Abstract

It is shown that the coherence lengths for terahertz (THz) generation based on difference-frequency generation within an ultrafast infrared pulse can be sufficiently long for a wide bandwidth about each phase-matching wavelength owing to a slight dispersion in the THz region. As a result, quasi-single-cycle THz pulses can be efficiently generated. An efficient conversion for the parametric process is made possible not only by use of the wide phase-matching bandwidth but also by optimization of the pulse width for each peak THz frequency. I have investigated the strong-pump regime and found the limits to the conversion efficiencies to generate high peak intensities efficiently for THz waves with which to explore nonlinear regimes of the THz interactions.

© 2004 Optical Society of America

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  1. M. P. Hasselbeck, D. Stalnaker, L. A. Schile, T. J. Rotter, A. Stintz, and M. Sheik-Bahae, Phys. Rev. B 65, 233203 (2002).
    [Crossref]
  2. A. E. Kaplan, Phys. Rev. Lett. 48, 138 (1982).
    [Crossref]
  3. L. Xu, X.-C. Zhang, and D. H. Auston, Appl. Phys. Lett. 61, 1784 (1992).
    [Crossref]
  4. D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984).
    [Crossref]
  5. D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984).
    [Crossref]
  6. T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, Appl. Phys. Lett. 66, 121 (1995).
    [Crossref]
  7. J.-C. Diels and W. Rudolph, Ultrafast Laser Pulse Phenomena (Academic, New York, 1996).
  8. R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).
  9. J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, Phys. Rev. Lett. 89, 047401 (2002).
    [Crossref]
  10. A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
    [Crossref]
  11. GaP: the Sellmeier equation is taken from A. N. Pikhtin, V. T. Prokopenko, and A. D. Yas’kov, Sov. Phys. Semicond. 10, 1224 (1976). GaAs: the near-IR Sellmeier equation is taken from A. N. Pikhtin and A. D. Yas’kov, Sov. Phys. Semicond. 12, 622 (1978), whereas the THz Sellmeier equation is in the form b1+b2λ2/λ2-b31/2, with the three constants, b1,b2, and b3, given by the best fit to the data in E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985), p. 443.
  12. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, New York, 1999), p. 139.
  13. W. Shi and Y. J. Ding, Appl. Phys. Lett. 82, 4435 (2003).
    [Crossref]
  14. Y. J. Ding and I. B. Zotova, J. Nonlinear Opt. Phys. Mater. 11, 75 (2002).
    [Crossref]
  15. I. Vurgaftman and J. R. Meyer, Appl. Phys. Lett. 75, 899 (1999).
    [Crossref]

2003 (1)

W. Shi and Y. J. Ding, Appl. Phys. Lett. 82, 4435 (2003).
[Crossref]

2002 (3)

Y. J. Ding and I. B. Zotova, J. Nonlinear Opt. Phys. Mater. 11, 75 (2002).
[Crossref]

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, Phys. Rev. Lett. 89, 047401 (2002).
[Crossref]

M. P. Hasselbeck, D. Stalnaker, L. A. Schile, T. J. Rotter, A. Stintz, and M. Sheik-Bahae, Phys. Rev. B 65, 233203 (2002).
[Crossref]

1999 (1)

I. Vurgaftman and J. R. Meyer, Appl. Phys. Lett. 75, 899 (1999).
[Crossref]

1996 (1)

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[Crossref]

1995 (1)

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, Appl. Phys. Lett. 66, 121 (1995).
[Crossref]

1992 (1)

L. Xu, X.-C. Zhang, and D. H. Auston, Appl. Phys. Lett. 61, 1784 (1992).
[Crossref]

1984 (2)

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984).
[Crossref]

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984).
[Crossref]

1982 (1)

A. E. Kaplan, Phys. Rev. Lett. 48, 138 (1982).
[Crossref]

1976 (1)

GaP: the Sellmeier equation is taken from A. N. Pikhtin, V. T. Prokopenko, and A. D. Yas’kov, Sov. Phys. Semicond. 10, 1224 (1976). GaAs: the near-IR Sellmeier equation is taken from A. N. Pikhtin and A. D. Yas’kov, Sov. Phys. Semicond. 12, 622 (1978), whereas the THz Sellmeier equation is in the form b1+b2λ2/λ2-b31/2, with the three constants, b1,b2, and b3, given by the best fit to the data in E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985), p. 443.

Auston, D. H.

L. Xu, X.-C. Zhang, and D. H. Auston, Appl. Phys. Lett. 61, 1784 (1992).
[Crossref]

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984).
[Crossref]

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).

Carrig, T. J.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, Appl. Phys. Lett. 66, 121 (1995).
[Crossref]

Caumes, J.-P.

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, Phys. Rev. Lett. 89, 047401 (2002).
[Crossref]

Cheung, K. P.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984).
[Crossref]

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984).
[Crossref]

Clement, T. S.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, Appl. Phys. Lett. 66, 121 (1995).
[Crossref]

Diels, J.-C.

J.-C. Diels and W. Rudolph, Ultrafast Laser Pulse Phenomena (Academic, New York, 1996).

