Abstract

Continuous-wave type-II (oeo) second-harmonic-generation (SHG) characterization of the linear and nonlinear properties of KTiOPO4 in the mid-IR range with a InGaAsP diode laser at λ = 1.30 μm and a tunable KCl:Li color-center laser at λ = 2.53 μm are reported. With accurate phase-matching-angle measurements we have tested the accuracy of the numerous published Sellmeier data. We also discuss a birefringence-assisted noncollinear phase-matching technique as an efficient means to increase the coherence length of type-II walk-off-limited SHG. Through measurements of the angular and wavelength acceptance bandwidths and experimental analysis of the far-field second-harmonic transverse pattern, we provide an experimental test of the relevancy of the modified Boyd–Kleinman theory of the walk-off-limited type-II parametric interaction. Measured values of the d24 nonlinear susceptibility at λ = 0.65 μm (d24 = 2.45 pm/V) and λ = 1.265 μm (d24 = 2.30 pm/V) with an accuracy of 8.5% have been deduced from our conversion-efficiency measurements performed in the undepleted cw pump regime. The extrapolated value at λ = 0.532 μm (d24 = 2.58 pm/V) is found to be 30% smaller than those reported thus far from phase-matched pulsed measurements.

© 1994 Optical Society of America

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  1. R. Masse and J.-C. Grenier, "Etude des monophosphates du type MITiOPO4 avec Ml = K, Rb et Ti," Bull. Soc. Fr. Min. Cristallogr. 94, 437 (1971).
  2. I. Tordjman, R. Masse, and J.-C. Guitel, "Structure cris-talline du monophosphate KTiO5," Z. Kristallogr. 139, 103 (1974).
    [CrossRef]
  3. F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, "KxRb1.xTiOPO4: a new nonlinear optical material," J. Appl. Phys. 47, 4980 (1976).
    [CrossRef]
  4. R. F. Belt, G. Gashurov, and Y. S. Liu, "KTP as a harmonic generator for Nd:YAG lasers," Laser Focus 21(10), 110 (1985).
  5. T. Y. Fan, C. E. Huang, B. Q. Hu, R. C. Eckhardt, Y. X. Fan, R. L. Byer, and R. S. Feigelson, "Second harmonic generation and accurate index of refraction measurements in flux-grown KTiOPO4," Appl. Opt. 26, 2390 (1987).
    [CrossRef] [PubMed]
  6. H. Vanherzeele, J. D. Bierlein, and F. C. Zumsteg, "Index of refraction measurements and parametric generation in hydrothermally-grown KTiOPO4," Appl. Opt. 27, 3314 (1988).
    [CrossRef] [PubMed]
  7. W. Wang, K. Nakagawa, Y. Toda, and M. Ohtsu, "1.5 µm diode laser-based nonlinear frequency conversions by using potassium titanyl phosphate," Appl. Phys. Lett. 61, 1886 (1992).
    [CrossRef]
  8. T. Nishikawa and N. Uesugi, "Angle tuning characteristics of second-harmonic generation in KTiOPC4," Appl. Phys. Lett. 55, 1943 (1989).
    [CrossRef]
  9. D. Lee and N. C. Wong, "Tunable optical frequency division using a phase-locked optical parametric oscillator," Opt. Lett. 17, 13 (1992).
    [CrossRef] [PubMed]
  10. K. Kato, "Parametric oscillation at 3.2 µm in KTP pumped at 1.064 µm," IEEE J. Quantum Electron. 27, 1137 (1991).
    [CrossRef]
  11. K. Kato and M. Masutani, "Widely tunable 90° phase-matched KTP parametric oscillator," Opt. Lett. 17, 178 (1992).
    [CrossRef]
  12. O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gerard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
    [CrossRef]
  13. G. D. Boyd and D. A. Kleinman, "Parametric interaction of focused light beams," J. Appl. Phys. 39, 3597 (1968).
    [CrossRef]
  14. S. A. Akhmanov, A. I. Kovrygin, and A. P. Sukhorukov, "Optical harmonic generation and optical frequency multipliers," in Quantum Electronics: A Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), p. 531.
  15. S. C. Mehendale and P. K Gupta, "Effect of double refraction on type-II phase-matched second harmonic generation," Opt. Commun. 68, 301 (1988).
    [CrossRef]
  16. J.-J. Zondy, "Comparative theory of walkoff-limited type-II versus type-I second harmonic generation with Gaussian beams," Opt. Commun. 81, 427 (1991). In Eq. (3.1a) of that paper exp(-x2) should read exp(-x2/2).
