Abstract

A fraction of the fundamental beam energy deposited into nonlinear crystals to generate second harmonic waves (SHW) causes a temperature gradient within the crystal. This temperature inhomogeneity can alter the refractive index of the medium leading to a well-known effect called thermal dispersion. Therefore, the generated SHW suffers from thermal lensing and a longitudinal thermal phase mismatching. In this work by coupling the heat equation with second harmonic generation (SHG) formalism applied to type-II configuration along with walk-off effect, we investigate the continuous wave (CW) SHW beam profile and conversion efficiency when a non-linear KTP crystal is under induced thermal load. We have demonstrated for average and high powers, the thermal de-phasing lead to considerable reduction in SHG compared to an ideal case in which induced heat is neglected.

© 2010 OSA

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    [CrossRef]
  8. J. Zheng, Sh. Zhao, Q. Wang, X. Zhang, and L. Chen, “Influence of thermal effect on KTP type-II phase-matching second-harmonic generation,” Opt. Commun. 199(1-4), 207–214 (2001).
    [CrossRef]
  9. M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. M. Sabaeian and H. Nadgaran, “Bessel-Gauss beams: Investigation of thermal effects on their generation,” Opt. Commun. 281(4), 672–678 (2008).
    [CrossRef]
  14. Zh. Ren, Zh. Huang, S. Jia, Y. Ge, and J. Bai, “532 nm laser based on V-type doubly resonant intra-cavity frequency-doubling,” Opt. Commun. 282(2), 263–266 (2009).
    [CrossRef]
  15. Ch. Liu, Th. Riesbeck, X. Wang, J. Ge, Zh. Xiang, J. Chen, and H. J. Eichler, “Influence of spherical aberrations on the performance of dynamically stable resonators,” Opt. Commun. 281, 5222–5228 (2008).
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    [CrossRef]
  19. R. G. Smith, “Theory of intraccavity optical second harmonic generation,” IEEE J. Quantum Electron. 6(4), 215–223 (1970).
    [CrossRef]
  20. J. D. Barry and C. J. Kennedly, “Thermooptical effects of intracavity Ba2Na(NbO3)5 on a frequency doubling NdYAG laser,” IEEE J. Quantum Electron. 11, 575–579 (1975).
    [CrossRef]
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    [CrossRef]
  24. M. Sabaeian, H. Nadgaran, and L. Mousave, “Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser,” Appl. Opt. 47(13), 2317–2325 (2008).
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    [CrossRef]
  26. D. Zhang, J. Lu, B. Feng, and J. Zhang, “Increased temperature bandwith of second harmonic generator using two KTiOPO4 crystals cut at different angles,” Opt. Commun. 281(10), 2918–2922 (2008).
    [CrossRef]
  27. Y. Bi, R. Li, Y. Feng, X. Lin, D. Cui, and Z. Xu, “Walk-off compensation of second harmonic generation in type-II phase-matched configuration with controled temperature,” Opt. Commun. 218(1-3), 183–187 (2003).
    [CrossRef]

2009

R. Peng, L. Guo, X. Zhang, F. Li, Q. Cui, Y. Bo, Q. Peng, D. Cui, Z. Xu, and L. Tang, “43 W picosecond laser and second-harmonic generation experiment,” Opt. Commun. 282(4), 611–613 (2009).
[CrossRef]

Zh. Ren, Zh. Huang, S. Jia, Y. Ge, and J. Bai, “532 nm laser based on V-type doubly resonant intra-cavity frequency-doubling,” Opt. Commun. 282(2), 263–266 (2009).
[CrossRef]

K. H. Hong, C. J. Lai, A. Siddiqui, and F. X. Kärtner, “130-W picosecond green laser based on a frequency-doubled hybrid cryogenic Yb:YAG amplifier,” Opt. Express 17(19), 16911–16919 (2009).
[CrossRef] [PubMed]

2008

M. Sabaeian, H. Nadgaran, and L. Mousave, “Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser,” Appl. Opt. 47(13), 2317–2325 (2008).
[CrossRef] [PubMed]

