Abstract

We extend the theory of Cherenkov radiation from an ultrashort laser pulse in an electro-optic medium to the realistic case when the laser pulse propagates as a tightly focused Gaussian beam. By applying the developed theory to the situation of practical interest—a LiNbO3 crystal pumped by a near-infrared (Ti:sapphire or Yb) laser, we explore how the emitted terahertz energy and the terahertz spectrum depend on the focusing conditions for different laser pulse durations. The cases of focusing to a line and a spot are considered. It is shown that there is an optimal size of the beam waist, which maximizes the terahertz yield. The theoretical predictions are verified experimentally.

© 2019 Optical Society of America

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References

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    [Crossref]
  4. D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
    [Crossref]
  5. B. B. Hu, X.-C. Zhang, D. H. Auston, and P. R. Smith, “Free-space radiation from electro-optics crystals,” Appl. Phys. Lett. 56, 506–508 (1990).
    [Crossref]
  6. A. G. Stepanov, J. Hebling, and J. Kuhl, “THz generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23–26 (2005).
    [Crossref]
  7. A. G. Stepanov, J. Kuhl, I. Z. Kozma, E. Riedle, G. Almási, and J. Hebling, “Scaling up the energy of THz pulses created by optical rectification,” Opt. Express 13, 5762–5768 (2005).
    [Crossref]
  8. M. Theuer, G. Torosyan, C. Rau, R. Beigang, K. Maki, C. Otani, and K. Kawase, “Efficient generation of Cherenkov-type terahertz radiation from a lithium niobate crystal with a silicon prism output coupler,” Appl. Phys. Lett. 88, 071122 (2006).
    [Crossref]
  9. S. B. Bodrov, A. N. Stepanov, M. I. Bakunov, B. V. Shishkin, I. E. Ilyakov, and R. A. Akhmedzhanov, “Highly efficient optical-to-terahertz conversion in a sandwich structure with LiNbO3 core,” Opt. Express 17, 1871–1879 (2009).
    [Crossref]
  10. S. B. Bodrov, I. E. Ilyakov, B. V. Shishkin, and A. N. Stepanov, “Efficient terahertz generation by optical rectification in Si-LiNbO3-air-metal sandwich structure with variable air gap,” Appl. Phys. Lett. 100, 201114 (2012).
    [Crossref]
  11. M. I. Bakunov, E. A. Mashkovich, M. V. Tsarev, and S. D. Gorelov, “Efficient Cherenkov-type terahertz generation in Si-prism-LiNbO3-slab structure pumped by nanojoule-level ultrashort laser pulses,” Appl. Phys. Lett. 101, 151102 (2012).
    [Crossref]
  12. S. Fan, H. Takeuchi, T. Ouchi, K. Takeya, and K. Kawase, “Broadband terahertz wave generation from a MgO:LiNbO3 ridge waveguide pumped by a 1.5 μm femtosecond fiber laser,” Opt. Lett. 38, 1654–1656 (2013).
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  13. K. Takeya, T. Minami, H. Okano, S. R. Tripathi, and K. Kawase, “Enhanced Cherenkov phase matching terahertz wave generation via a magnesium oxide doped lithium niobate ridged waveguide crystal,” APL Photon. 2, 016102 (2016).
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    [Crossref]
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    [Crossref]
  16. S. B. Bodrov, M. I. Bakunov, and M. Hangyo, “Efficient Cherenkov emission of broadband terahertz radiation from an ultrashort laser pulse in a sandwich structure with nonlinear core,” J. Appl. Phys. 104, 093105 (2008).
    [Crossref]
  17. K. Suizu, K. Koketsu, T. Shibuya, T. Tsutsui, T. Akiba, and K. Kawase, “Extremely frequency-widened terahertz wave generation using Cherenkov-type radiation,” Opt. Express 17, 6676–6681 (2009).
    [Crossref]
  18. J. Hebling, G. Almási, I. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large area THz-pulse generation,” Opt. Express 10, 1161–1166 (2002).
    [Crossref]
  19. S.-W. Huang, E. Granados, W. R. Huang, K.-H. Hong, L. E. Zapata, and F. X. Kärtner, “High conversion efficiency, high energy terahertz pulses by optical rectification in cryogenically cooled lithium niobate,” Opt. Lett. 38, 796–798 (2013).
    [Crossref]
  20. J. A. Fülöp, Z. Ollmann, C. Lombosi, C. Skrobol, S. Klingebiel, L. Pálfalvi, F. Krausz, S. Karsch, and J. Hebling, “Efficient generation of THz pulses with 0.4 mJ energy,” Opt. Express 22, 20155–20163 (2014).
    [Crossref]
  21. U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, “Difference-frequency excitation in nonlinear optics and the conditions for Cerenkov radiation emission,” Sov. Phys. JETP 39, 633–637 (1974).
  22. D. A. Kleinman and D. H. Auston, “Theory of electrooptic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20, 964–970 (1984).
    [Crossref]
  23. J. K. Wahlstrand and R. Merlin, “Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons,” Phys. Rev. B 68, 054301 (2003).
    [Crossref]
  24. M. I. Bakunov, S. B. Bodrov, A. V. Maslov, and M. Hangyo, “Theory of terahertz generation in a slab of electro-optic material using an ultrashort laser pulse focused to a line,” Phys. Rev. B 76, 085346 (2007).
    [Crossref]
  25. T. Shibuya, T. Tsutsui, K. Suizu, T. Akiba, and K. Kawase, “Efficient Cherenkov-type phase-matched widely tunable terahertz-wave generation via an optimized pump beam shape,” Appl. Phys. Express 2, 032302 (2009).
    [Crossref]
  26. P. Liu, D. Xu, H. Jiang, Z. Zhang, K. Zhong, Y. Wang, and J. Yao, “Theory of monochromatic terahertz generation via Cherenkov phase-matched difference frequency generation in LiNbO3 crystal,” J. Opt. Soc. Am. B 29, 2425–2430 (2012).
    [Crossref]
  27. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).
  28. D. E. Zelmon, D. L. Small, and D. Jundt, “Infrared corrected Sellmeier coefficients for congruently grown lithium niobite and 5 mol. % magnesium oxide-doped lithium niobate,” J. Opt. Soc. Am. B 14, 3319–3322 (1997).
    [Crossref]
  29. J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrasort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
    [Crossref]
  30. O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
    [Crossref]
  31. L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97, 123505 (2005).
    [Crossref]
  32. N. S. Stoyanov, T. Feurer, D. W. Ward, E. R. Statz, and K. A. Nelson, “Direct visualization of a polariton resonator in the THz regime,” Opt. Express 12, 2387–2396 (2004).
    [Crossref]
  33. M. I. Bakunov, S. B. Bodrov, and E. A. Mashkovich, “Terahertz generation with tilted-front laser pulses: dynamic theory for low-absorbing crystals,” J. Opt. Soc. Am. B 28, 1724–1734 (2011).
    [Crossref]
  34. D. Li, G. Ma, J. Ge, S. Hu, and N. Dai, “Terahertz pulse shaping via birefringence in lithium niobate crystal,” Appl. Phys. B 94, 623–628 (2009).
    [Crossref]

