Abstract

We explore optical-to-terahertz conversion efficiencies which can be achieved with femto- and picosecond optical pulses in electro-optic crystals with periodically inverted sign of second-order susceptibility. Optimal crystal lengths, pulse durations, pulse formats and focusing are regarded. We show that for sufficiently short (femtosecond) optical pulses, with a pulsewidth much shorter than the inverse terahertz frequency, conversion efficiency does not depend on pulse duration. We also show that by mixing two picosecond pulses (bandwidth-limited or chirped), one can achieve conversion efficiency, which is the same as in the case of femtosecond pulse with the same pulse energy. Additionally, when the group velocity dispersion of optical pulses is small, one can substantially exceed Manley‒Rowe conversion limit due to cascaded processes.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2005 (1)

2004 (2)

2003 (1)

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, "Determination of GaAs refractive index and its temperature dependence, with application to quasi-phasematched nonlinear optics," J. of Appl. Phys. 94, 6447-6455 (2003).
[CrossRef]

2002 (3)

B. Ferguson, and X.-C. Zhang, "Materials for terahertz science and technology," Nat. Mater. 1, 26-33 (2002).
[CrossRef]

PeterH. Siegel, "Terahertz technology," IEEE Transactions on Microwave Theory and Techniques 50, 910-28 (2002).
[CrossRef]

J.-P. Caumes, L. Videau, C. Touyez, E. Freysz, "Kerr-line nonlinearity induced via terahertz generation and the electro-optic effect in zinc blende crystals," Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef]

2000 (1)

Y.-S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, "Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate," Appl. Phys. Lett. 76, 2505-2507 (2000).
[CrossRef]

1999 (1)

R. A. Kaindl, F. Eickemeyer, M. Woerner, and T. Elsaesser, "Broadband phasematched difference frequency mixing of femtoseconds pulses in GaSe: Experiment and theory," Appl. Phys. Lett. 75, 1060-1062 (1999).
[CrossRef]

1998 (1)

S. Guha, "Focusing dependence of the efficiency of a singly resonant optical parametric oscillator," Appl. Phys. B 66, 663-675 (1998).
[CrossRef]

1996 (2)

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-23 (1996).
[CrossRef]

W. J. Moore, and R. T. Holm, "Infrared dielectric constant of gallium arsenide," J. Appl. Phys. 80, 6939-6942 (1996).
[CrossRef]

1995 (2)

T. J. Carrig, G. Rodriguez, T. S. Clement, and A. J. Taylor, "Scaling of terahertz radiation via optical rectification in electro-optic crystals," Appl. Phys. Lett. 66, 121-3 (1995).
[CrossRef]

A. Bonvalet, M. Joffre, J.-L. Martin, and A. Migus, "Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate," Appl. Phys. Lett. 67, 2907-2909 (1995).
[CrossRef]

1994 (1)

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, "Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas," Appl. Phys. Lett. 64, 137 (1994).
[CrossRef]

1992 (2)

1991 (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum Electron. 27, 1296-1309 (1991).
[CrossRef]

1990 (1)

1984 (1)

1977 (1)

J. R. Morris, and Y. R. Shen, "Theory of far infrared generation by optical mixing," Phys. Rev. A 15, 1143-56 (1977).
[CrossRef]

1976 (1)

Y. R. Shen, "Far-infrared generation by optical mixing," Prog. Quantum Electron. 4, 207-232 (1976).
[CrossRef]

1971 (1)

K. H. Yang, P. L. Richards, and Y. R. Shen, "Generation of far-infrared radiation by picosecond light pulses in LiNbO3," Appl. Phys. Lett. 19, 320-323 (1971).
[CrossRef]

1970 (2)

1. T. Yajima, and N. Takeuchi, "Far-infrared difference-frequency generation by picosecond laser pulses," Jpn. J. Appl. Phys. 9, 1361-1371 (1970).
[CrossRef]

T. K. Gustafson, J.-P.E. Taran, P. L. Kelley, and R. Y. Chiao, "Self-modulation of picosecond pulses in electro-optic crystals," Opt. Commun. 2, 17-21 (1970).
[CrossRef]

1968 (1)

G. D. Boyd, D. A. Kleinman, "Parametric interaction of focussed gaussian light beams," J. Appl. Phys. 39, 3597-3639 (1968).
[CrossRef]

Almási, G.