Ding, Y. J.

W. Shi and Y. J. Ding, Appl. Phys. Lett. 82, 4435 (2003).
[Crossref]

Y. J. Ding and I. B. Zotova, J. Nonlinear Opt. Phys. Mater. 11, 75 (2002).
[Crossref]

Dmitriev, V. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, New York, 1999), p. 139.

Freysz, E.

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, Phys. Rev. Lett. 89, 047401 (2002).
[Crossref]

Gurzadyan, G. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, New York, 1999), p. 139.

Hasselbeck, M. P.

M. P. Hasselbeck, D. Stalnaker, L. A. Schile, T. J. Rotter, A. Stintz, and M. Sheik-Bahae, Phys. Rev. B 65, 233203 (2002).
[Crossref]

Heinz, T. F.

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[Crossref]

Kaplan, A. E.

A. E. Kaplan, Phys. Rev. Lett. 48, 138 (1982).
[Crossref]

Kleinman, D. A.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984).
[Crossref]

Meyer, J. R.

I. Vurgaftman and J. R. Meyer, Appl. Phys. Lett. 75, 899 (1999).
[Crossref]

Nahata, A.

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[Crossref]

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, New York, 1999), p. 139.

Pikhtin, A. N.

GaP: the Sellmeier equation is taken from A. N. Pikhtin, V. T. Prokopenko, and A. D. Yas’kov, Sov. Phys. Semicond. 10, 1224 (1976). GaAs: the near-IR Sellmeier equation is taken from A. N. Pikhtin and A. D. Yas’kov, Sov. Phys. Semicond. 12, 622 (1978), whereas the THz Sellmeier equation is in the form b1+b2λ2/λ2-b31/2, with the three constants, b1,b2, and b3, given by the best fit to the data in E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985), p. 443.

Prokopenko, V. T.

GaP: the Sellmeier equation is taken from A. N. Pikhtin, V. T. Prokopenko, and A. D. Yas’kov, Sov. Phys. Semicond. 10, 1224 (1976). GaAs: the near-IR Sellmeier equation is taken from A. N. Pikhtin and A. D. Yas’kov, Sov. Phys. Semicond. 12, 622 (1978), whereas the THz Sellmeier equation is in the form b1+b2λ2/λ2-b31/2, with the three constants, b1,b2, and b3, given by the best fit to the data in E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985), p. 443.

Rodriguez, G.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, Appl. Phys. Lett. 66, 121 (1995).
[Crossref]

Rotter, T. J.

M. P. Hasselbeck, D. Stalnaker, L. A. Schile, T. J. Rotter, A. Stintz, and M. Sheik-Bahae, Phys. Rev. B 65, 233203 (2002).
[Crossref]

Rouyer, C.

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, Phys. Rev. Lett. 89, 047401 (2002).
[Crossref]

Rudolph, W.

J.-C. Diels and W. Rudolph, Ultrafast Laser Pulse Phenomena (Academic, New York, 1996).

Schile, L. A.

M. P. Hasselbeck, D. Stalnaker, L. A. Schile, T. J. Rotter, A. Stintz, and M. Sheik-Bahae, Phys. Rev. B 65, 233203 (2002).
[Crossref]

Sheik-Bahae, M.

M. P. Hasselbeck, D. Stalnaker, L. A. Schile, T. J. Rotter, A. Stintz, and M. Sheik-Bahae, Phys. Rev. B 65, 233203 (2002).
[Crossref]

Shi, W.

W. Shi and Y. J. Ding, Appl. Phys. Lett. 82, 4435 (2003).
[Crossref]

Smith, P. R.

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984).
[Crossref]

Stalnaker, D.

M. P. Hasselbeck, D. Stalnaker, L. A. Schile, T. J. Rotter, A. Stintz, and M. Sheik-Bahae, Phys. Rev. B 65, 233203 (2002).
[Crossref]

Stewart, K. R.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, Appl. Phys. Lett. 66, 121 (1995).
[Crossref]

Stintz, A.

M. P. Hasselbeck, D. Stalnaker, L. A. Schile, T. J. Rotter, A. Stintz, and M. Sheik-Bahae, Phys. Rev. B 65, 233203 (2002).
[Crossref]

Taylor, A. J.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, Appl. Phys. Lett. 66, 121 (1995).
[Crossref]

Valdmanis, J. A.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984).
[Crossref]

Videau, L.

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, Phys. Rev. Lett. 89, 047401 (2002).
[Crossref]

Vurgaftman, I.

I. Vurgaftman and J. R. Meyer, Appl. Phys. Lett. 75, 899 (1999).
[Crossref]

Weling, A. S.

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[Crossref]

Xu, L.

L. Xu, X.-C. Zhang, and D. H. Auston, Appl. Phys. Lett. 61, 1784 (1992).
[Crossref]

Yas’kov, A. D.