    [CrossRef]
  17. K. Asaumi, "Second harmonic generation of KTiOPO4 with double refraction," Appl. Phys. B 54, 265 (1992).
    [CrossRef]
  18. H. Vanherzeele and J. D. Bierlein, "Magnitude of the nonlinear optical coefficients of KTiOPO4," Opt. Lett. 17, 982 (1992).
    [CrossRef] [PubMed]
  19. R. C. Eckhardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficient of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation," IEEE J. Quantum Electron. 26, 922 (1990).
    [CrossRef]
  20. R. W. P. Drever, J. 1. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
    [CrossRef]
  21. Ph. Laurent, "Stabilization en fréquence de diodes laser par couplage optique résonant sur une cavité Fabry-Pérot con-focale," Thése de Doctorat 3° cycle (Université de Paris-XI, Orsay, France, 1989).
  22. Ph. Laurent, A. Clairon, and Ch. Bréant, "Frequency noise analysis of optically self-locked diode lasers," IEEE J. Quantum Electron. 25, 1131 (1989).
    [CrossRef]
  23. G. Marnier and B. Boulanger, "The sphere method: a new technique in linear and non-linear crystalline optical studies," Opt. Commun. 72, 139 (1989).
    [CrossRef]
  24. H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, "Second harmonic generation and sum frequency mixing of dual wavelength Nd:YAL03 laser in flux grown KTiOPO4 crystal," IEEE J. Quantum Electron. 28, 48 (1992).
    [CrossRef]
  25. J. D. Bierlein and H. Vanherzeele, "Potassium titanyl phosphate: properties and new applications," J. Opt. Soc. Am. B 6, 622 (1989).
    [CrossRef]
  26. G. C. Bhar, U. Chatterjee, and S. Das, "A technique for the calculation of phase-matching angle for type-II non-collinear sum-frequency generation in negative uniaxial crystal," Opt. Commun. 80, 381 (1991).
    [CrossRef]
  27. S. X. Dou, D. Josse, and J. Zyss, "Noncritical properties of noncollinear phase-matched second-harmonic and sum-frequency generation in 3-methyl-4-nitropyridine-l-oxide," J. Opt. Soc. Am. B 8, 1732 (1991).
    [CrossRef]
  28. S. X. Dou, D. Josse, R. Hierle, and J. Zyss, "Comparison between noncollinear phase-matching for second-harmonic and sum-frequency generation in 3-methyl-4-nitropyridine-1-oxide," J. Opt. Soc. Am. B 9, 687 (1992).
    [CrossRef]
  29. I. Ledoux, J. Badan, J. Zyss, A. Migus, D. Hulin, J. Etchepare, G. Grillon, and A. Antonetti, "Generation of high-peak-power tunable infrared femtosecond pulses in an organic crystal: application to time resolution of weak signals," J. Opt. Soc. Am. B 4, 987 (1987).
    [CrossRef]
  30. M. S. Webb, D. Eimerl, and S. P. Velsko, "Wavelength insensitive phase-matched second-harmonic generation in partially deuterated KDP," J. Opt. Soc. Am. B 9, 1118 (1992).
    [CrossRef]
  31. J. Mangin, A. Khodjaoui, and G. Marnier, "Optical absorption of KTP single crystals," Phys. Status Solidi A 120, K111 (1990).
    [CrossRef]
  32. D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, "Some optical properties of KTP, LiIO3 and LiNbO3," IEEE J. Quantum Electron. 24, 2231 (1988).
    [CrossRef]
  33. R. Miller, "Optical second harmonic generation in piezoelectric crystals," Appl. Phys. Lett. 5, 17 (1964).
    [CrossRef]
  34. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, "Self-focusing and self-defocusing by cascaded second-order effects in KTP," Opt. Lett. 17, 28 (1992).
    [CrossRef] [PubMed]
  35. B. Boulanger, J. P. Fève, G. Marnier, B. Ménaert, and X. Cabirol, personal communication of their submitted paper, "Relative sign and absolute magnitude of the X(2) coefficients of KTP by SHG measurements," J. Opt. Soc. Am. B 11,750–757 (1994).
    [CrossRef]
  36. H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. La-gendijk, "Phase modulation in second-order nonlinear-optical processes," Phys. Rev. A 42, 4085 (1990).
    [CrossRef] [PubMed]
  37. P. Pliszka and P. P. Banerjee, "Nonlinear transverse effects in second-harmonic generation," J. Opt. Soc. Am. B 10, 1810 (1993).
    [CrossRef]
  38. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, New York, 1965), p. 18.

