Abstract

We have presented a time-dependent theoretical model to describe the time behavior of a quasi-monochromatic nanosecond terahertz detector reported by Guo et. al. (2008 Appl. Phys. Lett. 93, 021106). The temporal input-output characteristic of the detector is investigated numerically by taking the system parameters close to the experimental ones, and the calculated pulse width for the incident terahertz wave agrees well with the experimental one. Our results demonstrate that the energy and width of an output idler wave pulse are proportional to those of the incident terahertz wave pulse. This study provides a strict theoretical basis and could be used to guide the design and optimization for the highly sensitive coherent terahertz detector.

© 2010 Optical Society of America

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  1. B. Ferguson, S. H. Wang, D. Gray, D. Abbot, and X.-C. Zhang, “T-ray computed tomography,” Opt. Lett. 27(15), 1312–1314 (2002).
    [CrossRef]
  2. A. J. Fitzgerald, E. Berry, N. N. Zinovev, G. C. Walker, M. A. Smith, and J. M. Chamberlain, “An introduction to medical imaging with coherent terahertz frequency radiation,” Phys. Med. Biol. 47(7), R67–R84 (2002).
    [CrossRef] [PubMed]
  3. J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
    [CrossRef]
  4. R. Guo, S. Ohno, H. Minamide, T. Ikari, and H. Ito, “Highly Sensitive coherent detection of terahertz waves at room temperature using a parametric process,” Appl. Phys. Lett. 93(2), 021106 (2008).
    [CrossRef]
  5. J. M. Yarborough, S. S. Sussman, H. E. Puthoff, R. H. Pantell, and B. C. Johnson, “Efficient, tunable optical emission from LiNbO3 without a resonator,” Appl. Phys. Lett. 15(3), 102–105 (1969).
    [CrossRef]
  6. B. C. Johnson, H. E. Puthoff, J. Soohoo, and S. S. Sussman, “Power and linewidth of tunable stimulated far infrared emission in LiNbO3,” Appl. Phys. Lett. 18(5), 181–183 (1971).
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    [CrossRef] [PubMed]
  9. C. Y. Jiang, J. S. Liu, B. Sun, K. J. Wang, and J. Q. Yao, “Steady-state theoretical model for terahertz wave detector using a parametric process,” J. Opt. 12(4), 045202 (2010).
    [CrossRef]
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  11. S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, “Nonstationary nonlinear optical effects and ultrashort light pulse formation,” IEEE J. Quantum Electron. QE-4(10), 598–605 (1968).
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  12. Y. R. Shen, “Theory of Stimulated Raman Effect. II,” Phys. Rev. 138(6A), A1741–A1746 (1965).
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  13. C. H. Henry, and C. G. B. Garrett, “Theory of parametric gain near a lattice resonance,” Phys. Rev. 171(3), 1058–1064 (1968).
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  14. C. G. B. Garrett, “Nonlinear optics, anharmonic oscillators, and pyroelectricity,” IEEE J. Quantum Electron. 4(3), 70–84 (1968).
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    [CrossRef]
  17. M. A. Porras, “Ultrashot pulsed Gaussian light beams,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(1), 1086–1093 (1998).
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    [CrossRef]
  20. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14(9), 2268–2294 (1997).
    [CrossRef]
  21. T. Qiu, and M. Maier, “Long-distance propagation and damping of low-frequency phonon polaritons in LiNbO3,” Phys. Rev. B 56(10), R5717–R5720 (1997).
    [CrossRef]
  22. J. Shikata, K. Kawasa, and H. Ito, “The generation and linewidth control of terahertz waves by parametric processes,” Electron. Commun. Japan 86(Part 2), 52–65 (2003).
  23. W. D. Johnston, Jr., and I. P. Kaminow, “Temperature dependence of Raman and Rayleigh scattering in LiNbO3 and LiTaO3,” Phys. Rev. 168(3), 1045–1054 (1968).
    [CrossRef]
  24. G. J. Edwards, and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
    [CrossRef]
  25. R. Guo, T. Ikari, H. Minamide, and H. Ito, “Detection of coherent tunable THz-wave using of stimulated polariton scattering in MgO:LiNbO3,” Proc. SPIE 6582, 65820Z (2007).
    [CrossRef]

2010

C. Y. Jiang, J. S. Liu, B. Sun, K. J. Wang, and J. Q. Yao, “Steady-state theoretical model for terahertz wave detector using a parametric process,” J. Opt. 12(4), 045202 (2010).
[CrossRef]