2016 (1)

K. Takeya, T. Minami, H. Okano, S. R. Tripathi, and K. Kawase, “Enhanced Cherenkov phase matching terahertz wave generation via a magnesium oxide doped lithium niobate ridged waveguide crystal,” APL Photon. 2, 016102 (2016).
[Crossref]

2014 (1)

2013 (2)

2012 (3)

S. B. Bodrov, I. E. Ilyakov, B. V. Shishkin, and A. N. Stepanov, “Efficient terahertz generation by optical rectification in Si-LiNbO3-air-metal sandwich structure with variable air gap,” Appl. Phys. Lett. 100, 201114 (2012).
[Crossref]

M. I. Bakunov, E. A. Mashkovich, M. V. Tsarev, and S. D. Gorelov, “Efficient Cherenkov-type terahertz generation in Si-prism-LiNbO3-slab structure pumped by nanojoule-level ultrashort laser pulses,” Appl. Phys. Lett. 101, 151102 (2012).
[Crossref]

P. Liu, D. Xu, H. Jiang, Z. Zhang, K. Zhong, Y. Wang, and J. Yao, “Theory of monochromatic terahertz generation via Cherenkov phase-matched difference frequency generation in LiNbO3 crystal,” J. Opt. Soc. Am. B 29, 2425–2430 (2012).
[Crossref]

2011 (1)

2010 (1)

T. Shibuya, K. Suizu, and K. Kawase, “Widely tunable monochromatic Cherenkov phase-matched terahertz wave generation from bulk lithium niobate,” Appl. Phys. Express 3, 082201 (2010).
[Crossref]

2009 (4)

S. B. Bodrov, A. N. Stepanov, M. I. Bakunov, B. V. Shishkin, I. E. Ilyakov, and R. A. Akhmedzhanov, “Highly efficient optical-to-terahertz conversion in a sandwich structure with LiNbO3 core,” Opt. Express 17, 1871–1879 (2009).
[Crossref]

D. Li, G. Ma, J. Ge, S. Hu, and N. Dai, “Terahertz pulse shaping via birefringence in lithium niobate crystal,” Appl. Phys. B 94, 623–628 (2009).
[Crossref]

T. Shibuya, T. Tsutsui, K. Suizu, T. Akiba, and K. Kawase, “Efficient Cherenkov-type phase-matched widely tunable terahertz-wave generation via an optimized pump beam shape,” Appl. Phys. Express 2, 032302 (2009).
[Crossref]

K. Suizu, K. Koketsu, T. Shibuya, T. Tsutsui, T. Akiba, and K. Kawase, “Extremely frequency-widened terahertz wave generation using Cherenkov-type radiation,” Opt. Express 17, 6676–6681 (2009).
[Crossref]

2008 (2)

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

S. B. Bodrov, M. I. Bakunov, and M. Hangyo, “Efficient Cherenkov emission of broadband terahertz radiation from an ultrashort laser pulse in a sandwich structure with nonlinear core,” J. Appl. Phys. 104, 093105 (2008).
[Crossref]

2007 (1)

M. I. Bakunov, S. B. Bodrov, A. V. Maslov, and M. Hangyo, “Theory of terahertz generation in a slab of electro-optic material using an ultrashort laser pulse focused to a line,” Phys. Rev. B 76, 085346 (2007).
[Crossref]

2006 (1)

M. Theuer, G. Torosyan, C. Rau, R. Beigang, K. Maki, C. Otani, and K. Kawase, “Efficient generation of Cherenkov-type terahertz radiation from a lithium niobate crystal with a silicon prism output coupler,” Appl. Phys. Lett. 88, 071122 (2006).
[Crossref]

2005 (3)

A. G. Stepanov, J. Hebling, and J. Kuhl, “THz generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23–26 (2005).
[Crossref]