1994

1993

P. Pliszka and P. P. Banerjee, "Nonlinear transverse effects in second-harmonic generation," J. Opt. Soc. Am. B 10, 1810 (1993).
[CrossRef]

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gerard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

1992

W. Wang, K. Nakagawa, Y. Toda, and M. Ohtsu, "1.5 µm diode laser-based nonlinear frequency conversions by using potassium titanyl phosphate," Appl. Phys. Lett. 61, 1886 (1992).
[CrossRef]

K. Asaumi, "Second harmonic generation of KTiOPO4 with double refraction," Appl. Phys. B 54, 265 (1992).
[CrossRef]

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, "Second harmonic generation and sum frequency mixing of dual wavelength Nd:YAL03 laser in flux grown KTiOPO4 crystal," IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

K. Kato and M. Masutani, "Widely tunable 90° phase-matched KTP parametric oscillator," Opt. Lett. 17, 178 (1992).
[CrossRef]

D. Lee and N. C. Wong, "Tunable optical frequency division using a phase-locked optical parametric oscillator," Opt. Lett. 17, 13 (1992).
[CrossRef] [PubMed]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, "Self-focusing and self-defocusing by cascaded second-order effects in KTP," Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

H. Vanherzeele and J. D. Bierlein, "Magnitude of the nonlinear optical coefficients of KTiOPO4," Opt. Lett. 17, 982 (1992).
[CrossRef] [PubMed]

S. X. Dou, D. Josse, R. Hierle, and J. Zyss, "Comparison between noncollinear phase-matching for second-harmonic and sum-frequency generation in 3-methyl-4-nitropyridine-1-oxide," J. Opt. Soc. Am. B 9, 687 (1992).
[CrossRef]

M. S. Webb, D. Eimerl, and S. P. Velsko, "Wavelength insensitive phase-matched second-harmonic generation in partially deuterated KDP," J. Opt. Soc. Am. B 9, 1118 (1992).
[CrossRef]

1991

J.-J. Zondy, "Comparative theory of walkoff-limited type-II versus type-I second harmonic generation with Gaussian beams," Opt. Commun. 81, 427 (1991). In Eq. (3.1a) of that paper exp(-x2) should read exp(-x2/2).
[CrossRef]

S. X. Dou, D. Josse, and J. Zyss, "Noncritical properties of noncollinear phase-matched second-harmonic and sum-frequency generation in 3-methyl-4-nitropyridine-l-oxide," J. Opt. Soc. Am. B 8, 1732 (1991).
[CrossRef]

G. C. Bhar, U. Chatterjee, and S. Das, "A technique for the calculation of phase-matching angle for type-II non-collinear sum-frequency generation in negative uniaxial crystal," Opt. Commun. 80, 381 (1991).
[CrossRef]

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

1990

R. C. Eckhardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficient of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation," IEEE J. Quantum Electron. 26, 922 (1990).
[CrossRef]

J. Mangin, A. Khodjaoui, and G. Marnier, "Optical absorption of KTP single crystals," Phys. Status Solidi A 120, K111 (1990).
[CrossRef]

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. La-gendijk, "Phase modulation in second-order nonlinear-optical processes," Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

1989

Ph. Laurent, A. Clairon, and Ch. Bréant, "Frequency noise analysis of optically self-locked diode lasers," IEEE J. Quantum Electron. 25, 1131 (1989).
[CrossRef]

G. Marnier and B. Boulanger, "The sphere method: a new technique in linear and non-linear crystalline optical studies," Opt. Commun. 72, 139 (1989).
[CrossRef]

J. D. Bierlein and H. Vanherzeele, "Potassium titanyl phosphate: properties and new applications," J. Opt. Soc. Am. B 6, 622 (1989).
[CrossRef]

T. Nishikawa and N. Uesugi, "Angle tuning characteristics of second-harmonic generation in KTiOPC4," Appl. Phys. Lett. 55, 1943 (1989).
[CrossRef]

1988

D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, "Some optical properties of KTP, LiIO3 and LiNbO3," IEEE J. Quantum Electron. 24, 2231 (1988).
[CrossRef]

S. C. Mehendale and P. K Gupta, "Effect of double refraction on type-II phase-matched second harmonic generation," Opt. Commun. 68, 301 (1988).
[CrossRef]

H. Vanherzeele, J. D. Bierlein, and F. C. Zumsteg, "Index of refraction measurements and parametric generation in hydrothermally-grown KTiOPO4," Appl. Opt. 27, 3314 (1988).
[CrossRef] [PubMed]