2008

R. Guo, S. Ohno, H. Minamide, T. Ikari, and H. Ito, “Highly Sensitive coherent detection of terahertz waves at room temperature using a parametric process,” Appl. Phys. Lett. 93(2), 021106 (2008).
[CrossRef]

2007

R. Guo, T. Ikari, H. Minamide, and H. Ito, “Detection of coherent tunable THz-wave using of stimulated polariton scattering in MgO:LiNbO3,” Proc. SPIE 6582, 65820Z (2007).
[CrossRef]

2006

2005

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[CrossRef]

2003

J. Shikata, K. Kawasa, and H. Ito, “The generation and linewidth control of terahertz waves by parametric processes,” Electron. Commun. Japan 86(Part 2), 52–65 (2003).

2002

A. J. Fitzgerald, E. Berry, N. N. Zinovev, G. C. Walker, M. A. Smith, and J. M. Chamberlain, “An introduction to medical imaging with coherent terahertz frequency radiation,” Phys. Med. Biol. 47(7), R67–R84 (2002).
[CrossRef] [PubMed]

B. Ferguson, S. H. Wang, D. Gray, D. Abbot, and X.-C. Zhang, “T-ray computed tomography,” Opt. Lett. 27(15), 1312–1314 (2002).
[CrossRef]

1998

M. A. Porras, “Ultrashot pulsed Gaussian light beams,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(1), 1086–1093 (1998).
[CrossRef]

1997

T. Qiu, and M. Maier, “Long-distance propagation and damping of low-frequency phonon polaritons in LiNbO3,” Phys. Rev. B 56(10), R5717–R5720 (1997).
[CrossRef]

I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14(9), 2268–2294 (1997).
[CrossRef]

1992

1984

G. J. Edwards, and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[CrossRef]

1977

R. Fischer, and L. A. Kulevskii, “Optical parametric oscillators (review),” Sov. J. Quantum Electron. 7(2), 135–159 (1977).
[CrossRef]

1974

M. F. Becker, D. J. Kuizenga, D. W. Phillion, and A. E. Siegman, “Analytic expressions for ultrashort pulse generation in mode-locked optical parametric oscillators,” J. Appl. Phys. 45(9), 3996–4005 (1974).
[CrossRef]

1971

B. C. Johnson, H. E. Puthoff, J. Soohoo, and S. S. Sussman, “Power and linewidth of tunable stimulated far infrared emission in LiNbO3,” Appl. Phys. Lett. 18(5), 181–183 (1971).
[CrossRef]

1969

J. M. Yarborough, S. S. Sussman, H. E. Puthoff, R. H. Pantell, and B. C. Johnson, “Efficient, tunable optical emission from LiNbO3 without a resonator,” Appl. Phys. Lett. 15(3), 102–105 (1969).
[CrossRef]

1968

W. D. Johnston, Jr., and I. P. Kaminow, “Temperature dependence of Raman and Rayleigh scattering in LiNbO3 and LiTaO3,” Phys. Rev. 168(3), 1045–1054 (1968).
[CrossRef]

C. H. Henry, and C. G. B. Garrett, “Theory of parametric gain near a lattice resonance,” Phys. Rev. 171(3), 1058–1064 (1968).
[CrossRef]

C. G. B. Garrett, “Nonlinear optics, anharmonic oscillators, and pyroelectricity,” IEEE J. Quantum Electron. 4(3), 70–84 (1968).
[CrossRef]

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, “Nonstationary nonlinear optical effects and ultrashort light pulse formation,” IEEE J. Quantum Electron. QE-4(10), 598–605 (1968).
[CrossRef]

1967

A. S. Baker, Jr., “R, Loudon, ‘Dielectric properties and optical phonons in LiNbO3,” Phys. Rev. 158(2), 433–445 (1967).
[CrossRef]

1965

Y. R. Shen, “Theory of Stimulated Raman Effect. II,” Phys. Rev. 138(6A), A1741–A1746 (1965).
[CrossRef]

Abbot, D.

Akhmanov, S. A.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, “Nonstationary nonlinear optical effects and ultrashort light pulse formation,” IEEE J. Quantum Electron. QE-4(10), 598–605 (1968).
[CrossRef]

Baker, A. S.