A. G. Stepanov, J. Kuhl, I. Z. Kozma, E. Riedle, G. Almási, and J. Hebling, “Scaling up the energy of THz pulses created by optical rectification,” Opt. Express 13, 5762–5768 (2005).
[Crossref]

L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97, 123505 (2005).
[Crossref]

2004 (2)

N. S. Stoyanov, T. Feurer, D. W. Ward, E. R. Statz, and K. A. Nelson, “Direct visualization of a polariton resonator in the THz regime,” Opt. Express 12, 2387–2396 (2004).
[Crossref]

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrasort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[Crossref]

2003 (1)

J. K. Wahlstrand and R. Merlin, “Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons,” Phys. Rev. B 68, 054301 (2003).
[Crossref]

2002 (1)

1997 (1)

1990 (1)

B. B. Hu, X.-C. Zhang, D. H. Auston, and P. R. Smith, “Free-space radiation from electro-optics crystals,” Appl. Phys. Lett. 56, 506–508 (1990).
[Crossref]

1986 (1)

G. A. Askaryan, “Cherenkov radiation from optical pulses,” Phys. Rev. Lett. 57, 2470 (1986).
[Crossref]

1984 (2)

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

D. A. Kleinman and D. H. Auston, “Theory of electrooptic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20, 964–970 (1984).
[Crossref]

1983 (1)

D. H. Auston, “Subpicosecond electro-optic shock waves,” Appl. Phys. Lett. 43, 713–715 (1983).
[Crossref]

1974 (1)

U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, “Difference-frequency excitation in nonlinear optics and the conditions for Cerenkov radiation emission,” Sov. Phys. JETP 39, 633–637 (1974).

1962 (1)

G. A. Askaryan, “Cerenkov radiation and transition radiation from electromagnetic waves,” Sov. Phys. JETP 15, 943–946 (1962).

1934 (1)

P. A. Cherenkov, “Visible emission of clean liquids by action of γ radiation,” Dokl. Akad. Nauk SSSR 2, 451–454 (1934).

Abdullin, U. A.

U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, “Difference-frequency excitation in nonlinear optics and the conditions for Cerenkov radiation emission,” Sov. Phys. JETP 39, 633–637 (1974).

Akhmanov, S. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Akhmedzhanov, R. A.

Akiba, T.

K. Suizu, K. Koketsu, T. Shibuya, T. Tsutsui, T. Akiba, and K. Kawase, “Extremely frequency-widened terahertz wave generation using Cherenkov-type radiation,” Opt. Express 17, 6676–6681 (2009).
[Crossref]

T. Shibuya, T. Tsutsui, K. Suizu, T. Akiba, and K. Kawase, “Efficient Cherenkov-type phase-matched widely tunable terahertz-wave generation via an optimized pump beam shape,” Appl. Phys. Express 2, 032302 (2009).
[Crossref]

Almási, G.

Arie, A.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

Askaryan, G. A.

G. A. Askaryan, “Cherenkov radiation from optical pulses,” Phys. Rev. Lett. 57, 2470 (1986).
[Crossref]

G. A. Askaryan, “Cerenkov radiation and transition radiation from electromagnetic waves,” Sov. Phys. JETP 15, 943–946 (1962).

Auston, D. H.

B. B. Hu, X.-C. Zhang, D. H. Auston, and P. R. Smith, “Free-space radiation from electro-optics crystals,” Appl. Phys. Lett. 56, 506–508 (1990).
[Crossref]

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

D. A. Kleinman and D. H. Auston, “Theory of electrooptic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20, 964–970 (1984).
[Crossref]

D. H. Auston, “Subpicosecond electro-optic shock waves,” Appl. Phys. Lett. 43, 713–715 (1983).
[Crossref]

Bakunov, M. I.

M. I. Bakunov, E. A. Mashkovich, M. V. Tsarev, and S. D. Gorelov, “Efficient Cherenkov-type terahertz generation in Si-prism-LiNbO3-slab structure pumped by nanojoule-level ultrashort laser pulses,” Appl. Phys. Lett. 101, 151102 (2012).
[Crossref]

M. I. Bakunov, S. B. Bodrov, and E. A. Mashkovich, “Terahertz generation with tilted-front laser pulses: dynamic theory for low-absorbing crystals,” J. Opt. Soc. Am. B 28, 1724–1734 (2011).
[Crossref]

S. B. Bodrov, A. N. Stepanov, M. I. Bakunov, B. V. Shishkin, I. E. Ilyakov, and R. A. Akhmedzhanov, “Highly efficient optical-to-terahertz conversion in a sandwich structure with LiNbO3 core,” Opt. Express 17, 1871–1879 (2009).
[Crossref]

S. B. Bodrov, M. I. Bakunov, and M. Hangyo, “Efficient Cherenkov emission of broadband terahertz radiation from an ultrashort laser pulse in a sandwich structure with nonlinear core,” J. Appl. Phys. 104, 093105 (2008).
[Crossref]

M. I. Bakunov, S. B. Bodrov, A. V. Maslov, and M. Hangyo, “Theory of terahertz generation in a slab of electro-optic material using an ultrashort laser pulse focused to a line,” Phys. Rev. B 76, 085346 (2007).
[Crossref]

Bartal, B.

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrasort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[Crossref]

Beigang, R.

M. Theuer, G. Torosyan, C. Rau, R. Beigang, K. Maki, C. Otani, and K. Kawase, “Efficient generation of Cherenkov-type terahertz radiation from a lithium niobate crystal with a silicon prism output coupler,” Appl. Phys. Lett. 88, 071122 (2006).
[Crossref]

Bodrov, S. B.