1987

1985

R. F. Belt, G. Gashurov, and Y. S. Liu, "KTP as a harmonic generator for Nd:YAG lasers," Laser Focus 21(10), 110 (1985).

1983

R. W. P. Drever, J. 1. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

1976

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, "KxRb1.xTiOPO4: a new nonlinear optical material," J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

1974

I. Tordjman, R. Masse, and J.-C. Guitel, "Structure cris-talline du monophosphate KTiO5," Z. Kristallogr. 139, 103 (1974).
[CrossRef]

1971

R. Masse and J.-C. Grenier, "Etude des monophosphates du type MITiOPO4 avec Ml = K, Rb et Ti," Bull. Soc. Fr. Min. Cristallogr. 94, 437 (1971).

1968

G. D. Boyd and D. A. Kleinman, "Parametric interaction of focused light beams," J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

1964

R. Miller, "Optical second harmonic generation in piezoelectric crystals," Appl. Phys. Lett. 5, 17 (1964).
[CrossRef]

Van Stryland, E. W.

Abed, M.

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gerard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Acef, O.

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gerard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, A. I. Kovrygin, and A. P. Sukhorukov, "Optical harmonic generation and optical frequency multipliers," in Quantum Electronics: A Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), p. 531.

Antonetti, A.

Asaumi, K.

K. Asaumi, "Second harmonic generation of KTiOPO4 with double refraction," Appl. Phys. B 54, 265 (1992).
[CrossRef]

Badan, J.

Bakker, H. J.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. La-gendijk, "Phase modulation in second-order nonlinear-optical processes," Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

Banerjee, P. P.

Barnes, N. P.

D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, "Some optical properties of KTP, LiIO3 and LiNbO3," IEEE J. Quantum Electron. 24, 2231 (1988).
[CrossRef]

Belt, R. F.

R. F. Belt, G. Gashurov, and Y. S. Liu, "KTP as a harmonic generator for Nd:YAG lasers," Laser Focus 21(10), 110 (1985).

Bhar, G. C.

G. C. Bhar, U. Chatterjee, and S. Das, "A technique for the calculation of phase-matching angle for type-II non-collinear sum-frequency generation in negative uniaxial crystal," Opt. Commun. 80, 381 (1991).
[CrossRef]

Bierlein, J. D.

Boulanger, B.

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, "Parametric interaction of focused light beams," J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

Bréant, Ch.

Ph. Laurent, A. Clairon, and Ch. Bréant, "Frequency noise analysis of optically self-locked diode lasers," IEEE J. Quantum Electron. 25, 1131 (1989).
[CrossRef]

Byer, R. L.

R. C. Eckhardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficient of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation," IEEE J. Quantum Electron. 26, 922 (1990).
[CrossRef]

T. Y. Fan, C. E. Huang, B. Q. Hu, R. C. Eckhardt, Y. X. Fan, R. L. Byer, and R. S. Feigelson, "Second harmonic generation and accurate index of refraction measurements in flux-grown KTiOPO4," Appl. Opt. 26, 2390 (1987).
[CrossRef] [PubMed]

Cabirol, X.

Chatterjee, U.

G. C. Bhar, U. Chatterjee, and S. Das, "A technique for the calculation of phase-matching angle for type-II non-collinear sum-frequency generation in negative uniaxial crystal," Opt. Commun. 80, 381 (1991).
[CrossRef]

Clairon, A.

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gerard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Ph. Laurent, A. Clairon, and Ch. Bréant, "Frequency noise analysis of optically self-locked diode lasers," IEEE J. Quantum Electron. 25, 1131 (1989).
[CrossRef]

Das, S.

G. C. Bhar, U. Chatterjee, and S. Das, "A technique for the calculation of phase-matching angle for type-II non-collinear sum-frequency generation in negative uniaxial crystal," Opt. Commun. 80, 381 (1991).
[CrossRef]

DeSalvo, R.

Dou, S. X.

Drever, R. W. P.

R. W. P. Drever, J. 1. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Eckhardt, R. C.

R. C. Eckhardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficient of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation," IEEE J. Quantum Electron. 26, 922 (1990).
[CrossRef]

T. Y. Fan, C. E. Huang, B. Q. Hu, R. C. Eckhardt, Y. X. Fan, R. L. Byer, and R. S. Feigelson, "Second harmonic generation and accurate index of refraction measurements in flux-grown KTiOPO4," Appl. Opt. 26, 2390 (1987).
[CrossRef] [PubMed]

Eimerl, D.