S. V. Tovstonog, S. Kurimura, I. Suzuki, K. Takeno, S. Moriwaki, N. Ohmae, N. Mio, and T. Katagai, “Thermal effects in high-power CW second harmonic generation in Mg-doped stoichiometric lithium tantalate,” Opt. Express 16(15), 11294–11299 (2008).
[CrossRef] [PubMed]

D. Zhang, J. Lu, B. Feng, and J. Zhang, “Increased temperature bandwith of second harmonic generator using two KTiOPO4 crystals cut at different angles,” Opt. Commun. 281(10), 2918–2922 (2008).
[CrossRef]

Ch. Liu, Th. Riesbeck, X. Wang, J. Ge, Zh. Xiang, J. Chen, and H. J. Eichler, “Influence of spherical aberrations on the performance of dynamically stable resonators,” Opt. Commun. 281, 5222–5228 (2008).
[CrossRef]

M. Sabaeian and H. Nadgaran, “Bessel-Gauss beams: Investigation of thermal effects on their generation,” Opt. Commun. 281(4), 672–678 (2008).
[CrossRef]

2007

2006

P. K. Mukhopadhyay, S. K. Sharma, K. Ranganthan, P. K. Gupta, and T. P. S. Nathan, “Efficient and high-power intracavity frequency doubled diode-side-pumped Nd:YAG/KTP continuous wave (CW) green laser,” Opt. Commun. 259(2), 805–811 (2006).
[CrossRef]

2003

Y. Bi, R. Li, Y. Feng, X. Lin, D. Cui, and Z. Xu, “Walk-off compensation of second harmonic generation in type-II phase-matched configuration with controled temperature,” Opt. Commun. 218(1-3), 183–187 (2003).
[CrossRef]

2001

J. Zheng, Sh. Zhao, Q. Wang, X. Zhang, and L. Chen, “Influence of thermal effect on KTP type-II phase-matching second-harmonic generation,” Opt. Commun. 199(1-4), 207–214 (2001).
[CrossRef]

1997

S. Seidel and G. Mann, “Numerical modeling of thermal effects in nonlinear crystal for high power second harmonic generation,” Proc. SPIE 2989, 204–214 (1997).
[CrossRef]

1992

K. Asaumi, “Second-Harmonic Power of KTiOPO4 with Double Refraction,” Appl. Phys. B 54(4), 265–270 (1992).
[CrossRef]

1991

K. Kato, “Parametric oscillation at 3.2 μm in KTP pumped at 1.064 μm,” IEEE J. Quantum Electron. 27(5), 1137–1140 (1991).
[CrossRef]

1990

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[CrossRef]

1989

1987

D. Eimerl, “High Average Power Harmonic Generation,” IEEE J. Quantum Electron. 23(5), 575–592 (1987).
[CrossRef]

1980

D. T. Hon and H. Bruesselabach, “Beam Shaping to Suppress Phase Mismatch in High Power Second-Harmonic Generation,” IEEE J. Quantum Electron. 16(12), 1356–1364 (1980).
[CrossRef]

1976

D. T. Hon, “Electro-optical compensation for self-heating in CD*A during second-harmonic generation,” IEEE J. Quantum Electron. 12(2), 148–151 (1976).
[CrossRef]

1975

J. D. Barry and C. J. Kennedy, “Thermo-optical effects of intracavity Ba2Na(NbO3) on a frequency-doubled Nd:YAG laser,” IEEE J. Quantum Electron. 11, 575–579 (1975).
[CrossRef]

J. D. Barry and C. J. Kennedly, “Thermooptical effects of intracavity Ba2Na(NbO3)5 on a frequency doubling NdYAG laser,” IEEE J. Quantum Electron. 11, 575–579 (1975).
[CrossRef]

1971

M. Okada and S. Ieiri, “Influence of self-induced thermal effects on second harmonic generation,” IEEE J. Quantum Electron. 7(9), 469–470 (1971).
[CrossRef]

1970

R. G. Smith, “Theory of intraccavity optical second harmonic generation,” IEEE J. Quantum Electron. 6(4), 215–223 (1970).
[CrossRef]

1962

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in nonlinear medium,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in nonlinear medium,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Asaumi, K.

