Abstract

A type of phase matching for difference frequency generation with Bessel-type pump beams is proposed. In this geometry, the phase matching is achieved in a cone around the laser path by properly controlling the beam profile. An experimental case that 1.5THz generation with ~2μm lasers pumped bulk GaAs crystal is considered. Calculations of the energy conversion characteristics are performed based on a semi-analytical model. The results indicate that this configuration could relax the phase matching condition in a wide range of nonlinear crystals and pump wavelengths.

© 2016 Optical Society of America

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References

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  1. W. Shi and Y. J. Ding, “A monochromatic and high-power terahertz source tunable in the ranges of 2.7–38.4 and 58.2–3540 μm for variety of potential applications,” Appl. Phys. Lett. 84(10), 1635–1637 (2004).
    [Crossref]
  2. H. Sun, Y. J. Ding, and I. B. Zotova, “THz spectroscopy by frequency-tuning monochromatic THz source: from single species to gas mixtures,” IEEE Sens. J. 10(3), 621–629 (2010).
    [Crossref]
  3. T. Tanabe, K. Suto, J. Nishizawa, T. Kimura, and K. Saito, “Frequency-tunable high-power terahertz wave generation from GaP,” J. Appl. Phys. 93(8), 4610–4615 (2003).
    [Crossref]
  4. J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut, “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quantum Electron. 14(2), 354–362 (2008).
    [Crossref]
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    [Crossref] [PubMed]
  8. M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
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    [Crossref]
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    [Crossref]
  16. P. Liu, D. Xu, J. Li, C. Yan, Z. Li, Y. Wang, and J. Yao, “Monochromatic Cherenkov THz source pumped by a singly resonant optical parametric oscillator,” IEEE Photonics Technol. Lett. 26(5), 494–496 (2014).
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    [Crossref] [PubMed]

2014 (1)

P. Liu, D. Xu, J. Li, C. Yan, Z. Li, Y. Wang, and J. Yao, “Monochromatic Cherenkov THz source pumped by a singly resonant optical parametric oscillator,” IEEE Photonics Technol. Lett. 26(5), 494–496 (2014).
[Crossref]

2012 (3)

2010 (2)

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[Crossref]

H. Sun, Y. J. Ding, and I. B. Zotova, “THz spectroscopy by frequency-tuning monochromatic THz source: from single species to gas mixtures,” IEEE Sens. J. 10(3), 621–629 (2010).
[Crossref]

2008 (2)

J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut, “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quantum Electron. 14(2), 354–362 (2008).
[Crossref]

K. L. Vodopyanov and Y. H. Avetisyan, “Optical terahertz wave generation in a planar GaAs waveguide,” Opt. Lett. 33(20), 2314–2316 (2008).
[Crossref] [PubMed]

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(8), 085346 (2007).
[Crossref]

2004 (1)

W. Shi and Y. J. Ding, “A monochromatic and high-power terahertz source tunable in the ranges of 2.7–38.4 and 58.2–3540 μm for variety of potential applications,” Appl. Phys. Lett. 84(10), 1635–1637 (2004).
[Crossref]

2003 (1)

T. Tanabe, K. Suto, J. Nishizawa, T. Kimura, and K. Saito, “Frequency-tunable high-power terahertz wave generation from GaP,” J. Appl. Phys. 93(8), 4610–4615 (2003).
[Crossref]

2002 (1)

1999 (1)

J. Arlt, K. Dholakia, L. Allen, and M. Padgett, “Efficiency of second-harmonic generation with Bessel beams,” Phys. Rev. A 60(3), 2438–2441 (1999).
[Crossref]

1997 (1)

1993 (1)

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70(10), 1401–1404 (1993).
[Crossref] [PubMed]

1987 (1)

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. Padgett, “Efficiency of second-harmonic generation with Bessel beams,” Phys. Rev. A 60(3), 2438–2441 (1999).
[Crossref]

Arisholm, G.

Arlt, J.

J. Arlt, K. Dholakia, L. Allen, and M. Padgett, “Efficiency of second-harmonic generation with Bessel beams,” Phys. Rev. A 60(3), 2438–2441 (1999).
[Crossref]

Avetisyan, Y. H.

Bakunov, M. I.