S. B. Bodrov, I. E. Ilyakov, B. V. Shishkin, and A. N. Stepanov, “Efficient terahertz generation by optical rectification in Si-LiNbO3-air-metal sandwich structure with variable air gap,” Appl. Phys. Lett. 100, 201114 (2012).
[Crossref]

M. I. Bakunov, S. B. Bodrov, and E. A. Mashkovich, “Terahertz generation with tilted-front laser pulses: dynamic theory for low-absorbing crystals,” J. Opt. Soc. Am. B 28, 1724–1734 (2011).
[Crossref]

S. B. Bodrov, A. N. Stepanov, M. I. Bakunov, B. V. Shishkin, I. E. Ilyakov, and R. A. Akhmedzhanov, “Highly efficient optical-to-terahertz conversion in a sandwich structure with LiNbO3 core,” Opt. Express 17, 1871–1879 (2009).
[Crossref]

S. B. Bodrov, M. I. Bakunov, and M. Hangyo, “Efficient Cherenkov emission of broadband terahertz radiation from an ultrashort laser pulse in a sandwich structure with nonlinear core,” J. Appl. Phys. 104, 093105 (2008).
[Crossref]

M. I. Bakunov, S. B. Bodrov, A. V. Maslov, and M. Hangyo, “Theory of terahertz generation in a slab of electro-optic material using an ultrashort laser pulse focused to a line,” Phys. Rev. B 76, 085346 (2007).
[Crossref]

Cherenkov, P. A.

P. A. Cherenkov, “Visible emission of clean liquids by action of γ radiation,” Dokl. Akad. Nauk SSSR 2, 451–454 (1934).

Cheung, K. P.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

Chirkin, A. S.

U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, “Difference-frequency excitation in nonlinear optics and the conditions for Cerenkov radiation emission,” Sov. Phys. JETP 39, 633–637 (1974).

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Dai, N.

D. Li, G. Ma, J. Ge, S. Hu, and N. Dai, “Terahertz pulse shaping via birefringence in lithium niobate crystal,” Appl. Phys. B 94, 623–628 (2009).
[Crossref]

Fan, S.

Feurer, T.

Fülöp, J. A.

Galun, E.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

Gayer, O.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

Ge, J.

D. Li, G. Ma, J. Ge, S. Hu, and N. Dai, “Terahertz pulse shaping via birefringence in lithium niobate crystal,” Appl. Phys. B 94, 623–628 (2009).
[Crossref]

Gorelov, S. D.

M. I. Bakunov, E. A. Mashkovich, M. V. Tsarev, and S. D. Gorelov, “Efficient Cherenkov-type terahertz generation in Si-prism-LiNbO3-slab structure pumped by nanojoule-level ultrashort laser pulses,” Appl. Phys. Lett. 101, 151102 (2012).
[Crossref]

Granados, E.

Hangyo, M.

S. B. Bodrov, M. I. Bakunov, and M. Hangyo, “Efficient Cherenkov emission of broadband terahertz radiation from an ultrashort laser pulse in a sandwich structure with nonlinear core,” J. Appl. Phys. 104, 093105 (2008).
[Crossref]

M. I. Bakunov, S. B. Bodrov, A. V. Maslov, and M. Hangyo, “Theory of terahertz generation in a slab of electro-optic material using an ultrashort laser pulse focused to a line,” Phys. Rev. B 76, 085346 (2007).
[Crossref]

Hebling, J.

J. A. Fülöp, Z. Ollmann, C. Lombosi, C. Skrobol, S. Klingebiel, L. Pálfalvi, F. Krausz, S. Karsch, and J. Hebling, “Efficient generation of THz pulses with 0.4 mJ energy,” Opt. Express 22, 20155–20163 (2014).
[Crossref]

A. G. Stepanov, J. Kuhl, I. Z. Kozma, E. Riedle, G. Almási, and J. Hebling, “Scaling up the energy of THz pulses created by optical rectification,” Opt. Express 13, 5762–5768 (2005).
[Crossref]

L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97, 123505 (2005).
[Crossref]

A. G. Stepanov, J. Hebling, and J. Kuhl, “THz generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23–26 (2005).
[Crossref]

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrasort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[Crossref]

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

Hong, K.-H.

Hu, B. B.

B. B. Hu, X.-C. Zhang, D. H. Auston, and P. R. Smith, “Free-space radiation from electro-optics crystals,” Appl. Phys. Lett. 56, 506–508 (1990).
[Crossref]

Hu, S.

D. Li, G. Ma, J. Ge, S. Hu, and N. Dai, “Terahertz pulse shaping via birefringence in lithium niobate crystal,” Appl. Phys. B 94, 623–628 (2009).
[Crossref]

Huang, S.-W.

Huang, W. R.

Ilyakov, I. E.

S. B. Bodrov, I. E. Ilyakov, B. V. Shishkin, and A. N. Stepanov, “Efficient terahertz generation by optical rectification in Si-LiNbO3-air-metal sandwich structure with variable air gap,” Appl. Phys. Lett. 100, 201114 (2012).
[Crossref]

S. B. Bodrov, A. N. Stepanov, M. I. Bakunov, B. V. Shishkin, I. E. Ilyakov, and R. A. Akhmedzhanov, “Highly efficient optical-to-terahertz conversion in a sandwich structure with LiNbO3 core,” Opt. Express 17, 1871–1879 (2009).
[Crossref]

Jiang, H.

Jundt, D.

Karsch, S.

Kärtner, F. X.

Kawase, K.