K. Asaumi, “Second-Harmonic Power of KTiOPO4 with Double Refraction,” Appl. Phys. B 54(4), 265–270 (1992).
[CrossRef]

Bai, J.

Zh. Ren, Zh. Huang, S. Jia, Y. Ge, and J. Bai, “532 nm laser based on V-type doubly resonant intra-cavity frequency-doubling,” Opt. Commun. 282(2), 263–266 (2009).
[CrossRef]

Barry, J. D.

J. D. Barry and C. J. Kennedy, “Thermo-optical effects of intracavity Ba2Na(NbO3) on a frequency-doubled Nd:YAG laser,” IEEE J. Quantum Electron. 11, 575–579 (1975).
[CrossRef]

J. D. Barry and C. J. Kennedly, “Thermooptical effects of intracavity Ba2Na(NbO3)5 on a frequency doubling NdYAG laser,” IEEE J. Quantum Electron. 11, 575–579 (1975).
[CrossRef]

Bi, Y.

Y. Bi, R. Li, Y. Feng, X. Lin, D. Cui, and Z. Xu, “Walk-off compensation of second harmonic generation in type-II phase-matched configuration with controled temperature,” Opt. Commun. 218(1-3), 183–187 (2003).
[CrossRef]

Bierlein, J. D.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in nonlinear medium,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Bo, Y.

R. Peng, L. Guo, X. Zhang, F. Li, Q. Cui, Y. Bo, Q. Peng, D. Cui, Z. Xu, and L. Tang, “43 W picosecond laser and second-harmonic generation experiment,” Opt. Commun. 282(4), 611–613 (2009).
[CrossRef]

Bruesselabach, H.

D. T. Hon and H. Bruesselabach, “Beam Shaping to Suppress Phase Mismatch in High Power Second-Harmonic Generation,” IEEE J. Quantum Electron. 16(12), 1356–1364 (1980).
[CrossRef]

Bu, Y. K.

Chen, J.

Ch. Liu, Th. Riesbeck, X. Wang, J. Ge, Zh. Xiang, J. Chen, and H. J. Eichler, “Influence of spherical aberrations on the performance of dynamically stable resonators,” Opt. Commun. 281, 5222–5228 (2008).
[CrossRef]

Chen, L.

J. Zheng, Sh. Zhao, Q. Wang, X. Zhang, and L. Chen, “Influence of thermal effect on KTP type-II phase-matching second-harmonic generation,” Opt. Commun. 199(1-4), 207–214 (2001).
[CrossRef]

Cui, D.

R. Peng, L. Guo, X. Zhang, F. Li, Q. Cui, Y. Bo, Q. Peng, D. Cui, Z. Xu, and L. Tang, “43 W picosecond laser and second-harmonic generation experiment,” Opt. Commun. 282(4), 611–613 (2009).
[CrossRef]

Y. Bi, R. Li, Y. Feng, X. Lin, D. Cui, and Z. Xu, “Walk-off compensation of second harmonic generation in type-II phase-matched configuration with controled temperature,” Opt. Commun. 218(1-3), 183–187 (2003).
[CrossRef]

Cui, Q.

R. Peng, L. Guo, X. Zhang, F. Li, Q. Cui, Y. Bo, Q. Peng, D. Cui, Z. Xu, and L. Tang, “43 W picosecond laser and second-harmonic generation experiment,” Opt. Commun. 282(4), 611–613 (2009).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in nonlinear medium,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Eichler, H. J.

Ch. Liu, Th. Riesbeck, X. Wang, J. Ge, Zh. Xiang, J. Chen, and H. J. Eichler, “Influence of spherical aberrations on the performance of dynamically stable resonators,” Opt. Commun. 281, 5222–5228 (2008).
[CrossRef]

Eimerl, D.

D. Eimerl, “High Average Power Harmonic Generation,” IEEE J. Quantum Electron. 23(5), 575–592 (1987).
[CrossRef]

Feng, B.