A. S. Baker, Jr., “R, Loudon, ‘Dielectric properties and optical phonons in LiNbO3,” Phys. Rev. 158(2), 433–445 (1967).
[CrossRef]

Barat, R.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[CrossRef]

Becker, M. F.

M. F. Becker, D. J. Kuizenga, D. W. Phillion, and A. E. Siegman, “Analytic expressions for ultrashort pulse generation in mode-locked optical parametric oscillators,” J. Appl. Phys. 45(9), 3996–4005 (1974).
[CrossRef]

Berry, E.

A. J. Fitzgerald, E. Berry, N. N. Zinovev, G. C. Walker, M. A. Smith, and J. M. Chamberlain, “An introduction to medical imaging with coherent terahertz frequency radiation,” Phys. Med. Biol. 47(7), R67–R84 (2002).
[CrossRef] [PubMed]

Chamberlain, J. M.

A. J. Fitzgerald, E. Berry, N. N. Zinovev, G. C. Walker, M. A. Smith, and J. M. Chamberlain, “An introduction to medical imaging with coherent terahertz frequency radiation,” Phys. Med. Biol. 47(7), R67–R84 (2002).
[CrossRef] [PubMed]

Chirkin, A. S.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, “Nonstationary nonlinear optical effects and ultrashort light pulse formation,” IEEE J. Quantum Electron. QE-4(10), 598–605 (1968).
[CrossRef]

Drabovich, K. N.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, “Nonstationary nonlinear optical effects and ultrashort light pulse formation,” IEEE J. Quantum Electron. QE-4(10), 598–605 (1968).
[CrossRef]

Edwards, G. J.

G. J. Edwards, and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[CrossRef]

Federici, J. F.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[CrossRef]

Ferguson, B.

Fischer, R.

R. Fischer, and L. A. Kulevskii, “Optical parametric oscillators (review),” Sov. J. Quantum Electron. 7(2), 135–159 (1977).
[CrossRef]

Fitzgerald, A. J.

A. J. Fitzgerald, E. Berry, N. N. Zinovev, G. C. Walker, M. A. Smith, and J. M. Chamberlain, “An introduction to medical imaging with coherent terahertz frequency radiation,” Phys. Med. Biol. 47(7), R67–R84 (2002).
[CrossRef] [PubMed]

Garrett, C. G. B.

C. G. B. Garrett, “Nonlinear optics, anharmonic oscillators, and pyroelectricity,” IEEE J. Quantum Electron. 4(3), 70–84 (1968).
[CrossRef]

C. H. Henry, and C. G. B. Garrett, “Theory of parametric gain near a lattice resonance,” Phys. Rev. 171(3), 1058–1064 (1968).
[CrossRef]

Gary, D.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[CrossRef]

Gray, D.

Guo, R.

R. Guo, S. Ohno, H. Minamide, T. Ikari, and H. Ito, “Highly Sensitive coherent detection of terahertz waves at room temperature using a parametric process,” Appl. Phys. Lett. 93(2), 021106 (2008).
[CrossRef]

R. Guo, T. Ikari, H. Minamide, and H. Ito, “Detection of coherent tunable THz-wave using of stimulated polariton scattering in MgO:LiNbO3,” Proc. SPIE 6582, 65820Z (2007).
[CrossRef]

Henry, C. H.

C. H. Henry, and C. G. B. Garrett, “Theory of parametric gain near a lattice resonance,” Phys. Rev. 171(3), 1058–1064 (1968).
[CrossRef]

Huang, F.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[CrossRef]

Ikari, T.

R. Guo, S. Ohno, H. Minamide, T. Ikari, and H. Ito, “Highly Sensitive coherent detection of terahertz waves at room temperature using a parametric process,” Appl. Phys. Lett. 93(2), 021106 (2008).
[CrossRef]

R. Guo, T. Ikari, H. Minamide, and H. Ito, “Detection of coherent tunable THz-wave using of stimulated polariton scattering in MgO:LiNbO3,” Proc. SPIE 6582, 65820Z (2007).
[CrossRef]

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]

Ito, H.

R. Guo, S. Ohno, H. Minamide, T. Ikari, and H. Ito, “Highly Sensitive coherent detection of terahertz waves at room temperature using a parametric process,” Appl. Phys. Lett. 93(2), 021106 (2008).
[CrossRef]

R. Guo, T. Ikari, H. Minamide, and H. Ito, “Detection of coherent tunable THz-wave using of stimulated polariton scattering in MgO:LiNbO3,” Proc. SPIE 6582, 65820Z (2007).
[CrossRef]

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]

J. Shikata, K. Kawasa, and H. Ito, “The generation and linewidth control of terahertz waves by parametric processes,” Electron. Commun. Japan 86(Part 2), 52–65 (2003).