Etchepare, J.

Fan, T. Y.

Fan, Y. X.

R. C. Eckhardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficient of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation," IEEE J. Quantum Electron. 26, 922 (1990).
[CrossRef]

T. Y. Fan, C. E. Huang, B. Q. Hu, R. C. Eckhardt, Y. X. Fan, R. L. Byer, and R. S. Feigelson, "Second harmonic generation and accurate index of refraction measurements in flux-grown KTiOPO4," Appl. Opt. 26, 2390 (1987).
[CrossRef] [PubMed]

Feigelson, R. S.

Fève, J. P.

Ford, G. M.

R. W. P. Drever, J. 1. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Gashurov, G.

R. F. Belt, G. Gashurov, and Y. S. Liu, "KTP as a harmonic generator for Nd:YAG lasers," Laser Focus 21(10), 110 (1985).

Gérard, A. H.

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gerard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Gettemy, D. J.

D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, "Some optical properties of KTP, LiIO3 and LiNbO3," IEEE J. Quantum Electron. 24, 2231 (1988).
[CrossRef]

Gier, T. E.

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, "KxRb1.xTiOPO4: a new nonlinear optical material," J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, New York, 1965), p. 18.

Grenier, J.-C.

R. Masse and J.-C. Grenier, "Etude des monophosphates du type MITiOPO4 avec Ml = K, Rb et Ti," Bull. Soc. Fr. Min. Cristallogr. 94, 437 (1971).

Grillon, G.

Guitel, J.-C.

I. Tordjman, R. Masse, and J.-C. Guitel, "Structure cris-talline du monophosphate KTiO5," Z. Kristallogr. 139, 103 (1974).
[CrossRef]

Gupta, P. K

S. C. Mehendale and P. K Gupta, "Effect of double refraction on type-II phase-matched second harmonic generation," Opt. Commun. 68, 301 (1988).
[CrossRef]

Hagan, D. J.

Hall, J. 1.

R. W. P. Drever, J. 1. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Harker, W. C.

D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, "Some optical properties of KTP, LiIO3 and LiNbO3," IEEE J. Quantum Electron. 24, 2231 (1988).
[CrossRef]

Hierle, R.

Hough, J.

R. W. P. Drever, J. 1. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Hu, B. Q.

Huang, C. E.

Huang, C. H.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, "Second harmonic generation and sum frequency mixing of dual wavelength Nd:YAL03 laser in flux grown KTiOPO4 crystal," IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

Hulin, D.

Jia, S. Q.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, "Second harmonic generation and sum frequency mixing of dual wavelength Nd:YAL03 laser in flux grown KTiOPO4 crystal," IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

Jiang, A. D.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, "Second harmonic generation and sum frequency mixing of dual wavelength Nd:YAL03 laser in flux grown KTiOPO4 crystal," IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

Josse, D.

Juncar, P.

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gerard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Kato, K.

K. Kato and M. Masutani, "Widely tunable 90° phase-matched KTP parametric oscillator," Opt. Lett. 17, 178 (1992).
[CrossRef]

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

Khodjaoui, A.

J. Mangin, A. Khodjaoui, and G. Marnier, "Optical absorption of KTP single crystals," Phys. Status Solidi A 120, K111 (1990).
[CrossRef]

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, "Parametric interaction of focused light beams," J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

Kovrygin, A. I.

S. A. Akhmanov, A. I. Kovrygin, and A. P. Sukhorukov, "Optical harmonic generation and optical frequency multipliers," in Quantum Electronics: A Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), p. 531.

Kowalski, F. V.

R. W. P. Drever, J. 1. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Kuipers, L.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. La-gendijk, "Phase modulation in second-order nonlinear-optical processes," Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

La-gendijk, A.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. La-gendijk, "Phase modulation in second-order nonlinear-optical processes," Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

Laurent, Ph.

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gerard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Ph. Laurent, A. Clairon, and Ch. Bréant, "Frequency noise analysis of optically self-locked diode lasers," IEEE J. Quantum Electron. 25, 1131 (1989).
[CrossRef]

Ph. Laurent, "Stabilization en fréquence de diodes laser par couplage optique résonant sur une cavité Fabry-Pérot con-focale," Thése de Doctorat 3° cycle (Université de Paris-XI, Orsay, France, 1989).

Ledoux, I.

Lee, D.

Lin, W. X.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, "Second harmonic generation and sum frequency mixing of dual wavelength Nd:YAL03 laser in flux grown KTiOPO4 crystal," IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

Lindholm, G.