D. Zhang, J. Lu, B. Feng, and J. Zhang, “Increased temperature bandwith of second harmonic generator using two KTiOPO4 crystals cut at different angles,” Opt. Commun. 281(10), 2918–2922 (2008).
[CrossRef]

Feng, Y.

Y. Bi, R. Li, Y. Feng, X. Lin, D. Cui, and Z. Xu, “Walk-off compensation of second harmonic generation in type-II phase-matched configuration with controled temperature,” Opt. Commun. 218(1-3), 183–187 (2003).
[CrossRef]

Fields, R. A.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[CrossRef]

Fincher, C. L.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[CrossRef]

Ge, J.

Ch. Liu, Th. Riesbeck, X. Wang, J. Ge, Zh. Xiang, J. Chen, and H. J. Eichler, “Influence of spherical aberrations on the performance of dynamically stable resonators,” Opt. Commun. 281, 5222–5228 (2008).
[CrossRef]

Ge, Y.

Zh. Ren, Zh. Huang, S. Jia, Y. Ge, and J. Bai, “532 nm laser based on V-type doubly resonant intra-cavity frequency-doubling,” Opt. Commun. 282(2), 263–266 (2009).
[CrossRef]

Guo, L.

R. Peng, L. Guo, X. Zhang, F. Li, Q. Cui, Y. Bo, Q. Peng, D. Cui, Z. Xu, and L. Tang, “43 W picosecond laser and second-harmonic generation experiment,” Opt. Commun. 282(4), 611–613 (2009).
[CrossRef]

Gupta, P. K.

P. K. Mukhopadhyay, S. K. Sharma, K. Ranganthan, P. K. Gupta, and T. P. S. Nathan, “Efficient and high-power intracavity frequency doubled diode-side-pumped Nd:YAG/KTP continuous wave (CW) green laser,” Opt. Commun. 259(2), 805–811 (2006).
[CrossRef]

Hon, D. T.

D. T. Hon and H. Bruesselabach, “Beam Shaping to Suppress Phase Mismatch in High Power Second-Harmonic Generation,” IEEE J. Quantum Electron. 16(12), 1356–1364 (1980).
[CrossRef]

D. T. Hon, “Electro-optical compensation for self-heating in CD*A during second-harmonic generation,” IEEE J. Quantum Electron. 12(2), 148–151 (1976).
[CrossRef]

Hong, K. H.

Huang, Zh.

Zh. Ren, Zh. Huang, S. Jia, Y. Ge, and J. Bai, “532 nm laser based on V-type doubly resonant intra-cavity frequency-doubling,” Opt. Commun. 282(2), 263–266 (2009).
[CrossRef]

Ieiri, S.

M. Okada and S. Ieiri, “Influence of self-induced thermal effects on second harmonic generation,” IEEE J. Quantum Electron. 7(9), 469–470 (1971).
[CrossRef]

Innocenzi, M. E.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[CrossRef]

Jia, F. Q.

Jia, S.

Zh. Ren, Zh. Huang, S. Jia, Y. Ge, and J. Bai, “532 nm laser based on V-type doubly resonant intra-cavity frequency-doubling,” Opt. Commun. 282(2), 263–266 (2009).
[CrossRef]

Kärtner, F. X.

Katagai, T.

Kato, K.

K. Kato, “Parametric oscillation at 3.2 μm in KTP pumped at 1.064 μm,” IEEE J. Quantum Electron. 27(5), 1137–1140 (1991).
[CrossRef]

Kennedly, C. J.

J. D. Barry and C. J. Kennedly, “Thermooptical effects of intracavity Ba2Na(NbO3)5 on a frequency doubling NdYAG laser,” IEEE J. Quantum Electron. 11, 575–579 (1975).
[CrossRef]

Kennedy, C. J.

J. D. Barry and C. J. Kennedy, “Thermo-optical effects of intracavity Ba2Na(NbO3) on a frequency-doubled Nd:YAG laser,” IEEE J. Quantum Electron. 11, 575–579 (1975).
[CrossRef]

Kurimura, S.

Lai, C. J.

Li, F.