Ito, R.

Jiang, C. Y.

C. Y. Jiang, J. S. Liu, B. Sun, K. J. Wang, and J. Q. Yao, “Steady-state theoretical model for terahertz wave detector using a parametric process,” J. Opt. 12(4), 045202 (2010).
[CrossRef]

Johnson, B. C.

B. C. Johnson, H. E. Puthoff, J. Soohoo, and S. S. Sussman, “Power and linewidth of tunable stimulated far infrared emission in LiNbO3,” Appl. Phys. Lett. 18(5), 181–183 (1971).
[CrossRef]

J. M. Yarborough, S. S. Sussman, H. E. Puthoff, R. H. Pantell, and B. C. Johnson, “Efficient, tunable optical emission from LiNbO3 without a resonator,” Appl. Phys. Lett. 15(3), 102–105 (1969).
[CrossRef]

Johnston, W. D.

W. D. Johnston, Jr., and I. P. Kaminow, “Temperature dependence of Raman and Rayleigh scattering in LiNbO3 and LiTaO3,” Phys. Rev. 168(3), 1045–1054 (1968).
[CrossRef]

Judkins, J. B.

Kaminow, I. P.

W. D. Johnston, Jr., and I. P. Kaminow, “Temperature dependence of Raman and Rayleigh scattering in LiNbO3 and LiTaO3,” Phys. Rev. 168(3), 1045–1054 (1968).
[CrossRef]

Kawasa, K.

J. Shikata, K. Kawasa, and H. Ito, “The generation and linewidth control of terahertz waves by parametric processes,” Electron. Commun. Japan 86(Part 2), 52–65 (2003).

Khokhlov, R. V.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, “Nonstationary nonlinear optical effects and ultrashort light pulse formation,” IEEE J. Quantum Electron. QE-4(10), 598–605 (1968).
[CrossRef]

Kitamoto, A.

Kondo, T.

Kovrigin, A. I.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, “Nonstationary nonlinear optical effects and ultrashort light pulse formation,” IEEE J. Quantum Electron. QE-4(10), 598–605 (1968).
[CrossRef]

Kuizenga, D. J.

M. F. Becker, D. J. Kuizenga, D. W. Phillion, and A. E. Siegman, “Analytic expressions for ultrashort pulse generation in mode-locked optical parametric oscillators,” J. Appl. Phys. 45(9), 3996–4005 (1974).
[CrossRef]

Kulevskii, L. A.

R. Fischer, and L. A. Kulevskii, “Optical parametric oscillators (review),” Sov. J. Quantum Electron. 7(2), 135–159 (1977).
[CrossRef]

Lawrence, M.

G. J. Edwards, and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[CrossRef]

Liu, J. S.

C. Y. Jiang, J. S. Liu, B. Sun, K. J. Wang, and J. Q. Yao, “Steady-state theoretical model for terahertz wave detector using a parametric process,” J. Opt. 12(4), 045202 (2010).
[CrossRef]

Maier, M.

T. Qiu, and M. Maier, “Long-distance propagation and damping of low-frequency phonon polaritons in LiNbO3,” Phys. Rev. B 56(10), R5717–R5720 (1997).
[CrossRef]

Minamide, H.

R. Guo, S. Ohno, H. Minamide, T. Ikari, and H. Ito, “Highly Sensitive coherent detection of terahertz waves at room temperature using a parametric process,” Appl. Phys. Lett. 93(2), 021106 (2008).
[CrossRef]

R. Guo, T. Ikari, H. Minamide, and H. Ito, “Detection of coherent tunable THz-wave using of stimulated polariton scattering in MgO:LiNbO3,” Proc. SPIE 6582, 65820Z (2007).
[CrossRef]

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]

Ohno, S.

R. Guo, S. Ohno, H. Minamide, T. Ikari, and H. Ito, “Highly Sensitive coherent detection of terahertz waves at room temperature using a parametric process,” Appl. Phys. Lett. 93(2), 021106 (2008).
[CrossRef]

Oliveira, F.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[CrossRef]

Pantell, R. H.