K. Takeya, T. Minami, H. Okano, S. R. Tripathi, and K. Kawase, “Enhanced Cherenkov phase matching terahertz wave generation via a magnesium oxide doped lithium niobate ridged waveguide crystal,” APL Photon. 2, 016102 (2016).
[Crossref]

S. Fan, H. Takeuchi, T. Ouchi, K. Takeya, and K. Kawase, “Broadband terahertz wave generation from a MgO:LiNbO3 ridge waveguide pumped by a 1.5 μm femtosecond fiber laser,” Opt. Lett. 38, 1654–1656 (2013).
[Crossref]

T. Shibuya, K. Suizu, and K. Kawase, “Widely tunable monochromatic Cherenkov phase-matched terahertz wave generation from bulk lithium niobate,” Appl. Phys. Express 3, 082201 (2010).
[Crossref]

T. Shibuya, T. Tsutsui, K. Suizu, T. Akiba, and K. Kawase, “Efficient Cherenkov-type phase-matched widely tunable terahertz-wave generation via an optimized pump beam shape,” Appl. Phys. Express 2, 032302 (2009).
[Crossref]

K. Suizu, K. Koketsu, T. Shibuya, T. Tsutsui, T. Akiba, and K. Kawase, “Extremely frequency-widened terahertz wave generation using Cherenkov-type radiation,” Opt. Express 17, 6676–6681 (2009).
[Crossref]

M. Theuer, G. Torosyan, C. Rau, R. Beigang, K. Maki, C. Otani, and K. Kawase, “Efficient generation of Cherenkov-type terahertz radiation from a lithium niobate crystal with a silicon prism output coupler,” Appl. Phys. Lett. 88, 071122 (2006).
[Crossref]

Kleinman, D. A.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

D. A. Kleinman and D. H. Auston, “Theory of electrooptic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20, 964–970 (1984).
[Crossref]

Klingebiel, S.

Koketsu, K.

Kozma, I.

Kozma, I. Z.

Krausz, F.

Kuhl, J.

A. G. Stepanov, J. Kuhl, I. Z. Kozma, E. Riedle, G. Almási, and J. Hebling, “Scaling up the energy of THz pulses created by optical rectification,” Opt. Express 13, 5762–5768 (2005).
[Crossref]

L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97, 123505 (2005).
[Crossref]

A. G. Stepanov, J. Hebling, and J. Kuhl, “THz generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23–26 (2005).
[Crossref]

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrasort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[Crossref]

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

Li, D.

D. Li, G. Ma, J. Ge, S. Hu, and N. Dai, “Terahertz pulse shaping via birefringence in lithium niobate crystal,” Appl. Phys. B 94, 623–628 (2009).
[Crossref]

Liu, P.

Lombosi, C.

Lyakhov, G. A.

U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, “Difference-frequency excitation in nonlinear optics and the conditions for Cerenkov radiation emission,” Sov. Phys. JETP 39, 633–637 (1974).

Ma, G.

D. Li, G. Ma, J. Ge, S. Hu, and N. Dai, “Terahertz pulse shaping via birefringence in lithium niobate crystal,” Appl. Phys. B 94, 623–628 (2009).
[Crossref]

Maki, K.

M. Theuer, G. Torosyan, C. Rau, R. Beigang, K. Maki, C. Otani, and K. Kawase, “Efficient generation of Cherenkov-type terahertz radiation from a lithium niobate crystal with a silicon prism output coupler,” Appl. Phys. Lett. 88, 071122 (2006).
[Crossref]

Mashkovich, E. A.

M. I. Bakunov, E. A. Mashkovich, M. V. Tsarev, and S. D. Gorelov, “Efficient Cherenkov-type terahertz generation in Si-prism-LiNbO3-slab structure pumped by nanojoule-level ultrashort laser pulses,” Appl. Phys. Lett. 101, 151102 (2012).
[Crossref]

M. I. Bakunov, S. B. Bodrov, and E. A. Mashkovich, “Terahertz generation with tilted-front laser pulses: dynamic theory for low-absorbing crystals,” J. Opt. Soc. Am. B 28, 1724–1734 (2011).
[Crossref]

Maslov, A. V.

M. I. Bakunov, S. B. Bodrov, A. V. Maslov, and M. Hangyo, “Theory of terahertz generation in a slab of electro-optic material using an ultrashort laser pulse focused to a line,” Phys. Rev. B 76, 085346 (2007).
[Crossref]

Merlin, R.

J. K. Wahlstrand and R. Merlin, “Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons,” Phys. Rev. B 68, 054301 (2003).
[Crossref]

Minami, T.

K. Takeya, T. Minami, H. Okano, S. R. Tripathi, and K. Kawase, “Enhanced Cherenkov phase matching terahertz wave generation via a magnesium oxide doped lithium niobate ridged waveguide crystal,” APL Photon. 2, 016102 (2016).
[Crossref]

Nelson, K. A.

Okano, H.

K. Takeya, T. Minami, H. Okano, S. R. Tripathi, and K. Kawase, “Enhanced Cherenkov phase matching terahertz wave generation via a magnesium oxide doped lithium niobate ridged waveguide crystal,” APL Photon. 2, 016102 (2016).
[Crossref]

Ollmann, Z.

Otani, C.

M. Theuer, G. Torosyan, C. Rau, R. Beigang, K. Maki, C. Otani, and K. Kawase, “Efficient generation of Cherenkov-type terahertz radiation from a lithium niobate crystal with a silicon prism output coupler,” Appl. Phys. Lett. 88, 071122 (2006).
[Crossref]

Ouchi, T.