R. Peng, L. Guo, X. Zhang, F. Li, Q. Cui, Y. Bo, Q. Peng, D. Cui, Z. Xu, and L. Tang, “43 W picosecond laser and second-harmonic generation experiment,” Opt. Commun. 282(4), 611–613 (2009).
[CrossRef]

Li, R.

Y. Bi, R. Li, Y. Feng, X. Lin, D. Cui, and Z. Xu, “Walk-off compensation of second harmonic generation in type-II phase-matched configuration with controled temperature,” Opt. Commun. 218(1-3), 183–187 (2003).
[CrossRef]

Lin, X.

Y. Bi, R. Li, Y. Feng, X. Lin, D. Cui, and Z. Xu, “Walk-off compensation of second harmonic generation in type-II phase-matched configuration with controled temperature,” Opt. Commun. 218(1-3), 183–187 (2003).
[CrossRef]

Liu, Ch.

Ch. Liu, Th. Riesbeck, X. Wang, J. Ge, Zh. Xiang, J. Chen, and H. J. Eichler, “Influence of spherical aberrations on the performance of dynamically stable resonators,” Opt. Commun. 281, 5222–5228 (2008).
[CrossRef]

Lu, J.

D. Zhang, J. Lu, B. Feng, and J. Zhang, “Increased temperature bandwith of second harmonic generator using two KTiOPO4 crystals cut at different angles,” Opt. Commun. 281(10), 2918–2922 (2008).
[CrossRef]

Mann, G.

S. Seidel and G. Mann, “Numerical modeling of thermal effects in nonlinear crystal for high power second harmonic generation,” Proc. SPIE 2989, 204–214 (1997).
[CrossRef]

Mio, N.

Moriwaki, S.

Mousave, L.

Mukhopadhyay, P. K.

P. K. Mukhopadhyay, S. K. Sharma, K. Ranganthan, P. K. Gupta, and T. P. S. Nathan, “Efficient and high-power intracavity frequency doubled diode-side-pumped Nd:YAG/KTP continuous wave (CW) green laser,” Opt. Commun. 259(2), 805–811 (2006).
[CrossRef]

Nadgaran, H.

M. Sabaeian, H. Nadgaran, and L. Mousave, “Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser,” Appl. Opt. 47(13), 2317–2325 (2008).
[CrossRef] [PubMed]

M. Sabaeian and H. Nadgaran, “Bessel-Gauss beams: Investigation of thermal effects on their generation,” Opt. Commun. 281(4), 672–678 (2008).
[CrossRef]

Nathan, T. P. S.

P. K. Mukhopadhyay, S. K. Sharma, K. Ranganthan, P. K. Gupta, and T. P. S. Nathan, “Efficient and high-power intracavity frequency doubled diode-side-pumped Nd:YAG/KTP continuous wave (CW) green laser,” Opt. Commun. 259(2), 805–811 (2006).
[CrossRef]

Ohmae, N.

Okada, M.

M. Okada and S. Ieiri, “Influence of self-induced thermal effects on second harmonic generation,” IEEE J. Quantum Electron. 7(9), 469–470 (1971).
[CrossRef]

Peng, Q.

R. Peng, L. Guo, X. Zhang, F. Li, Q. Cui, Y. Bo, Q. Peng, D. Cui, Z. Xu, and L. Tang, “43 W picosecond laser and second-harmonic generation experiment,” Opt. Commun. 282(4), 611–613 (2009).
[CrossRef]

Peng, R.

R. Peng, L. Guo, X. Zhang, F. Li, Q. Cui, Y. Bo, Q. Peng, D. Cui, Z. Xu, and L. Tang, “43 W picosecond laser and second-harmonic generation experiment,” Opt. Commun. 282(4), 611–613 (2009).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in nonlinear medium,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Qian, L. S.

Ranganthan, K.

P. K. Mukhopadhyay, S. K. Sharma, K. Ranganthan, P. K. Gupta, and T. P. S. Nathan, “Efficient and high-power intracavity frequency doubled diode-side-pumped Nd:YAG/KTP continuous wave (CW) green laser,” Opt. Commun. 259(2), 805–811 (2006).
[CrossRef]

Ren, Zh.