J. M. Yarborough, S. S. Sussman, H. E. Puthoff, R. H. Pantell, and B. C. Johnson, “Efficient, tunable optical emission from LiNbO3 without a resonator,” Appl. Phys. Lett. 15(3), 102–105 (1969).
[CrossRef]

Phillion, D. W.

M. F. Becker, D. J. Kuizenga, D. W. Phillion, and A. E. Siegman, “Analytic expressions for ultrashort pulse generation in mode-locked optical parametric oscillators,” J. Appl. Phys. 45(9), 3996–4005 (1974).
[CrossRef]

Porras, M. A.

M. A. Porras, “Ultrashot pulsed Gaussian light beams,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(1), 1086–1093 (1998).
[CrossRef]

Puthoff, H. E.

B. C. Johnson, H. E. Puthoff, J. Soohoo, and S. S. Sussman, “Power and linewidth of tunable stimulated far infrared emission in LiNbO3,” Appl. Phys. Lett. 18(5), 181–183 (1971).
[CrossRef]

J. M. Yarborough, S. S. Sussman, H. E. Puthoff, R. H. Pantell, and B. C. Johnson, “Efficient, tunable optical emission from LiNbO3 without a resonator,” Appl. Phys. Lett. 15(3), 102–105 (1969).
[CrossRef]

Qiu, T.

T. Qiu, and M. Maier, “Long-distance propagation and damping of low-frequency phonon polaritons in LiNbO3,” Phys. Rev. B 56(10), R5717–R5720 (1997).
[CrossRef]

Schulkin, B.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications—explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[CrossRef]

Shen, Y. R.

Y. R. Shen, “Theory of Stimulated Raman Effect. II,” Phys. Rev. 138(6A), A1741–A1746 (1965).
[CrossRef]

Shikata, J.

J. Shikata, K. Kawasa, and H. Ito, “The generation and linewidth control of terahertz waves by parametric processes,” Electron. Commun. Japan 86(Part 2), 52–65 (2003).

Shirane, M.

Shoji, I.

Siegman, A. E.

M. F. Becker, D. J. Kuizenga, D. W. Phillion, and A. E. Siegman, “Analytic expressions for ultrashort pulse generation in mode-locked optical parametric oscillators,” J. Appl. Phys. 45(9), 3996–4005 (1974).
[CrossRef]

Smith, M. A.

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B. C. Johnson, H. E. Puthoff, J. Soohoo, and S. S. Sussman, “Power and linewidth of tunable stimulated far infrared emission in LiNbO3,” Appl. Phys. Lett. 18(5), 181–183 (1971).
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C. Y. Jiang, J. S. Liu, B. Sun, K. J. Wang, and J. Q. Yao, “Steady-state theoretical model for terahertz wave detector using a parametric process,” J. Opt. 12(4), 045202 (2010).
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C. Y. Jiang, J. S. Liu, B. Sun, K. J. Wang, and J. Q. Yao, “Steady-state theoretical model for terahertz wave detector using a parametric process,” J. Opt. 12(4), 045202 (2010).
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[CrossRef]

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A. J. Fitzgerald, E. Berry, N. N. Zinovev, G. C. Walker, M. A. Smith, and J. M. Chamberlain, “An introduction to medical imaging with coherent terahertz frequency radiation,” Phys. Med. Biol. 47(7), R67–R84 (2002).
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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagrams (a) the THz wave detector made of two LN crystals reported in [4], and (b) wave configuration, boundary conditions and coordinate system.

Fig. 2.
Fig. 2.

The calculated time-dependent power envelope of the incident THz pulse with regard to an incident pump pulse (left insert drawing) and an output idler pulse (right insert drawing). The system parameters are τ p = 15 ns, λ p = 1.064 µm, τ id = 4.13 ns, λ id = 1.0697 µm, W p = 16 mJ, P 0id = 85 mW, SA = 1.3 × 1.1 mm2, l 1 = 5 mm and l 2 = 50 mm.

Fig. 3.
Fig. 3.

The curves of the incident THz pulse varying with the output idler wave with τ p = 15 ns, W p = 16 mJ, l 1 = 5 mm and l 2 = 50 mm. The blue one (left coordinate) is the curve between P 0T and P 0id with τ id = 4.13ns, while the red one (right coordinate) is the curve between τ T and τ id with P 0id = 85 mW.

Fig. 4.
Fig. 4.