Auston, D. H.

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, "Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas," Appl. Phys. Lett. 64, 137 (1994).
[CrossRef]

L. Xu, X.-C. Zhang, and D. H. Auston, "Terahertz beam generation by femtosecond optical pulses in electro-optic materials," Appl. Phys. Lett. 61, 1784-6 (1992).
[CrossRef]

Bonvalet, A.

A. Bonvalet, M. Joffre, J.-L. Martin, and A. Migus, "Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate," Appl. Phys. Lett. 67, 2907-2909 (1995).
[CrossRef]

Boyd, G. D.

G. D. Boyd, D. A. Kleinman, "Parametric interaction of focussed gaussian light beams," J. Appl. Phys. 39, 3597-3639 (1968).
[CrossRef]

Carrig, T. J.

T. J. Carrig, G. Rodriguez, T. S. Clement, and A. J. Taylor, "Scaling of terahertz radiation via optical rectification in electro-optic crystals," Appl. Phys. Lett. 66, 121-3 (1995).
[CrossRef]

Caumes, J.-P.

J.-P. Caumes, L. Videau, C. Touyez, E. Freysz, "Kerr-line nonlinearity induced via terahertz generation and the electro-optic effect in zinc blende crystals," Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef]

Chiao, R. Y.

T. K. Gustafson, J.-P.E. Taran, P. L. Kelley, and R. Y. Chiao, "Self-modulation of picosecond pulses in electro-optic crystals," Opt. Commun. 2, 17-21 (1970).
[CrossRef]

Clement, T. S.

T. J. Carrig, G. Rodriguez, T. S. Clement, and A. J. Taylor, "Scaling of terahertz radiation via optical rectification in electro-optic crystals," Appl. Phys. Lett. 66, 121-3 (1995).
[CrossRef]

Cronin-Golomb, M.

Ding, Y. J.

Eickemeyer, F.

R. A. Kaindl, F. Eickemeyer, M. Woerner, and T. Elsaesser, "Broadband phasematched difference frequency mixing of femtoseconds pulses in GaSe: Experiment and theory," Appl. Phys. Lett. 75, 1060-1062 (1999).
[CrossRef]

Elsaesser, T.

R. A. Kaindl, F. Eickemeyer, M. Woerner, and T. Elsaesser, "Broadband phasematched difference frequency mixing of femtoseconds pulses in GaSe: Experiment and theory," Appl. Phys. Lett. 75, 1060-1062 (1999).
[CrossRef]

Eyres, L. A.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, "Determination of GaAs refractive index and its temperature dependence, with application to quasi-phasematched nonlinear optics," J. of Appl. Phys. 94, 6447-6455 (2003).
[CrossRef]

Fattinger, Ch.

Fejer, M. M.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, "Determination of GaAs refractive index and its temperature dependence, with application to quasi-phasematched nonlinear optics," J. of Appl. Phys. 94, 6447-6455 (2003).
[CrossRef]

Ferguson, B.

B. Ferguson, and X.-C. Zhang, "Materials for terahertz science and technology," Nat. Mater. 1, 26-33 (2002).
[CrossRef]

Freysz, E.

J.-P. Caumes, L. Videau, C. Touyez, E. Freysz, "Kerr-line nonlinearity induced via terahertz generation and the electro-optic effect in zinc blende crystals," Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef]

Froberg, N. M.

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, "Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas," Appl. Phys. Lett. 64, 137 (1994).
[CrossRef]

Galvanauskas, A.

Y.-S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, "Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate," Appl. Phys. Lett. 76, 2505-2507 (2000).
[CrossRef]

Grischkovsky, D.