Zh. Ren, Zh. Huang, S. Jia, Y. Ge, and J. Bai, “532 nm laser based on V-type doubly resonant intra-cavity frequency-doubling,” Opt. Commun. 282(2), 263–266 (2009).
[CrossRef]

Riesbeck, Th.

Ch. Liu, Th. Riesbeck, X. Wang, J. Ge, Zh. Xiang, J. Chen, and H. J. Eichler, “Influence of spherical aberrations on the performance of dynamically stable resonators,” Opt. Commun. 281, 5222–5228 (2008).
[CrossRef]

Sabaeian, M.

M. Sabaeian and H. Nadgaran, “Bessel-Gauss beams: Investigation of thermal effects on their generation,” Opt. Commun. 281(4), 672–678 (2008).
[CrossRef]

M. Sabaeian, H. Nadgaran, and L. Mousave, “Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser,” Appl. Opt. 47(13), 2317–2325 (2008).
[CrossRef] [PubMed]

Seidel, S.

S. Seidel and G. Mann, “Numerical modeling of thermal effects in nonlinear crystal for high power second harmonic generation,” Proc. SPIE 2989, 204–214 (1997).
[CrossRef]

Sharma, S. K.

P. K. Mukhopadhyay, S. K. Sharma, K. Ranganthan, P. K. Gupta, and T. P. S. Nathan, “Efficient and high-power intracavity frequency doubled diode-side-pumped Nd:YAG/KTP continuous wave (CW) green laser,” Opt. Commun. 259(2), 805–811 (2006).
[CrossRef]

Siddiqui, A.

Smith, R. G.

R. G. Smith, “Theory of intraccavity optical second harmonic generation,” IEEE J. Quantum Electron. 6(4), 215–223 (1970).
[CrossRef]

Suzuki, I.

Takeno, K.

Tang, L.

R. Peng, L. Guo, X. Zhang, F. Li, Q. Cui, Y. Bo, Q. Peng, D. Cui, Z. Xu, and L. Tang, “43 W picosecond laser and second-harmonic generation experiment,” Opt. Commun. 282(4), 611–613 (2009).
[CrossRef]

Tovstonog, S. V.

Vanherzeele, H.

Wang, Q.

J. Zheng, Sh. Zhao, Q. Wang, X. Zhang, and L. Chen, “Influence of thermal effect on KTP type-II phase-matching second-harmonic generation,” Opt. Commun. 199(1-4), 207–214 (2001).
[CrossRef]

Wang, X.

Ch. Liu, Th. Riesbeck, X. Wang, J. Ge, Zh. Xiang, J. Chen, and H. J. Eichler, “Influence of spherical aberrations on the performance of dynamically stable resonators,” Opt. Commun. 281, 5222–5228 (2008).
[CrossRef]

Xiang, Zh.

Ch. Liu, Th. Riesbeck, X. Wang, J. Ge, Zh. Xiang, J. Chen, and H. J. Eichler, “Influence of spherical aberrations on the performance of dynamically stable resonators,” Opt. Commun. 281, 5222–5228 (2008).
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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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J. Zheng, Sh. Zhao, Q. Wang, X. Zhang, and L. Chen, “Influence of thermal effect on KTP type-II phase-matching second-harmonic generation,” Opt. Commun. 199(1-4), 207–214 (2001).
[CrossRef]

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J. Zheng, Sh. Zhao, Q. Wang, X. Zhang, and L. Chen, “Influence of thermal effect on KTP type-II phase-matching second-harmonic generation,” Opt. Commun. 199(1-4), 207–214 (2001).
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[CrossRef]

J. Zheng, Sh. Zhao, Q. Wang, X. Zhang, and L. Chen, “Influence of thermal effect on KTP type-II phase-matching second-harmonic generation,” Opt. Commun. 199(1-4), 207–214 (2001).
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Figures (8)

Fig. 1
Fig. 1

(a) The entrance face of KTP crystal showing the coincidence of the two components of FW electric field to ordinary and extraordinary components of fundamental wave at frequency ω. (b) KTP exit face with extraordinary component of SHW at frequency 2ω. (c) The relation between crystallographic axes XYZ and optical beam axes xyz within XY crystallographic plane [17].