The curves of the output idler pulse energy E id varying with the incident THz pulse energy E T under (a) different effective lengths of the first crystal, (b) different effective lengths of the second crystal, (c) different pulse energies of the incident pump beam, and (d) different pulse widths of the incident pump beam. The other system parameters are SA = 1.3 × 1.1 mm2, λ p = 1.064µm, τ T = 4 ns and ν 0T = ω 0T/2π = 1.5 THz.

Equations (51)

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( z + 1 u t ) A ( z , t ) = i ω 0 2 2 k 0 z ε 0 c 2 p NL ( z , t ) exp [ i ( k 0 z z + φ 0 ) ] ,
( z + 1 u p t ) A p ( z , t ) = i ω 0 p 2 n 0 p c { χ p ( 3 ) ( ω 0 p ; ω 0 p ω 0 id , ω 0 id ) A id ( z , t ) 2 A p ( z , t )
+ χ p ( 2 ) ( ω 0 p ; ω 0 id , ω 0 T ) A id ( z , t ) A T ( z , t ) exp [ i ( Δ k 0 z z + Δ φ ) ] } ,
( z + 1 u T t ) A T ( z , t ) = i ω 0 T 2 n 0 T c { χ T ( 1 ) ( ω 0 T ) A T ( z , t )
+ χ T ( 2 ) ( ω 0 T ; ω 0 p , ω 0 id ) A p ( z , t ) A id * ( z , t ) exp [ i ( Δ k 0 z z + Δ φ ) ] } ,
( z + 1 u id t ) A id ( z , t ) = i ω 0 id 2 n 0 id c { χ id ( 3 ) ( ω 0 id ; ω 0 p ω 0 p , ω 0 id ) A p ( z , t ) 2 A id ( z , t )
+ χ id ( 2 ) ( ω 0 id ; ω 0 p , ω 0 T ) A p ( z , t ) A T * ( z , t ) exp [ i ( Δ k 0 z z + Δ φ ) ] } ,
z = z and τ = t z u .
A T ( z , τ ) = 1 g + g { [ β T A id * ( 0 , τ ) ( g α T + i Δ k 0 z 2 ) A T ( 0 , τ ) ] exp ( g + z )
[ β T A id * ( 0 , τ ) ( g + α T + i Δ k 0 z 2 ) A T ( 0 , τ ) ] exp ( g z ) } exp ( i Δ k 0 z z 2 ) ,
A id * ( z , τ ) = 1 g + g { [ ( g + α T + i Δ k z 2 ) A id * ( 0 , τ ) + β id * A T ( 0 , τ ) ] exp ( g + z )
[ ( g α T + i Δ k z 2 ) A id * ( 0 , τ ) + β id * A T ( 0 , τ ) ] exp ( g z ) } exp ( i Δ k 0 z z 2 ) ,
α T = i ω 0 T 2 n 0 T c cos φ χ T ( 1 ) ,
β T = i ω 0 T 2 n 0 T c cos φ χ T ( 2 ) A p ( 0 , τ ) exp ( i Δ φ ) ,
α id = i ω 0 id 2 n 0 id c cos θ χ id ( 3 ) A p ( 0 , τ ) 2 ,
β id = i ω 0 id 2 n 0 id c cos θ χ id ( 2 ) A p ( 0 , τ ) exp ( i Δ φ ) ,
g ± = 1 2 ( α T + α id * ) ± 1 2 ( α T + α id * + i Δ k 0 z ) 2 + 4 β T β id * ,
A id * ( z , τ ) = exp ( g + z ) exp ( g z ) g + g β id * A T ( 0 , τ ) exp ( i Δ k 0 z z 2 ) .
A id * ( z + l 1 , τ ) = ( g + α T + i Δ k z 2 ) exp ( g + z ) ( g α T + i Δ k z 2 ) exp ( g z ) g + g
× A id * ( l 1 , τ ) exp ( i Δ k 0 z z 2 ) ,
A id * ( l 1 + l 2 , τ ) = i ω 0 id 2 n 0 id c cos θ k χ id ( 2 ) * A p * ( 0 , τ ) A T ( 0 , τ ) exp { i [ Δ k 0 z 2 ( l 1 + l 2 ) + Δ φ ] } ,