GaP: the Sellmeier equation is taken from A. N. Pikhtin, V. T. Prokopenko, and A. D. Yas’kov, Sov. Phys. Semicond. 10, 1224 (1976). GaAs: the near-IR Sellmeier equation is taken from A. N. Pikhtin and A. D. Yas’kov, Sov. Phys. Semicond. 12, 622 (1978), whereas the THz Sellmeier equation is in the form b1+b2λ2/λ2-b31/2, with the three constants, b1,b2, and b3, given by the best fit to the data in E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985), p. 443.

Zhang, X.-C.

L. Xu, X.-C. Zhang, and D. H. Auston, Appl. Phys. Lett. 61, 1784 (1992).
[Crossref]

Zotova, I. B.

Y. J. Ding and I. B. Zotova, J. Nonlinear Opt. Phys. Mater. 11, 75 (2002).
[Crossref]

Appl. Phys. Lett. (6)

L. Xu, X.-C. Zhang, and D. H. Auston, Appl. Phys. Lett. 61, 1784 (1992).
[Crossref]

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984).
[Crossref]

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, Appl. Phys. Lett. 66, 121 (1995).
[Crossref]

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[Crossref]

W. Shi and Y. J. Ding, Appl. Phys. Lett. 82, 4435 (2003).
[Crossref]

I. Vurgaftman and J. R. Meyer, Appl. Phys. Lett. 75, 899 (1999).
[Crossref]

J. Nonlinear Opt. Phys. Mater. (1)

Y. J. Ding and I. B. Zotova, J. Nonlinear Opt. Phys. Mater. 11, 75 (2002).
[Crossref]

Phys. Rev. B (1)

M. P. Hasselbeck, D. Stalnaker, L. A. Schile, T. J. Rotter, A. Stintz, and M. Sheik-Bahae, Phys. Rev. B 65, 233203 (2002).
[Crossref]

Phys. Rev. Lett. (3)

A. E. Kaplan, Phys. Rev. Lett. 48, 138 (1982).
[Crossref]

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984).
[Crossref]

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, Phys. Rev. Lett. 89, 047401 (2002).
[Crossref]

Sov. Phys. Semicond. (1)

GaP: the Sellmeier equation is taken from A. N. Pikhtin, V. T. Prokopenko, and A. D. Yas’kov, Sov. Phys. Semicond. 10, 1224 (1976). GaAs: the near-IR Sellmeier equation is taken from A. N. Pikhtin and A. D. Yas’kov, Sov. Phys. Semicond. 12, 622 (1978), whereas the THz Sellmeier equation is in the form b1+b2λ2/λ2-b31/2, with the three constants, b1,b2, and b3, given by the best fit to the data in E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985), p. 443.

Other (3)

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, New York, 1999), p. 139.

J.-C. Diels and W. Rudolph, Ultrafast Laser Pulse Phenomena (Academic, New York, 1996).

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).

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Figures (2)

Fig. 1
Fig. 1

Solid curves, normalized spectral electric-field amplitude versus normalized frequency Ωτ, based on Eq. (3), for broadband phase-matched DFG or an ideal case, i.e., sincΩnpg-nL/2c=1, for any Ω and hyperbolic-secant pump pulses. For comparison, normalized spectral electric-field amplitude is also plotted versus normalized frequency for 2-mm-long GaP and ZnGeP2 crystals at pump wavelengths of 1.034 and 1.218 µm to produce central output wavelengths of 550 and 300 µm, respectively, based on Eq. (3) for hyperbolic-secant pulses and with the Sellmeier equations given by Refs. 11 and 12, which correspond to dotted and dashed curves.

Fig. 2
Fig. 2

For a 2-mm-long GaP crystal (λp1.031 µm and kp=1.3 fs2/µm), normalized instantaneous electric field versus normalized time, t-npgL/c/τ, for three pump intensities: 1.5 GW/cm2, solid curve; 14 GW/cm2, dashed curve; and 38 GW/cm2, dotted curve.

Equations (10)

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

2+Ω2c2n2ΩE¯THzr,Ω=2deffc2-+2Ep2t2×exp-iΩtdt=-deffΩ2c2ϵ˜2¯,
i2kpt2+z+inpgΩc+i2kpΩ2ϵ˜¯=-2ideffωpcnpETHzϵ˜¯,
2z2+Ω2c2n2ΩE¯THzz,Ω=-deffE02Ω2g2¯0,Ωc2×exp-iΩnpgzc.
E¯THzL,Ω=-ideffE02Ωg2¯0,ΩLcnpg+n×sincΩ2cnpg-nLexp-iΩ2cnpg+nL,
nΩTHz=npgωp;
ETHzL,t=-iE02L2πc-+deffΩg2¯0,Ωnpg+n×sincΔkL2expiΩt-L2cnpg+ndΩ,
ETHzL,t=-deffE02L2cnpgg2t-npgL/c/τt;
ETHzL,t=deffE02Lcnpgτtanht-npgL/c/τcosh2t-npgL/c/τ,
η=JTHzJp=2deff2L2η015c2npgnp2τ3JpAp,
ϵ˜L,tE0cosht-npgL/c/τ×exp-iη15ωpτ2tanht-npgL/c/τcosh2t-npgL/c/τ.

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