Fig. 2
Fig. 2

The thermal phase mismatching versus x at y = 0 and z = c/2 for ωF = 0.2 mm (a) and ωF = 0.3 mm (b).

Fig. 3
Fig. 3

The thermal phase mismatching versus z along the crystal axis (x = 0, y = 0) for ωF = 0.1 mm (a), ωF = 0.2 mm (b) and ωF = = 0.2 mm (c) for various powers of fundamental wave.

Fig. 4
Fig. 4

Variation of η3 versus z for ωF = 0.1mm (a), ωF = 0.2mm (b) and ωF = 0.3mm (c) when thermal effects exist for various powers of fundamental wave. Efficiency of SHG for ωF = 0.2mm for non-thermal case (d).

Fig. 5
Fig. 5

The maximum efficiency of SHG (η3) versus the total input power for three fundamental beam spot sizes for thermal case (a) and non-thermal case (b).

Fig. 6
Fig. 6

The profiles of η 3 at the exit face of the crystal versus x for thermal case for ωF = 0.2mm (a), ωF = 0.3mm (b) and for non-thermal case for ωF = 0.2mm (c) for various total fundamental powers.

Fig. 7
Fig. 7

Profiles of temperature change along x at y = 0 and z = c/2 for ωF = 0.2mm (a), ωF = 0.3mm (b).

Fig. 8
Fig. 8

Temperature change versus z along the crystal axis (x = 0 and y = 0) for ωF = 0.2mm (a), ωF = 0.3mm (b) for various fundamental powers.

Equations (36)