D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, "Some optical properties of KTP, LiIO3 and LiNbO3," IEEE J. Quantum Electron. 24, 2231 (1988).
[CrossRef]

Liu, Y. S.

R. F. Belt, G. Gashurov, and Y. S. Liu, "KTP as a harmonic generator for Nd:YAG lasers," Laser Focus 21(10), 110 (1985).

Mangin, J.

J. Mangin, A. Khodjaoui, and G. Marnier, "Optical absorption of KTP single crystals," Phys. Status Solidi A 120, K111 (1990).
[CrossRef]

Marnier, G.

B. Boulanger, J. P. Fève, G. Marnier, B. Ménaert, and X. Cabirol, personal communication of their submitted paper, "Relative sign and absolute magnitude of the X(2) coefficients of KTP by SHG measurements," J. Opt. Soc. Am. B 11,750–757 (1994).
[CrossRef]

J. Mangin, A. Khodjaoui, and G. Marnier, "Optical absorption of KTP single crystals," Phys. Status Solidi A 120, K111 (1990).
[CrossRef]

G. Marnier and B. Boulanger, "The sphere method: a new technique in linear and non-linear crystalline optical studies," Opt. Commun. 72, 139 (1989).
[CrossRef]

Masse, R.

I. Tordjman, R. Masse, and J.-C. Guitel, "Structure cris-talline du monophosphate KTiO5," Z. Kristallogr. 139, 103 (1974).
[CrossRef]

R. Masse and J.-C. Grenier, "Etude des monophosphates du type MITiOPO4 avec Ml = K, Rb et Ti," Bull. Soc. Fr. Min. Cristallogr. 94, 437 (1971).

Masuda, H.

R. C. Eckhardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficient of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation," IEEE J. Quantum Electron. 26, 922 (1990).
[CrossRef]

Masutani, M.

Mehendale, S. C.

S. C. Mehendale and P. K Gupta, "Effect of double refraction on type-II phase-matched second harmonic generation," Opt. Commun. 68, 301 (1988).
[CrossRef]

Ménaert, B.

Migus, A.

Miller, R.

R. Miller, "Optical second harmonic generation in piezoelectric crystals," Appl. Phys. Lett. 5, 17 (1964).
[CrossRef]

Millerioux, Y.

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gerard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. 1. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Nakagawa, K.

W. Wang, K. Nakagawa, Y. Toda, and M. Ohtsu, "1.5 µm diode laser-based nonlinear frequency conversions by using potassium titanyl phosphate," Appl. Phys. Lett. 61, 1886 (1992).
[CrossRef]

Nishikawa, T.

T. Nishikawa and N. Uesugi, "Angle tuning characteristics of second-harmonic generation in KTiOPC4," Appl. Phys. Lett. 55, 1943 (1989).
[CrossRef]

Ohtsu, M.

W. Wang, K. Nakagawa, Y. Toda, and M. Ohtsu, "1.5 µm diode laser-based nonlinear frequency conversions by using potassium titanyl phosphate," Appl. Phys. Lett. 61, 1886 (1992).
[CrossRef]

Planken, P. C. M.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. La-gendijk, "Phase modulation in second-order nonlinear-optical processes," Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

Pliszka, P.

Rovera, D. G.

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gerard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, New York, 1965), p. 18.

Sheik-Bahae, M.

Shen, D. Z.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, "Second harmonic generation and sum frequency mixing of dual wavelength Nd:YAL03 laser in flux grown KTiOPO4 crystal," IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

Shen, H. Y.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, "Second harmonic generation and sum frequency mixing of dual wavelength Nd:YAL03 laser in flux grown KTiOPO4 crystal," IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

Stegeman, G.

Sukhorukov, A. P.

S. A. Akhmanov, A. I. Kovrygin, and A. P. Sukhorukov, "Optical harmonic generation and optical frequency multipliers," in Quantum Electronics: A Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), p. 531.

Toda, Y.

W. Wang, K. Nakagawa, Y. Toda, and M. Ohtsu, "1.5 µm diode laser-based nonlinear frequency conversions by using potassium titanyl phosphate," Appl. Phys. Lett. 61, 1886 (1992).
[CrossRef]

Tordjman, I.

I. Tordjman, R. Masse, and J.-C. Guitel, "Structure cris-talline du monophosphate KTiO5," Z. Kristallogr. 139, 103 (1974).
[CrossRef]

Uesugi, N.

T. Nishikawa and N. Uesugi, "Angle tuning characteristics of second-harmonic generation in KTiOPC4," Appl. Phys. Lett. 55, 1943 (1989).
[CrossRef]

Vanherzeele, H.