M. I. Bakunov, M. V. Tsarev, and E. A. Mashkovich, “Terahertz difference-frequency generation by tilted amplitude front excitation,” Opt. Express 20(27), 28573–28585 (2012).
[Crossref] [PubMed]

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(8), 085346 (2007).
[Crossref]

Beaurepaire, E.

Becouarn, L.

Bliss, D.

J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut, “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quantum Electron. 14(2), 354–362 (2008).
[Crossref]

Bodrov, S. B.

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(8), 085346 (2007).
[Crossref]

DéBarre, D.

Dholakia, K.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[Crossref]

J. Arlt, K. Dholakia, L. Allen, and M. Padgett, “Efficiency of second-harmonic generation with Bessel beams,” Phys. Rev. A 60(3), 2438–2441 (1999).
[Crossref]

Ding, Y. J.

H. Sun, Y. J. Ding, and I. B. Zotova, “THz spectroscopy by frequency-tuning monochromatic THz source: from single species to gas mixtures,” IEEE Sens. J. 10(3), 621–629 (2010).
[Crossref]

W. Shi and Y. J. Ding, “A monochromatic and high-power terahertz source tunable in the ranges of 2.7–38.4 and 58.2–3540 μm for variety of potential applications,” Appl. Phys. Lett. 84(10), 1635–1637 (2004).
[Crossref]

Durnin, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Eberly, J. H.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Eyres, L. A.

Fejer, M. M.

J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut, “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quantum Electron. 14(2), 354–362 (2008).
[Crossref]

T. Skauli, K. L. Vodopyanov, T. J. Pinguet, A. Schober, O. Levi, L. A. Eyres, M. M. Fejer, J. S. Harris, B. Gerard, L. Becouarn, E. Lallier, and G. Arisholm, “Measurement of the nonlinear coefficient of orientation-patterned GaAs and demonstration of highly efficient second-harmonic generation,” Opt. Lett. 27(8), 628–630 (2002).
[Crossref] [PubMed]

Gerard, B.

Gunn-Moore, F.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[Crossref]

Hangyo, M.

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(8), 085346 (2007).
[Crossref]

Harris, J. S.

J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut, “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quantum Electron. 14(2), 354–362 (2008).
[Crossref]

T. Skauli, K. L. Vodopyanov, T. J. Pinguet, A. Schober, O. Levi, L. A. Eyres, M. M. Fejer, J. S. Harris, B. Gerard, L. Becouarn, E. Lallier, and G. Arisholm, “Measurement of the nonlinear coefficient of orientation-patterned GaAs and demonstration of highly efficient second-harmonic generation,” Opt. Lett. 27(8), 628–630 (2002).
[Crossref] [PubMed]

Herminghaus, S.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70(10), 1401–1404 (1993).
[Crossref] [PubMed]

Hurlbut, W.

J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut, “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quantum Electron. 14(2), 354–362 (2008).
[Crossref]

Jiang, H.

Kimura, T.

T. Tanabe, K. Suto, J. Nishizawa, T. Kimura, and K. Saito, “Frequency-tunable high-power terahertz wave generation from GaP,” J. Appl. Phys. 93(8), 4610–4615 (2003).
[Crossref]

Kozlov, V. G.

J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut, “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quantum Electron. 14(2), 354–362 (2008).
[Crossref]

Kuo, P. S.

J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut, “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quantum Electron. 14(2), 354–362 (2008).
[Crossref]

Lallier, E.

Levi, O.

Li, J.

P. Liu, D. Xu, J. Li, C. Yan, Z. Li, Y. Wang, and J. Yao, “Monochromatic Cherenkov THz source pumped by a singly resonant optical parametric oscillator,” IEEE Photonics Technol. Lett. 26(5), 494–496 (2014).
[Crossref]

Li, Z.

P. Liu, D. Xu, J. Li, C. Yan, Z. Li, Y. Wang, and J. Yao, “Monochromatic Cherenkov THz source pumped by a singly resonant optical parametric oscillator,” IEEE Photonics Technol. Lett. 26(5), 494–496 (2014).
[Crossref]

Lin, A.

J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut, “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quantum Electron. 14(2), 354–362 (2008).
[Crossref]

Liu, P.