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E o , ω ( x , y , z ) = E 0 o , ω exp [ ( x + ρ 2 z ) 2 + y 2 ω F 2 ] ,
E e , ω ( x , y , z ) = E 0 e , ω exp [ ( x + ρ 3 z ) 2 + y 2 ω F 2 ] ,
d E o , ω d z + γ 1 2 E o , ω = 2 i ω d eff ε 0 n o ω c E e , 2 ω E * e , ω ,
d E e , ω d z + γ 2 2 E e , ω = 2 i ω d eff ε 0 n e ω c E e , 2 ω E * o , ω ,
d E e , 2 ω d z + γ 3 2 E e , 2 ω = 4 i ω d eff ε 0 n e 2 ω c E o , ω E e , ω ,
E 0 o , ω ( x , y , z = 0 ) = 2 P o c / n o ω ε 0 π ω F 2 ,
E 0 e , ω ( x , y , z = 0 ) = 2 P e c / n e ω ε 0 π ω F 2 ,
E e , 2 ω ( x , y , z = 0 ) = 0.
2 T ( x , y , z ) = S ( x , y , z ) / K ,
K T ( x , y , z ) z | z = 0 = h [ T ( x , y , z = 0 ) T 0 ] ,
K T ( x , y , z ) z | z = c = h [ T ( x , y , z = c ) T 0 ] ,
T ( x = 0 , y , z ) T 0 = T ( x = a , y , z ) T 0 = 0 ,
T ( x , y = 0 , z ) T 0 = T ( x , y = b , z ) T 0 = 0 ,
S = 1 2 c ε 0 [ γ 1 n o ω | E 0 o , ω | 2 e 2 [ ( x + ρ 2 z ) 2 + y 2 ] / ω F 2 + γ 2 n e ω | E 0 e , ω | 2 e 2 [ ( x + ρ 3 z ) 2 + y 2 ] / ω F 2 + γ 3 n e 2 ω | E e , 2 ω | 2 ] ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​     .
n x 2 ( λ , T 0 ) = 3.0065 + 0.03901 λ 2 0.04251 0.01327 λ 2 ,
n y 2 ( λ , T 0 ) = 3.0333 + 0.04154 λ 2 0.04547 0.01408 λ 2 ,
n z 2 ( λ , T 0 ) = 3.3134 + 0.05694 λ 2 0.05658 0.01682 λ 2 ,
n x ( λ , T ) = n x ( λ , T 0 ) + d n x d T ( T T 0 ) ,
n y ( λ , T ) = n y ( λ , T 0 ) + d n y d T ( T T 0 ) ,
n z ( λ , T ) = n z ( λ , T 0 ) + d n z d T ( T T 0 ) ,
d n x d T = ( 0.1323 λ 3 0.4385 λ 2 + 1.2307 λ 1 + 0.7709 ) × 10 5 ( C 1 ) ,
d n y d T = ( 0.5014 λ 3 2.0030 λ 2 + 3.3016 λ 1 + 0.7498 ) × 10 5 ( C 1 ) ,
d n z d T = ( 0.3896 λ 3 1.3332 λ 2 + 2.2762 λ 1 + 2.1151 ) × 10 5 ( C 1 ) .
n = 2 B ± B 2 4 C ,
B = sin 2 θ cos 2 ϕ ( b + c ) sin 2 θ sin 2 ϕ ( a + c ) cos 2 θ ( a + b ) ,
C = sin 2 θ cos 2 ϕ     b c + sin 2 θ sin 2 ϕ a c + cos 2 θ a b ,
a = n x 2 ,     b = n y 2 ,     c = n z 2 .
Δ Φ = 2 π λ 1 0 z [ n e ω ( T ) n e ω ( T 0 ) ] d z + 2 π λ 1 0 z [ n o ω ( T ) n o ω ( T 0 ) ] d z 2 π λ 2 0 z [ n e 2 ω ( T ) n e 2 ω ( T 0 ) ] d z ,
ψ 1 = I o , ω ( x , y , z ) I 0 o , ω ( x , y , z = 0 ) = E 0 o , ω ( x , y , z ) 2 P / n o ω c ε 0 π ω F 2 ,
ψ 2 = I e , ω ( x , y , z ) I 0 e , ω ( x , y , z = 0 ) = E 0 e , ω ( x , y , z ) 2 P / n e ω c ε 0 π ω F 2 ,
ψ 3 = I e , 2 ω ( x , y , z ) 2 I 0 o ( e ) ( x , y , z = 0 ) = E e , 2 ω ( x , y , z ) 4 P / n e 2 ω c ε 0 π ω F 2 .
d ψ 1 d z + ψ 1 [ γ 1 2 2 ρ 2 ( x + ρ 2 z ) ω F 2 ] = 2 n 1 n 2 n 3 i l ψ 3 ψ 2 * e [ ( x + ρ 2 z ) 2 + y 2 ] / ω F 2 e [ ( x + ρ 3 z ) 2 + y 2 ] / ω F 2 e i Δ Φ ,
d ψ 2 d z + ψ 2 [ γ 2 2 2 ρ 3 ( x + ρ 3 z ) ω F 2 ] = 2 n 1 n 2 n 3 i l ψ 3 ψ 1 * e [ ( x + ρ 2 z ) 2 + y 2 ] / ω F 2 e [ ( x + ρ 3 z ) 2 + y 2 ] / ω F 2 e i Δ Φ ,
d ψ 3 d z + γ 3 2 ψ 3 = 2 n 1 n 2 n 3 i l ψ 1 ψ 2 e [ ( x + ρ 2 z ) 2 + y 2 ] / ω F 2 e [ ( x + ρ 3 z ) 2 + y 2 ] / ω F 2 e i Δ Φ ,
d 2 T d x 2 + d 2 T d y 2 + d 2 T d z 2 = P π ω F 2 K ( γ 1 | ψ 1 | 2 e 2 [ ( x + ρ 2 z ) 2 + y 2 ] / ω F 2 + γ 2 | ψ 2 | 2 e 2 [ ( x + ρ 3 z ) 2 + y 2 ] / ω F 2 + γ 3 | ψ 3 | 2 )         ,
Δ Φ = 2 π λ 1 0 z [ Δ n 1 ( T ) + Δ n 2 ( T ) 2 Δ n 3 ( T ) ] d z ,

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