Velsko, S. P.

Wang, W.

W. Wang, K. Nakagawa, Y. Toda, and M. Ohtsu, "1.5 µm diode laser-based nonlinear frequency conversions by using potassium titanyl phosphate," Appl. Phys. Lett. 61, 1886 (1992).
[CrossRef]

Ward, H.

R. W. P. Drever, J. 1. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Webb, M. S.

Wong, N. C.

Yu, G. F.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, "Second harmonic generation and sum frequency mixing of dual wavelength Nd:YAL03 laser in flux grown KTiOPO4 crystal," IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

Zeng, R. R.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, "Second harmonic generation and sum frequency mixing of dual wavelength Nd:YAL03 laser in flux grown KTiOPO4 crystal," IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

Zeng, Z. D.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, "Second harmonic generation and sum frequency mixing of dual wavelength Nd:YAL03 laser in flux grown KTiOPO4 crystal," IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

Zhou, Y. P.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, "Second harmonic generation and sum frequency mixing of dual wavelength Nd:YAL03 laser in flux grown KTiOPO4 crystal," IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

Zondy, J.-J.

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gerard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

J.-J. Zondy, "Comparative theory of walkoff-limited type-II versus type-I second harmonic generation with Gaussian beams," Opt. Commun. 81, 427 (1991). In Eq. (3.1a) of that paper exp(-x2) should read exp(-x2/2).
[CrossRef]

Zumsteg, F. C.

Zyss, J.

Appl. Opt.

Appl. Phys. B

K. Asaumi, "Second harmonic generation of KTiOPO4 with double refraction," Appl. Phys. B 54, 265 (1992).
[CrossRef]

R. W. P. Drever, J. 1. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Appl. Phys. Lett.

W. Wang, K. Nakagawa, Y. Toda, and M. Ohtsu, "1.5 µm diode laser-based nonlinear frequency conversions by using potassium titanyl phosphate," Appl. Phys. Lett. 61, 1886 (1992).
[CrossRef]

T. Nishikawa and N. Uesugi, "Angle tuning characteristics of second-harmonic generation in KTiOPC4," Appl. Phys. Lett. 55, 1943 (1989).
[CrossRef]

R. Miller, "Optical second harmonic generation in piezoelectric crystals," Appl. Phys. Lett. 5, 17 (1964).
[CrossRef]

Bull. Soc. Fr. Min. Cristallogr.

R. Masse and J.-C. Grenier, "Etude des monophosphates du type MITiOPO4 avec Ml = K, Rb et Ti," Bull. Soc. Fr. Min. Cristallogr. 94, 437 (1971).

IEEE J. Quantum Electron.

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

R. C. Eckhardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficient of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation," IEEE J. Quantum Electron. 26, 922 (1990).
[CrossRef]

Ph. Laurent, A. Clairon, and Ch. Bréant, "Frequency noise analysis of optically self-locked diode lasers," IEEE J. Quantum Electron. 25, 1131 (1989).
[CrossRef]

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, "Second harmonic generation and sum frequency mixing of dual wavelength Nd:YAL03 laser in flux grown KTiOPO4 crystal," IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, "Some optical properties of KTP, LiIO3 and LiNbO3," IEEE J. Quantum Electron. 24, 2231 (1988).
[CrossRef]

J. Appl. Phys.

G. D. Boyd and D. A. Kleinman, "Parametric interaction of focused light beams," J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, "KxRb1.xTiOPO4: a new nonlinear optical material," J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

J. Opt. Soc. Am. B

Laser Focus

R. F. Belt, G. Gashurov, and Y. S. Liu, "KTP as a harmonic generator for Nd:YAG lasers," Laser Focus 21(10), 110 (1985).

Opt. Commun.

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gerard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

S. C. Mehendale and P. K Gupta, "Effect of double refraction on type-II phase-matched second harmonic generation," Opt. Commun. 68, 301 (1988).
[CrossRef]

J.-J. Zondy, "Comparative theory of walkoff-limited type-II versus type-I second harmonic generation with Gaussian beams," Opt. Commun. 81, 427 (1991). In Eq. (3.1a) of that paper exp(-x2) should read exp(-x2/2).
[CrossRef]

G. C. Bhar, U. Chatterjee, and S. Das, "A technique for the calculation of phase-matching angle for type-II non-collinear sum-frequency generation in negative uniaxial crystal," Opt. Commun. 80, 381 (1991).
[CrossRef]

G. Marnier and B. Boulanger, "The sphere method: a new technique in linear and non-linear crystalline optical studies," Opt. Commun. 72, 139 (1989).
[CrossRef]

Opt. Lett.