Guha, S.

S. Guha, "Focusing dependence of the efficiency of a singly resonant optical parametric oscillator," Appl. Phys. B 66, 663-675 (1998).
[CrossRef]

Gustafson, T. K.

T. K. Gustafson, J.-P.E. Taran, P. L. Kelley, and R. Y. Chiao, "Self-modulation of picosecond pulses in electro-optic crystals," Opt. Commun. 2, 17-21 (1970).
[CrossRef]

Hagan, D. J.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, "Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe," J. Opt. Soc. Am. B 9, 405-414 (1992).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum Electron. 27, 1296-1309 (1991).
[CrossRef]

Harris, J. S.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, "Determination of GaAs refractive index and its temperature dependence, with application to quasi-phasematched nonlinear optics," J. of Appl. Phys. 94, 6447-6455 (2003).
[CrossRef]

Hebling, J.

Heinz, T. F.

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-23 (1996).
[CrossRef]

Holm, R. T.

W. J. Moore, and R. T. Holm, "Infrared dielectric constant of gallium arsenide," J. Appl. Phys. 80, 6939-6942 (1996).
[CrossRef]

Hu, B. B.

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, "Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas," Appl. Phys. Lett. 64, 137 (1994).
[CrossRef]

Hutchings, D. C.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum Electron. 27, 1296-1309 (1991).
[CrossRef]

Joffre, M.

A. Bonvalet, M. Joffre, J.-L. Martin, and A. Migus, "Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate," Appl. Phys. Lett. 67, 2907-2909 (1995).
[CrossRef]

Kaindl, R. A.

R. A. Kaindl, F. Eickemeyer, M. Woerner, and T. Elsaesser, "Broadband phasematched difference frequency mixing of femtoseconds pulses in GaSe: Experiment and theory," Appl. Phys. Lett. 75, 1060-1062 (1999).
[CrossRef]

Keiding, S.

Kelley, P. L.

T. K. Gustafson, J.-P.E. Taran, P. L. Kelley, and R. Y. Chiao, "Self-modulation of picosecond pulses in electro-optic crystals," Opt. Commun. 2, 17-21 (1970).
[CrossRef]

Kleinman, D. A.

G. D. Boyd, D. A. Kleinman, "Parametric interaction of focussed gaussian light beams," J. Appl. Phys. 39, 3597-3639 (1968).
[CrossRef]

Kozma, I. Z.

Kuhl, J.

Kuo, P. S.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, "Determination of GaAs refractive index and its temperature dependence, with application to quasi-phasematched nonlinear optics," J. of Appl. Phys. 94, 6447-6455 (2003).
[CrossRef]

Lee, Y.-S.

Y.-S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, "Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate," Appl. Phys. Lett. 76, 2505-2507 (2000).
[CrossRef]

Levi, O.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, "Determination of GaAs refractive index and its temperature dependence, with application to quasi-phasematched nonlinear optics," J. of Appl. Phys. 94, 6447-6455 (2003).
[CrossRef]

Martin, J.-L.

A. Bonvalet, M. Joffre, J.-L. Martin, and A. Migus, "Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate," Appl. Phys. Lett. 67, 2907-2909 (1995).
[CrossRef]

Meade, T.

Y.-S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, "Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate," Appl. Phys. Lett. 76, 2505-2507 (2000).
[CrossRef]

Migus, A.

A. Bonvalet, M. Joffre, J.-L. Martin, and A. Migus, "Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate," Appl. Phys. Lett. 67, 2907-2909 (1995).
[CrossRef]

Moore, W. J.

W. J. Moore, and R. T. Holm, "Infrared dielectric constant of gallium arsenide," J. Appl. Phys. 80, 6939-6942 (1996).
[CrossRef]

Morris, J. R.

J. R. Morris, and Y. R. Shen, "Theory of far infrared generation by optical mixing," Phys. Rev. A 15, 1143-56 (1977).
[CrossRef]

Nahata, A.

