (green) incident pulse energy. The green curve was scaled by 100× to account for the lower energy. The gray bands show the absorption bands caused by water vapor in the ambient air, which causes additional absorption that was not included in the numerical simulation.

Equations (10)

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

[2z21c22t2]E=μ0[2t2P+tJ],
P^(z,ω)=ϵ0[n2(ω)1]E^(z,ω),
E^(Δz,ω)=E^(0,ω)exp[iωcn(ω)Δz],
2Ez21v¯22Et2=μ0Jt,
E(Δz,t)=E(0,tΔz/v¯)+v¯2μ04t3Δz/v¯tΔz/v[J(t)J(tΔz/v¯)]dt.
ΔE(t)=v¯2μ04t2Δz/v¯t[J(t)J(t)]dt.
dvdt+Γm(ε)v=qEm*,
dεdt+Γεε=qEv,
Γm(ε)=Γ0+Γεεm*vsat2.
v^(ω)=μ1iω/Γ0E^(ω),

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