Pálfalvi, L.

J. A. Fülöp, Z. Ollmann, C. Lombosi, C. Skrobol, S. Klingebiel, L. Pálfalvi, F. Krausz, S. Karsch, and J. Hebling, “Efficient generation of THz pulses with 0.4 mJ energy,” Opt. Express 22, 20155–20163 (2014).
[Crossref]

L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97, 123505 (2005).
[Crossref]

Péter, Á.

L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97, 123505 (2005).
[Crossref]

Polgár, K.

L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97, 123505 (2005).
[Crossref]

Rau, C.

M. Theuer, G. Torosyan, C. Rau, R. Beigang, K. Maki, C. Otani, and K. Kawase, “Efficient generation of Cherenkov-type terahertz radiation from a lithium niobate crystal with a silicon prism output coupler,” Appl. Phys. Lett. 88, 071122 (2006).
[Crossref]

Riedle, E.

Rudenko, O. V.

U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, “Difference-frequency excitation in nonlinear optics and the conditions for Cerenkov radiation emission,” Sov. Phys. JETP 39, 633–637 (1974).

Sacks, Z.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

Shibuya, T.

T. Shibuya, K. Suizu, and K. Kawase, “Widely tunable monochromatic Cherenkov phase-matched terahertz wave generation from bulk lithium niobate,” Appl. Phys. Express 3, 082201 (2010).
[Crossref]

T. Shibuya, T. Tsutsui, K. Suizu, T. Akiba, and K. Kawase, “Efficient Cherenkov-type phase-matched widely tunable terahertz-wave generation via an optimized pump beam shape,” Appl. Phys. Express 2, 032302 (2009).
[Crossref]

K. Suizu, K. Koketsu, T. Shibuya, T. Tsutsui, T. Akiba, and K. Kawase, “Extremely frequency-widened terahertz wave generation using Cherenkov-type radiation,” Opt. Express 17, 6676–6681 (2009).
[Crossref]

Shishkin, B. V.

S. B. Bodrov, I. E. Ilyakov, B. V. Shishkin, and A. N. Stepanov, “Efficient terahertz generation by optical rectification in Si-LiNbO3-air-metal sandwich structure with variable air gap,” Appl. Phys. Lett. 100, 201114 (2012).
[Crossref]

S. B. Bodrov, A. N. Stepanov, M. I. Bakunov, B. V. Shishkin, I. E. Ilyakov, and R. A. Akhmedzhanov, “Highly efficient optical-to-terahertz conversion in a sandwich structure with LiNbO3 core,” Opt. Express 17, 1871–1879 (2009).
[Crossref]

Skrobol, C.

Small, D. L.

Smith, P. R.

B. B. Hu, X.-C. Zhang, D. H. Auston, and P. R. Smith, “Free-space radiation from electro-optics crystals,” Appl. Phys. Lett. 56, 506–508 (1990).
[Crossref]

Statz, E. R.

Stepanov, A. G.

A. G. Stepanov, J. Kuhl, I. Z. Kozma, E. Riedle, G. Almási, and J. Hebling, “Scaling up the energy of THz pulses created by optical rectification,” Opt. Express 13, 5762–5768 (2005).
[Crossref]

A. G. Stepanov, J. Hebling, and J. Kuhl, “THz generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23–26 (2005).
[Crossref]

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrasort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[Crossref]

Stepanov, A. N.

S. B. Bodrov, I. E. Ilyakov, B. V. Shishkin, and A. N. Stepanov, “Efficient terahertz generation by optical rectification in Si-LiNbO3-air-metal sandwich structure with variable air gap,” Appl. Phys. Lett. 100, 201114 (2012).
[Crossref]

S. B. Bodrov, A. N. Stepanov, M. I. Bakunov, B. V. Shishkin, I. E. Ilyakov, and R. A. Akhmedzhanov, “Highly efficient optical-to-terahertz conversion in a sandwich structure with LiNbO3 core,” Opt. Express 17, 1871–1879 (2009).
[Crossref]

Stoyanov, N. S.

Suizu, K.

T. Shibuya, K. Suizu, and K. Kawase, “Widely tunable monochromatic Cherenkov phase-matched terahertz wave generation from bulk lithium niobate,” Appl. Phys. Express 3, 082201 (2010).
[Crossref]

T. Shibuya, T. Tsutsui, K. Suizu, T. Akiba, and K. Kawase, “Efficient Cherenkov-type phase-matched widely tunable terahertz-wave generation via an optimized pump beam shape,” Appl. Phys. Express 2, 032302 (2009).
[Crossref]

K. Suizu, K. Koketsu, T. Shibuya, T. Tsutsui, T. Akiba, and K. Kawase, “Extremely frequency-widened terahertz wave generation using Cherenkov-type radiation,” Opt. Express 17, 6676–6681 (2009).
[Crossref]

Takeuchi, H.

Takeya, K.

K. Takeya, T. Minami, H. Okano, S. R. Tripathi, and K. Kawase, “Enhanced Cherenkov phase matching terahertz wave generation via a magnesium oxide doped lithium niobate ridged waveguide crystal,” APL Photon. 2, 016102 (2016).
[Crossref]

S. Fan, H. Takeuchi, T. Ouchi, K. Takeya, and K. Kawase, “Broadband terahertz wave generation from a MgO:LiNbO3 ridge waveguide pumped by a 1.5 μm femtosecond fiber laser,” Opt. Lett. 38, 1654–1656 (2013).
[Crossref]

Theuer, M.