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-23 (1996).
[CrossRef]

Norris, T. B.

Y.-S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, "Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate," Appl. Phys. Lett. 76, 2505-2507 (2000).
[CrossRef]

Perlin, V.

Y.-S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, "Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate," Appl. Phys. Lett. 76, 2505-2507 (2000).
[CrossRef]

Peter,

PeterH. Siegel, "Terahertz technology," IEEE Transactions on Microwave Theory and Techniques 50, 910-28 (2002).
[CrossRef]

Pinguet, T. J.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, "Determination of GaAs refractive index and its temperature dependence, with application to quasi-phasematched nonlinear optics," J. of Appl. Phys. 94, 6447-6455 (2003).
[CrossRef]

Richards, P. L.

K. H. Yang, P. L. Richards, and Y. R. Shen, "Generation of far-infrared radiation by picosecond light pulses in LiNbO3," Appl. Phys. Lett. 19, 320-323 (1971).
[CrossRef]

Riedle, E.

Rodriguez, G.

T. J. Carrig, G. Rodriguez, T. S. Clement, and A. J. Taylor, "Scaling of terahertz radiation via optical rectification in electro-optic crystals," Appl. Phys. Lett. 66, 121-3 (1995).
[CrossRef]

Said, A. A.

Sheik-Bahae, M.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, "Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe," J. Opt. Soc. Am. B 9, 405-414 (1992).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum Electron. 27, 1296-1309 (1991).
[CrossRef]

Shen, Y. R.

J. R. Morris, and Y. R. Shen, "Theory of far infrared generation by optical mixing," Phys. Rev. A 15, 1143-56 (1977).
[CrossRef]

Y. R. Shen, "Far-infrared generation by optical mixing," Prog. Quantum Electron. 4, 207-232 (1976).
[CrossRef]

K. H. Yang, P. L. Richards, and Y. R. Shen, "Generation of far-infrared radiation by picosecond light pulses in LiNbO3," Appl. Phys. Lett. 19, 320-323 (1971).
[CrossRef]

Skauli, T.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, "Determination of GaAs refractive index and its temperature dependence, with application to quasi-phasematched nonlinear optics," J. of Appl. Phys. 94, 6447-6455 (2003).
[CrossRef]

Stepanov, A. G.

Takeuchi, N.

1. T. Yajima, and N. Takeuchi, "Far-infrared difference-frequency generation by picosecond laser pulses," Jpn. J. Appl. Phys. 9, 1361-1371 (1970).
[CrossRef]

Taran, J.-P.E.

T. K. Gustafson, J.-P.E. Taran, P. L. Kelley, and R. Y. Chiao, "Self-modulation of picosecond pulses in electro-optic crystals," Opt. Commun. 2, 17-21 (1970).
[CrossRef]

Taylor, A. J.

T. J. Carrig, G. Rodriguez, T. S. Clement, and A. J. Taylor, "Scaling of terahertz radiation via optical rectification in electro-optic crystals," Appl. Phys. Lett. 66, 121-3 (1995).
[CrossRef]

Touyez, C.

J.-P. Caumes, L. Videau, C. Touyez, E. Freysz, "Kerr-line nonlinearity induced via terahertz generation and the electro-optic effect in zinc blende crystals," Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef]

van Exter, M.

Van Stryland, E. W.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, "Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe," J. Opt. Soc. Am. B 9, 405-414 (1992).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum Electron. 27, 1296-1309 (1991).
[CrossRef]

Videau, L.

J.-P. Caumes, L. Videau, C. Touyez, E. Freysz, "Kerr-line nonlinearity induced via terahertz generation and the electro-optic effect in zinc blende crystals," Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef]

Vodopyanov, K. L.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, "Determination of GaAs refractive index and its temperature dependence, with application to quasi-phasematched nonlinear optics," J. of Appl. Phys. 94, 6447-6455 (2003).
[CrossRef]

Wang, J.

Wei, T. H.

Weling, A. S.