κ = ( g + α T + i Δ k 0 z 2 ) exp ( g + l 2 ) ( g α T + i Δ k 0 z 2 ) exp ( g l 2 ) ( g + g ) 2
× [ exp ( g + l 1 ) exp ( g l 1 ) ] ,
E id * ( l 1 + l 2 , τ ) = i ω 0 id 2 n 0 id c cos θ κ χ id ( 2 ) * E p * ( 0 , τ ) E T ( 0 , τ ) ,
I id ( l 1 + l 2 , τ ) = ω 0 id 2 8 c 3 ε 0 n 0 p n 0 id n 0 T cos 2 θ κ χ id ( 2 ) * 2 I p ( 0 , τ ) I T ( 0 , τ ) .
n 0 T = Re ε + χ i ( 1 ) ( ω 0 T ) ,
W m ( z ) = P m ( z , τ ) d τ = P 0 m ( z ) τ m π ( 2 ln 2 ) .
2 E = 1 ε 0 c 2 2 D ( 1 ) t 2 + 1 ε 0 c 2 2 P NL t 2 ,
E ( x , z , t ) = E ˜ ( x , z , ω ) e i ω t d ω 2 π ,
D ( 1 ) ( x , z , t ) = D ˜ ( 1 ) ( x , z , ω ) e i ω t d ω 2 π ,
P NL ( x , z , t ) = P ˜ NL ( x , z , ω ) e i ω t d ω 2 π ,
D ˜ ( 1 ) ( x , z , ω ) = ε 0 ε r ( ω ) E ˜ ( x , z , ω ) .
2 E ˜ ( x , z , ω ) = ω 2 ε r ( ω ) c 2 E ˜ ( x , z , ω ) ω 2 ε 0 c 2 P ˜ NL ( x , z , ω ) .
E ( x , z , t ) = A ( x , z , t ) exp [ i ( ω 0 t k 0 x x k 0 z z φ 0 ) ] + c . c . ,
A ( x , z , t ) = A ˜ ( x , z , ω ) e i ω t d ω 2 π .
E ˜ ( x , z , ω ) = A ˜ ( x , z , ω ω 0 ) exp [ i ( k 0 x x + k 0 z z + φ 0 ) ]
+ A ˜ * ( x , z , ω + ω 0 ) exp [ i ( k 0 x x + k 0 z z + φ 0 ) ] .
[ 2 x 2 + 2 z 2 + 2 i ( k 0 x x + k 0 z z ) + k 2 ( ω ) k 0 x 2 k 0 z 2 ] A ˜ ( x , z , ω ω 0 )
× exp [ i ( k 0 x x + k 0 z z + φ 0 ) ] + c . c . = ω 2 ε 0 c 2 P ˜ NL ( x , z , ω ) ,
k 2 ( ω ) = ε r ( ω ) ω 2 c 2 .
k ( ω ) = k 0 + dk ( ω ) d ω ω 0 ( ω ω 0 ) + high order dispersion .
k 2 ( ω ) = k 0 2 + 2 k 0 u ( ω ω 0 ) + 1 u 2 ( ω ω 0 ) 2 ,
[ 2 x 2 + 2 z 2 + 2 i ( k 0 x x + k 0 z z ) + 2 k 0 u ( ω ω 0 ) + 1 u 2 ( ω ω 0 ) 2 ] A ˜ ( x , z , ω ω 0 )
× exp [ i ( k 0 x x + k 0 z z + φ 0 ) ] + c . c . = ω 2 ε 0 c 2 P ˜ NL ( x , z , ω ) .
[ 2 x 2 + 2 z 2 + 2 i ( k 0 x x + k 0 z z ) + 2 i k 0 u t 1 u 2 2 t 2 ] A ( x , z , t )
× exp [ i ( k 0 x x + k 0 z z + φ 0 ω 0 t ) ] + c . c . = 1 ε 0 c 2 2 P NL ( x , z , t ) t 2 .
2 ik 0 z ( z + 1 u t ) A ( z , t ) exp [ i ( k 0 z z + φ 0 ω 0 t ) ] + c . c . = 1 ε 0 c 2 2 P NL ( z , t ) t 2 .
P NL ( z , t ) = p NL ( z , t ) exp ( i ω 0 t ) + c . c .
2 P NL ( z , t ) t 2 = ( 2 t 2 2 i ω 0 t ω 0 2 ) p NL ( z , t ) exp ( i ω 0 t ) + c . c . .
2 P NL ( z , t ) t 2 = ω 0 2 p NL ( z , t ) exp ( i ω 0 t ) + c . c . .
( z + 1 u t ) A ( z , t ) = i ω 0 2 2 k 0 z ε 0 c 2 p NL ( z , t ) exp [ i ( k 0 z z + φ 0 ) ] .

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