M. Theuer, G. Torosyan, C. Rau, R. Beigang, K. Maki, C. Otani, and K. Kawase, “Efficient generation of Cherenkov-type terahertz radiation from a lithium niobate crystal with a silicon prism output coupler,” Appl. Phys. Lett. 88, 071122 (2006).
[Crossref]

Torosyan, G.

M. Theuer, G. Torosyan, C. Rau, R. Beigang, K. Maki, C. Otani, and K. Kawase, “Efficient generation of Cherenkov-type terahertz radiation from a lithium niobate crystal with a silicon prism output coupler,” Appl. Phys. Lett. 88, 071122 (2006).
[Crossref]

Tripathi, S. R.

K. Takeya, T. Minami, H. Okano, S. R. Tripathi, and K. Kawase, “Enhanced Cherenkov phase matching terahertz wave generation via a magnesium oxide doped lithium niobate ridged waveguide crystal,” APL Photon. 2, 016102 (2016).
[Crossref]

Tsarev, M. V.

M. I. Bakunov, E. A. Mashkovich, M. V. Tsarev, and S. D. Gorelov, “Efficient Cherenkov-type terahertz generation in Si-prism-LiNbO3-slab structure pumped by nanojoule-level ultrashort laser pulses,” Appl. Phys. Lett. 101, 151102 (2012).
[Crossref]

Tsutsui, T.

T. Shibuya, T. Tsutsui, K. Suizu, T. Akiba, and K. Kawase, “Efficient Cherenkov-type phase-matched widely tunable terahertz-wave generation via an optimized pump beam shape,” Appl. Phys. Express 2, 032302 (2009).
[Crossref]

K. Suizu, K. Koketsu, T. Shibuya, T. Tsutsui, T. Akiba, and K. Kawase, “Extremely frequency-widened terahertz wave generation using Cherenkov-type radiation,” Opt. Express 17, 6676–6681 (2009).
[Crossref]

Valdmanis, J. A.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

Vysloukh, V. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Wahlstrand, J. K.

J. K. Wahlstrand and R. Merlin, “Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons,” Phys. Rev. B 68, 054301 (2003).
[Crossref]

Wang, Y.

Ward, D. W.

Xu, D.

Yao, J.

Zapata, L. E.

Zelmon, D. E.

Zhang, X.-C.

B. B. Hu, X.-C. Zhang, D. H. Auston, and P. R. Smith, “Free-space radiation from electro-optics crystals,” Appl. Phys. Lett. 56, 506–508 (1990).
[Crossref]

Zhang, Z.

Zhong, K.

APL Photon. (1)

K. Takeya, T. Minami, H. Okano, S. R. Tripathi, and K. Kawase, “Enhanced Cherenkov phase matching terahertz wave generation via a magnesium oxide doped lithium niobate ridged waveguide crystal,” APL Photon. 2, 016102 (2016).
[Crossref]

Appl. Phys. B (4)

A. G. Stepanov, J. Hebling, and J. Kuhl, “THz generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23–26 (2005).
[Crossref]

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrasort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[Crossref]

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

D. Li, G. Ma, J. Ge, S. Hu, and N. Dai, “Terahertz pulse shaping via birefringence in lithium niobate crystal,” Appl. Phys. B 94, 623–628 (2009).
[Crossref]

Appl. Phys. Express (2)

T. Shibuya, T. Tsutsui, K. Suizu, T. Akiba, and K. Kawase, “Efficient Cherenkov-type phase-matched widely tunable terahertz-wave generation via an optimized pump beam shape,” Appl. Phys. Express 2, 032302 (2009).
[Crossref]

T. Shibuya, K. Suizu, and K. Kawase, “Widely tunable monochromatic Cherenkov phase-matched terahertz wave generation from bulk lithium niobate,” Appl. Phys. Express 3, 082201 (2010).
[Crossref]

Appl. Phys. Lett. (5)

D. H. Auston, “Subpicosecond electro-optic shock waves,” Appl. Phys. Lett. 43, 713–715 (1983).
[Crossref]

S. B. Bodrov, I. E. Ilyakov, B. V. Shishkin, and A. N. Stepanov, “Efficient terahertz generation by optical rectification in Si-LiNbO3-air-metal sandwich structure with variable air gap,” Appl. Phys. Lett. 100, 201114 (2012).
[Crossref]

M. I. Bakunov, E. A. Mashkovich, M. V. Tsarev, and S. D. Gorelov, “Efficient Cherenkov-type terahertz generation in Si-prism-LiNbO3-slab structure pumped by nanojoule-level ultrashort laser pulses,” Appl. Phys. Lett. 101, 151102 (2012).
[Crossref]

M. Theuer, G. Torosyan, C. Rau, R. Beigang, K. Maki, C. Otani, and K. Kawase, “Efficient generation of Cherenkov-type terahertz radiation from a lithium niobate crystal with a silicon prism output coupler,” Appl. Phys. Lett. 88, 071122 (2006).
[Crossref]

B. B. Hu, X.-C. Zhang, D. H. Auston, and P. R. Smith, “Free-space radiation from electro-optics crystals,” Appl. Phys. Lett. 56, 506–508 (1990).
[Crossref]

Dokl. Akad. Nauk SSSR (1)

P. A. Cherenkov, “Visible emission of clean liquids by action of γ radiation,” Dokl. Akad. Nauk SSSR 2, 451–454 (1934).

IEEE J. Quantum Electron. (1)