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-23 (1996).
[CrossRef]

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, "Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas," Appl. Phys. Lett. 64, 137 (1994).
[CrossRef]

Wherrett, B. S.

Winful, H.

Y.-S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, "Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate," Appl. Phys. Lett. 76, 2505-2507 (2000).
[CrossRef]

Woerner, M.

R. A. Kaindl, F. Eickemeyer, M. Woerner, and T. Elsaesser, "Broadband phasematched difference frequency mixing of femtoseconds pulses in GaSe: Experiment and theory," Appl. Phys. Lett. 75, 1060-1062 (1999).
[CrossRef]

Xu, L.

L. Xu, X.-C. Zhang, and D. H. Auston, "Terahertz beam generation by femtosecond optical pulses in electro-optic materials," Appl. Phys. Lett. 61, 1784-6 (1992).
[CrossRef]

Yajima, T.

1. T. Yajima, and N. Takeuchi, "Far-infrared difference-frequency generation by picosecond laser pulses," Jpn. J. Appl. Phys. 9, 1361-1371 (1970).
[CrossRef]

Yang, K. H.

K. H. Yang, P. L. Richards, and Y. R. Shen, "Generation of far-infrared radiation by picosecond light pulses in LiNbO3," Appl. Phys. Lett. 19, 320-323 (1971).
[CrossRef]

Young, J.

Zhang, X.-C.

B. Ferguson, and X.-C. Zhang, "Materials for terahertz science and technology," Nat. Mater. 1, 26-33 (2002).
[CrossRef]

L. Xu, X.-C. Zhang, and D. H. Auston, "Terahertz beam generation by femtosecond optical pulses in electro-optic materials," Appl. Phys. Lett. 61, 1784-6 (1992).
[CrossRef]

Appl. Phys. B (1)

S. Guha, "Focusing dependence of the efficiency of a singly resonant optical parametric oscillator," Appl. Phys. B 66, 663-675 (1998).
[CrossRef]

Appl. Phys. Lett. (8)

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, "Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas," Appl. Phys. Lett. 64, 137 (1994).
[CrossRef]

K. H. Yang, P. L. Richards, and Y. R. Shen, "Generation of far-infrared radiation by picosecond light pulses in LiNbO3," Appl. Phys. Lett. 19, 320-323 (1971).
[CrossRef]

L. Xu, X.-C. Zhang, and D. H. Auston, "Terahertz beam generation by femtosecond optical pulses in electro-optic materials," Appl. Phys. Lett. 61, 1784-6 (1992).
[CrossRef]

A. Bonvalet, M. Joffre, J.-L. Martin, and A. Migus, "Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate," Appl. Phys. Lett. 67, 2907-2909 (1995).
[CrossRef]

R. A. Kaindl, F. Eickemeyer, M. Woerner, and T. Elsaesser, "Broadband phasematched difference frequency mixing of femtoseconds pulses in GaSe: Experiment and theory," Appl. Phys. Lett. 75, 1060-1062 (1999).
[CrossRef]

T. J. Carrig, G. Rodriguez, T. S. Clement, and A. J. Taylor, "Scaling of terahertz radiation via optical rectification in electro-optic crystals," Appl. Phys. Lett. 66, 121-3 (1995).
[CrossRef]

Y.-S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, "Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate," Appl. Phys. Lett. 76, 2505-2507 (2000).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-23 (1996).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum Electron. 27, 1296-1309 (1991).
[CrossRef]

IEEE Transactions on Microwave Theory and Techniques (1)

PeterH. Siegel, "Terahertz technology," IEEE Transactions on Microwave Theory and Techniques 50, 910-28 (2002).
[CrossRef]

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W. J. Moore, and R. T. Holm, "Infrared dielectric constant of gallium arsenide," J. Appl. Phys. 80, 6939-6942 (1996).
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G. D. Boyd, D. A. Kleinman, "Parametric interaction of focussed gaussian light beams," J. Appl. Phys. 39, 3597-3639 (1968).
[CrossRef]