P. Liu, D. Xu, J. Li, C. Yan, Z. Li, Y. Wang, and J. Yao, “Monochromatic Cherenkov THz source pumped by a singly resonant optical parametric oscillator,” IEEE Photonics Technol. Lett. 26(5), 494–496 (2014).
[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(9), 2425–2430 (2012).
[Crossref]

Lynch, C.

J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut, “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quantum Electron. 14(2), 354–362 (2008).
[Crossref]

Mahou, P.

Mashkovich, E. A.

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(8), 085346 (2007).
[Crossref]

Mazilu, M.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[Crossref]

Miceli, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Nishizawa, J.

T. Tanabe, K. Suto, J. Nishizawa, T. Kimura, and K. Saito, “Frequency-tunable high-power terahertz wave generation from GaP,” J. Appl. Phys. 93(8), 4610–4615 (2003).
[Crossref]

Olivier, N.

Padgett, M.

J. Arlt, K. Dholakia, L. Allen, and M. Padgett, “Efficiency of second-harmonic generation with Bessel beams,” Phys. Rev. A 60(3), 2438–2441 (1999).
[Crossref]

Pinguet, T. J.

Piskarskas, A. P.

Saito, K.

T. Tanabe, K. Suto, J. Nishizawa, T. Kimura, and K. Saito, “Frequency-tunable high-power terahertz wave generation from GaP,” J. Appl. Phys. 93(8), 4610–4615 (2003).
[Crossref]

Schaar, J. E.

J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut, “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quantum Electron. 14(2), 354–362 (2008).
[Crossref]

Schober, A.

Shi, W.

W. Shi and Y. J. Ding, “A monochromatic and high-power terahertz source tunable in the ranges of 2.7–38.4 and 58.2–3540 μm for variety of potential applications,” Appl. Phys. Lett. 84(10), 1635–1637 (2004).
[Crossref]

Skauli, T.

Smilgevic Ius, V.

Stabinis, A. P.

Stevenson, D. J.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[Crossref]

Sun, H.

H. Sun, Y. J. Ding, and I. B. Zotova, “THz spectroscopy by frequency-tuning monochromatic THz source: from single species to gas mixtures,” IEEE Sens. J. 10(3), 621–629 (2010).
[Crossref]

Suto, K.

T. Tanabe, K. Suto, J. Nishizawa, T. Kimura, and K. Saito, “Frequency-tunable high-power terahertz wave generation from GaP,” J. Appl. Phys. 93(8), 4610–4615 (2003).
[Crossref]

Tanabe, T.

T. Tanabe, K. Suto, J. Nishizawa, T. Kimura, and K. Saito, “Frequency-tunable high-power terahertz wave generation from GaP,” J. Appl. Phys. 93(8), 4610–4615 (2003).
[Crossref]

Tsarev, M. V.

Vodopyanov, K. L.

Wang, Y.

P. Liu, D. Xu, J. Li, C. Yan, Z. Li, Y. Wang, and J. Yao, “Monochromatic Cherenkov THz source pumped by a singly resonant optical parametric oscillator,” IEEE Photonics Technol. Lett. 26(5), 494–496 (2014).
[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(9), 2425–2430 (2012).
[Crossref]

Wulle, T.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70(10), 1401–1404 (1993).
[Crossref] [PubMed]

Xu, D.

P. Liu, D. Xu, J. Li, C. Yan, Z. Li, Y. Wang, and J. Yao, “Monochromatic Cherenkov THz source pumped by a singly resonant optical parametric oscillator,” IEEE Photonics Technol. Lett. 26(5), 494–496 (2014).
[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(9), 2425–2430 (2012).
[Crossref]

Yan, C.

P. Liu, D. Xu, J. Li, C. Yan, Z. Li, Y. Wang, and J. Yao, “Monochromatic Cherenkov THz source pumped by a singly resonant optical parametric oscillator,” IEEE Photonics Technol. Lett. 26(5), 494–496 (2014).
[Crossref]

Yao, J.

P. Liu, D. Xu, J. Li, C. Yan, Z. Li, Y. Wang, and J. Yao, “Monochromatic Cherenkov THz source pumped by a singly resonant optical parametric oscillator,” IEEE Photonics Technol. Lett. 26(5), 494–496 (2014).
[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(9), 2425–2430 (2012).
[Crossref]

Yu, X.