D. A. Kleinman and D. H. Auston, “Theory of electrooptic shock radiation in nonlinear optical media,” IEEE J. Quantum Electron. 20, 964–970 (1984).
[Crossref]

J. Appl. Phys. (2)

L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97, 123505 (2005).
[Crossref]

S. B. Bodrov, M. I. Bakunov, and M. Hangyo, “Efficient Cherenkov emission of broadband terahertz radiation from an ultrashort laser pulse in a sandwich structure with nonlinear core,” J. Appl. Phys. 104, 093105 (2008).
[Crossref]

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

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. B (2)

J. K. Wahlstrand and R. Merlin, “Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons,” Phys. Rev. B 68, 054301 (2003).
[Crossref]

M. I. Bakunov, S. B. Bodrov, A. V. Maslov, and M. Hangyo, “Theory of terahertz generation in a slab of electro-optic material using an ultrashort laser pulse focused to a line,” Phys. Rev. B 76, 085346 (2007).
[Crossref]

Phys. Rev. Lett. (2)

G. A. Askaryan, “Cherenkov radiation from optical pulses,” Phys. Rev. Lett. 57, 2470 (1986).
[Crossref]

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

Sov. Phys. JETP (2)

G. A. Askaryan, “Cerenkov radiation and transition radiation from electromagnetic waves,” Sov. Phys. JETP 15, 943–946 (1962).

U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, “Difference-frequency excitation in nonlinear optics and the conditions for Cerenkov radiation emission,” Sov. Phys. JETP 39, 633–637 (1974).

Other (1)

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

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Figures (7)

Fig. 1.
Fig. 1. Ultrashort laser pulse propagating as a beam focused to (a) a line and (b) a spot.
Fig. 2.
Fig. 2. 2D case of focusing to a line. (a) Snapshot of the electric field Ey(t,x,z) for a0FWHM=10μm, τFWHM=150fs, and I0=100GW/cm2. The orange region shows the laser beam. The dashed lines show the terahertz wavepaths from the laser beam to Points 1–4 at x=1mm. (b) Terahertz waveforms at Points 1–4 depicted in (a). (c) Corresponding amplitude spectra.
Fig. 3.
Fig. 3. Terahertz energy W2D (normalized to the optical pulse energy Wopt=3.4μJ/cm) as a function of a0FWHM for different τFWHM. The curves are plotted by using accurate approach with dispersion included (solid) and neglected (dashed) and in the adiabatic approximation with (stars) and without (dots) dispersion.
Fig. 4.
Fig. 4. 3D case of focusing to a spot. (a) Snapshots of the electric field Ey(t,x,z) in the planes z=0,1, and 2 mm (the laser pulse is at z=2.5mm) for a0FWHM=10μm, τFWHM=150fs, and I0=100GW/cm2. (b) Terahertz waveforms at Points 1–4 depicted in Fig. 2(a). (c) Corresponding amplitude spectra.
Fig. 5.
Fig. 5. Terahertz energy W3D (normalized to the optical pulse energy Wopt=1.1nJ) as a function of the beam width a0FWHM for different τFWHM.
Fig. 6.
Fig. 6. Schematic of the experimental setup.
Fig. 7.
Fig. 7. Experimental dependence of the terahertz energy on the focal spot size (large dots), theoretical curve for τFWHM=100fs reproduced from Fig. 5 (dashed), and modified theoretical curve (solid). Two other curves show the contributions from the terahertz absorption (dash-dotted) and terahertz beam divergence (dotted).

Tables (1)

Tables Icon

Table 1. Parameters of the Dielectric Functions ε, of LiNbO3 [29,3134]

Equations (22)

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

I(t,z,r)=I0F(ξ)G(r,z),
F(ξ)=eξ2/τ2,G(r,z)=a0mam(z)er2/a2(z),
PNL=P0F(ξ)G(r,z),
×E=1cBt,
×B=1cDt+4πcPNLt,
2E˜yz2+κl2E˜y=4πω2c2P˜NL,
P˜NL(ω,g,z)=P0F˜(ω)G˜(g,z)eiωz/V,
E˜y(ω,g,z)=2πω2iκlc2dzP˜NL(ω,g,z)eiκl|zz|.
Ey(t,x,z)=dωdgE˜y(ω,g,z)eiωtigx,
W2D=Szdxdt.
W2D=64π4zR2c2a020dω0ωε/cdgω3κlg2[P˜NL(ω,g,0)]2exp[2(κlω/V)2zR2g2a02].
w2D=π3/2(P0aτ)22cτeff3(εng2)1/2,
W2Dad=23/2π5/2zR(P0a0τ)2a0τmin2(εng2),
a0max=cτ(εng2)1/2.
W2Dad=23/2π5/2zR(P0a0τ)2a00dωωexp{ω2τmin2(ω)/2}ε(ω)ng2,
2B˜zz2+κs2B˜z=4πωgcP˜NL,
B˜z(ω,g,h,z)=2πωgiκscdzP˜NL(ω,g,h,z)eiκs|zz|.
E˜x=chωεB˜z,E˜y=ωcg(1c2h2ω2ε)B˜z,
E˜z=chigωεB˜zz,B˜x=1igB˜zz.
Bz(t,x,y,z)=dωdgdhB˜zeiωtigxihy.
W3D=Szdxdydt=64π5zR2ε1/2a02ε3/20dω0ωε/cdK02πdϕKω(κs2+g2)κs(h2+g2)×[P˜NL(ω,g,h,0)]2exp[2(κsω/V)2zR2(h2+g2)a02],
ε,=ε+(ε0ε)ωTO2ωTO2ω2+iνω,

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