J. of Appl. Phys. (1)

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, "Determination of GaAs refractive index and its temperature dependence, with application to quasi-phasematched nonlinear optics," J. of Appl. Phys. 94, 6447-6455 (2003).
[CrossRef]

J. Opt. Soc. Am. B (3)

Jpn. J. Appl. Phys. (1)

1. T. Yajima, and N. Takeuchi, "Far-infrared difference-frequency generation by picosecond laser pulses," Jpn. J. Appl. Phys. 9, 1361-1371 (1970).
[CrossRef]

Nat. Mater. (1)

B. Ferguson, and X.-C. Zhang, "Materials for terahertz science and technology," Nat. Mater. 1, 26-33 (2002).
[CrossRef]

Opt. Commun. (1)

T. K. Gustafson, J.-P.E. Taran, P. L. Kelley, and R. Y. Chiao, "Self-modulation of picosecond pulses in electro-optic crystals," Opt. Commun. 2, 17-21 (1970).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

J. R. Morris, and Y. R. Shen, "Theory of far infrared generation by optical mixing," Phys. Rev. A 15, 1143-56 (1977).
[CrossRef]

Phys. Rev. Lett. (1)

J.-P. Caumes, L. Videau, C. Touyez, E. Freysz, "Kerr-line nonlinearity induced via terahertz generation and the electro-optic effect in zinc blende crystals," Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef]

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Y. R. Shen, "Far-infrared generation by optical mixing," Prog. Quantum Electron. 4, 207-232 (1976).
[CrossRef]

Other (5)

A. E. Siegman, Lasers, (University Science Books, Mill Valley, 1986), Chap. 9.

K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, V. G. Kozlov, and Y.-S. Lee, "Terahertz-wave generation in periodically-inverted GaAs," Conference on Lasers and Electro Optics, May 2005, Baltimore MD, Technical Digest (Optical Society of America, Washington DC, 2005), paper CWM1.

A. Yariv, Quantum Electronics, (Wiley, New York, 3rd edition, 1988), Chap. 16.

R. L. Byer, and R. L. Herbst, "Parametric oscillation and mixing," in Topics in Applied Physics: Nonlinear Infrared Generation, ed. by Y.R. Shen (Springer, Berlin, 1977), Vol. 16, p. 81-137.
[CrossRef]

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, (Springer, Berlin, 1997).

Supplementary Material (1)

» Media 1: AVI (1391 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Illustration of optical rectification in a media with periodically inverted χ (2) sign, using femtosecond pump pulses. The static picture shows optical and THz electric fields, while the animation shows the nonlinear driving polarization and the THz electric field (779kB).

Fig. 2.
Fig. 2.

Reduction factor g 1 as a function of vTHzT for the case of femtosecond pump pulses (νTHz=Ω/2π).

Fig. 3.
Fig. 3.

Reduction factor g 2 as a function of l w/L for the case of picosecond pump pulses.

Fig. 4.
Fig. 4.

Scheme to generate tunable THZ radiation from the overlap of two linearly chirped pulses.

Fig. 5.
Fig. 5.

Enhancement factor h as a function of the focusing parameter ξ. Solid curve is based on ref. 22. Dashed curve ‒ plane-wave approximation. Dots represent our calculations based on the Green’s function method. Inset: far field THz intensity profiles at different ξ for a 1-cm-long GaAs.

Fig. 6.
Fig. 6.

Number of THz cascading cycles as a function of THz frequency and pump wavelength for GaAs, L=1cm.

Fig. 7.
Fig. 7.

(a) The optical pulse intensity profile, (b) rectified field profile, (c) phase profile across the optical pulse after traveling the crystal, and (d) frequency shift of the optical pulse.