J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut, “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quantum Electron. 14(2), 354–362 (2008).
[Crossref]

Zhang, Z.

Zhong, K.

Zotova, I. B.

H. Sun, Y. J. Ding, and I. B. Zotova, “THz spectroscopy by frequency-tuning monochromatic THz source: from single species to gas mixtures,” IEEE Sens. J. 10(3), 621–629 (2010).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

W. Shi and Y. J. Ding, “A monochromatic and high-power terahertz source tunable in the ranges of 2.7–38.4 and 58.2–3540 μm for variety of potential applications,” Appl. Phys. Lett. 84(10), 1635–1637 (2004).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut, “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quantum Electron. 14(2), 354–362 (2008).
[Crossref]

IEEE Photonics Technol. Lett. (1)

P. Liu, D. Xu, J. Li, C. Yan, Z. Li, Y. Wang, and J. Yao, “Monochromatic Cherenkov THz source pumped by a singly resonant optical parametric oscillator,” IEEE Photonics Technol. Lett. 26(5), 494–496 (2014).
[Crossref]

IEEE Sens. J. (1)

H. Sun, Y. J. Ding, and I. B. Zotova, “THz spectroscopy by frequency-tuning monochromatic THz source: from single species to gas mixtures,” IEEE Sens. J. 10(3), 621–629 (2010).
[Crossref]

J. Appl. Phys. (1)

T. Tanabe, K. Suto, J. Nishizawa, T. Kimura, and K. Saito, “Frequency-tunable high-power terahertz wave generation from GaP,” J. Appl. Phys. 93(8), 4610–4615 (2003).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photonics Rev. 4(4), 529–547 (2010).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (1)

J. Arlt, K. Dholakia, L. Allen, and M. Padgett, “Efficiency of second-harmonic generation with Bessel beams,” Phys. Rev. A 60(3), 2438–2441 (1999).
[Crossref]

Phys. Rev. B (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(8), 085346 (2007).
[Crossref]

Phys. Rev. Lett. (2)

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[Crossref] [PubMed]

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[Crossref] [PubMed]

Other (2)

P. E. Powers, Fundamentals of Nonlinear Optics, (CRC, 2011) Chap. 10.

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Figures (4)

Fig. 1
Fig. 1 Wavevector diagram of Bessel-beam-pumped SHG and DFG.
Fig. 2
Fig. 2 Wavenumber mismatch Δk (dashed and dotted), required Bessel beam radius for type-I (solid) and type-II PM (dotted) versus the pump wavelength at 1.5THz generation (a) and the oblique angle of conic THz wavevector θ in type-I at different frequencies versus the pump wavelength (b).
Fig. 3
Fig. 3 Variation of THz intensity in radial and longitudinal directions during the process of Bessel beam pumped type-I PM DFG.
Fig. 4
Fig. 4 (a) Dynamic of energy conversion among the three waves: high-frequency pump λ1 (dashed), low-frequency pump λ2 (dotted) and THz wave (solid curve), (b) comparison between THz powers generated by type-I PM (solid), collinear non-PM (dotted) and QPM DFG (dashed curve) under the same pump condition.

Equations (5)

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E ( ρ , z , t ) J 0 ( κ ρ ) exp [ i ( β z ω t ) ]
κ I 2 = 4 k 1 2 k 2 2 ( k 1 2 + k 2 2 k T 2 ) 2 4 ( 2 k 1 2 + 2 k 2 2 k T 2 )
κ II 2 = k 1 2 ( k 1 2 + k T 2 k 2 2 2 k T ) 2
E m ( ρ , z , t ) = A m ( ρ , z ) exp [ i( β m z - ω m t ) ]
{ A T z = i 2 β T 2 A T + κ T 2 β T A T ρ α T 2 A T + i ω T d eff c n effT A 1 A 2 * A 1 z = i 2 β 1 2 A 1 + κ I 2 β 1 A 1 ρ α 1 2 A 1 + i ω 1 d eff c n eff1 A 2 A T A 2 z = i 2 β 2 2 A 2 + κ I 2 β 2 A 2 ρ α 2 2 A 2 + i ω 2 d eff c n eff2 A 1 A T *

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