Equations (51)

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

E ( t ) = Re { E 0 exp ( t 2 τ 2 ) exp [ i ( ω 0 t ) ] } = 1 2 { E 0 exp ( t 2 τ 2 ) exp [ i ( ω 0 t ) ] + c . c . } ,
f ( t ) = f ( ω ) exp ( iωt )
f ( ω ) = 1 2 π f ( t ) exp ( iωt ) dt ,
E ( ω ) = E 0 τ 2 π exp ( τ 2 ( ω ω 0 ) 2 4 )
E ω z = E ( ω ) exp [ ik ( ω ) z ] ,
dE Ω z dz = i μ 0 Ω c 2 n 1 P NL ( Ω ) exp ( i Δ kz ) ,
P NL ( Ω ) = ε 0 χ ( 2 ) E ( ω + Ω ) E * ( ω )
P NL ( Ω ) = ε 0 χ ( 2 ) E 0 2 τ 2 2 π exp ( τ 2 Ω 2 8 )
dE Ω z dz = i Ω χ ( 2 ) E 0 2 τ 4 2 π c n 1 exp ( τ 2 Ω 2 8 ) exp ( i Δ kz ) .
Δ k = k ( Ω ) + k ( ω ) k ( ω + Ω ) 2 π ʌ .
Δ k = Ω n THz c ( dk ) opt Ω 2 π ʌ = Ω c ( n THz n opt gr ) 2 π ʌ ,
E Ω L 2 = Ω 2 d eff 2 E 0 4 τ 2 8 π c 2 n 1 2 L 2 exp ( τ 2 Ω 2 4 ) sin c 2 ( Δ kL 2 ) .
Ω 0 = 2 πc Λ Δ n , λ THz = Λ Δn ,
Δ Ω accept = c Δ n Δ k accept = 2 πc L Δ n
l c = πc ΩΔ n ,
Ω c ( n THz + n opt gr ) 2 π Λ = 0
η THz PW = Fluence ( THz ) Fluence ( pump ) .
F pu = c ε 0 n 2 2 E t 0 2 dt = π 2 c ε 0 n 2 2 E 0 2 τ ,
F THz = c ε 0 n 1 2 E THz t L 2 dt = c ε 0 n 1 2 2 π 0 E Ω L 2 d Ω ,
η THz PW = Ω 2 d eff 2 E 0 2 τ 2 2 π c 2 n 1 n 2 L 2 0 exp ( τ 2 Ω 2 4 ) sinc 2 [ Δ n ( Ω Ω 0 ) L 2 c ] d Ω
η THz PW = g 1 2 Ω 0 3 d eff 2 π ε 0 c 3 n 1 n 2 2 Ll c F pu = g 1 2 Ω 0 3 d eff 2 L ε 0 c 3 n 1 n 2 2 Δ n F pu
g 1 = exp ( ( τ Ω 0 2 ) 2 ) = exp ( ( π ν THz τ ) 2 )
E i ( t ) = Re { E i exp ( t 2 τ 2 ) exp [ i ( ω i t ) ] } ,
E i ( ω ) = E i τ 2 π exp ( τ 2 ( ω ω i ) 2 4 ) .
P NL ( Ω ) = ε 0 χ ( 2 ) 0 E 3 ( ω + Ω ) E 2 * ( ω ) = ε 0 χ ( 2 ) E 2 E 3 τ 2 2 π exp ( τ 2 ( Ω Ω 0 ) 2 8 ) .
E Ω L 2 = Ω 2 d eff 2 E 2 2 E 3 2 τ 2 8 π c 2 n 1 2 L 2 exp ( τ 2 ( Ω Ω 0 ) 2 4 ) sinc 2 ( Δ kL 2 ) ,
η THz PW = Fluence ( THz ) Fluence ( ω 2 ) = Ω 2 d eff 2 E 3 2 τ 2 2 π c 2 n 1 n 2 L 2 0 exp ( τ 2 Ω' 2 4 ) sin c 2 [ Δ n Ω' L 2 c ] d Ω'
l w = π Δ n ,
η THz PW = Ω 2 d eff 2 E 3 2 τ 2 2 π c 2 n 1 n 2 L 2 0 exp ( τ 2 Ω' 2 4 ) sin c 2 [ π 2 ( L l w ) τ Ω' ] d Ω'
η THz = Ω 2 d eff 2 E 3 2 L 2 2 c 2 n 1 n 2 = 2 Ω 2 d eff 2 L 2 ε 0 c 2 n 1 n 2 n 3 I 3 2 ,
η THz = Ω 2 d eff 2 E 3 2 L l w 2 c 2 n 1 n 2 = 2 Ω 2 d eff 2 L l w ε 0 c 2 n 1 n 2 n 3 I 3 2 ,
η THz = 2 Ω 3 d eff 2 L l c π ε 0 c 3 n 1 n 2 n 3 F 3 ,
η THz = g 2 2 Ω 3 d eff 2 L l c π ε 0 c 3 n 1 n 2 n 3 F 3 = g 2 2 Ω 2 d eff 2 L ε 0 c 2 n 1 n 2 n 3 Δ n F 3 ,
g 2 ( x ) = 1 π 0 exp ( x 2 μ 2 π ) sin c 2 ( μ ) .
E 2 ( t ) = Re { E 0 exp ( t 2 τ 2 ) exp [ i ( ω 0 t + b t 2 ) ] }
E 3 ( t ) = E 2 ( t + Δ t ) = Re { E 0 exp ( ( t + Δ t ) 2 τ 2 ) exp [ i ( ω 0 ( t + Δ t ) + b ( t + Δ t ) 2 ) ] }
P NL ( t ) = Re { ε 0 χ ( 2 ) ( E 2 ( t ) + E 3 ( t ) ) 2 ω = 0 }
= Re { ε 0 χ ( 2 ) E 0 2 exp [ 2 τ 2 ( t 2 + Δ tt + Δ t 2 2 ) + i ( 2 b Δ tt + b Δ t 2 ) ] }
P NL ( Ω ) = ε 0 χ ( 2 ) E 0 2 2 π exp [ 2 τ 2 ( t 2 + Δ tt + Δ t 2 2 ) + i ( 2 b Δ tt + b Δ t 2 Ω t ) ] dt
= ε 0 χ ( 2 ) E 0 2 τ 2 2 π exp ( τ 2 Ω' 2 8 1 2 Δ t 2 τ 2 ) exp ( i φ 1 )
η THz PW = Ω 2 d eff 2 E 0 2 τ 2 2 π c 2 n 1 n 2 L 2 0 exp ( τ 2 Ω' 2 4 Δ t 2 τ 2 ) sin c 2 [ Δ n ( Ω' + Ω" ) L 2 c ] d Ω'
η THz = g 2 exp ( Δ t 2 τ 2 ) 2 Ω 2 d eff 2 Ll c π ε 0 c 3 n 1 n 2 n 3 F 3 ,
η THz = g 1 g 2 2 Ω 2 d eff 2 Ll c π ε 0 c 3 n 1 n 2 n 3 F 3 .
η THz ( L ) 1 α [ 1 exp ( αL ) ] = L eff ,
η THz ( L ) g 3 L ; g 3 = 1 αL [ 1 exp ( αL ) ]
η THz = U THz U pu = g 1 g 3 2 Ω 2 d eff 2 L ε 0 c 3 n 1 n 2 2 Δ n U pu π w 2 ,
η THz = U THz U pu = g 1 g 3 2 Ω 3 d eff 2 π ε 0 c 3 n 1 n 2 2 Δ n U pu h ( ξ ) ,
η THz = U THz U 2 = g 2 g 3 2 Ω 3 d eff 2 π ε 0 c 3 n 2 n 3 Δ n U 3 h ( ξ ) ,
Δ k z = k 1 z ( k 3 k 2 ) = k 1 cos θ ( k 3 k 2 ) Δ k 0 k 1 2 θ 2 = 0
ξ = λ 1 L 2 π n 1 w 2 < π .
Δ ω pump accept = 2 πc L ω pump Ω ( λ d n gr ) 1

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