Phys. Rev. A

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. La-gendijk, "Phase modulation in second-order nonlinear-optical processes," Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

Phys. Status Solidi A

J. Mangin, A. Khodjaoui, and G. Marnier, "Optical absorption of KTP single crystals," Phys. Status Solidi A 120, K111 (1990).
[CrossRef]

Z. Kristallogr.

I. Tordjman, R. Masse, and J.-C. Guitel, "Structure cris-talline du monophosphate KTiO5," Z. Kristallogr. 139, 103 (1974).
[CrossRef]

Other

S. A. Akhmanov, A. I. Kovrygin, and A. P. Sukhorukov, "Optical harmonic generation and optical frequency multipliers," in Quantum Electronics: A Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), p. 531.

Ph. Laurent, "Stabilization en fréquence de diodes laser par couplage optique résonant sur une cavité Fabry-Pérot con-focale," Thése de Doctorat 3° cycle (Université de Paris-XI, Orsay, France, 1989).

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, New York, 1965), p. 18.

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Figures (9)

Fig. 1
Fig. 1

KCl:Li laser frequency-doubling setup. EOM, LiTaO3 electro-optic modulator, rf driven at 11 MHz. YIG, Faraday isolator; ULE, ultralow-expansion glass resonator; EOM, electro-optic modulator; L1, L2, lenses. Inset: type-II wave-vector geometry when the normal to the (∑) entrance face of the KTP crystal makes an angle i with the beam axis. The ordinary energy flows are along the corresponding wave-vector directions, while the Poynting vector Se(ω) of the fundamental e waves makes an angle ρeff (larger or smaller than ρ, depending on the algebraic value of i) with So(ω).

Fig. 2
Fig. 2

Birefringence-assisted type-II (oeo) noncollinear PM, showing the vectorial relation k1 + k2 = k3 with respect to the index surfaces. The Poynting vectors S1 and S3 of the o rays [with their electric fields along the (b) axis] are along k1 and k3. S2 is along the normal to the tangent plane (dashed) on the extraordinary index surface of the e fundamental wave and ρ = (k2, S2). Note that if the physical crystal dimension corresponds to the perpendicular surfaces (∑) and (∑′) then collinear SHG with the (∑′) facet is possible at a wavelength for which the PM angle equals θc = π/2 − θcut.

Fig. 3
Fig. 3

Comparison of the measured PM angles (circles) with published Sellmeier data for type-II SHG in the (ac) plane of KTP. The calculated curves correspond to data of Fan et al.,5 Kato,10 Shen et al.,24 and Bierlein and Vanherzeele.25

Fig. 4
Fig. 4

BANC phase-matching loci (i, θcut) at λ = 2.532 μm in the (ac) plane of KTP. The VB data (Ref. 24) were used for the computation. The various angles are defined in Fig. 2. Δi is the external angular tolerance for a crystal length lc = 6 mm.

Fig. 5
Fig. 5

Top, BANC pseudo-type-I phase-matching loci (λ, i, θcut) leading to perfect cancellation of the walk-off ρeff between the fundamental beams near 1.1 μm. The remaining walk-off ρ1–3 with the SH wave is ρ(λ)/2. θN is the type-II collinear (i = 0) phase-matching angle, with walk-off ρ(λ). Bottom, ratio of the conversion efficiencies between BANC-pseudo type-I and collinear type-II geometries. The solid curve is the internal ratios; the dashed curve is the ratios corrected for Fresnel losses that are due to oblique incidence for an uncoated crystal with lc = 10 mm. B and Beff the walk-off parameters.

Fig. 6
Fig. 6

Internal angular tuning curve for type-II-SHG in the (ac) plane of KTP at λ = 2.532 μm, showing an acceptance angle of ≈0.3°. The circles are experimental data. The dashed curve is the sinc2klc/2) unbounded plane-wave function, and the solid curve the (normalized) aperture function of Eq. (10) with λ = (αωα2ω)w0/ρ = 0.

Fig. 7
Fig. 7

Spectral acceptance tuning curve for collinear type-II-SHG in the (ac) plane of KTP (θcut = 56.6°). The filled circles are measured conversion efficiencies relative to the conversion efficiency at λ0 = 2.5545 μm. The dashed curve is again the sinc2klc/2) function, and the solid curve is obtained from Eq. (10).

Fig. 8
Fig. 8

Far-field SH beam intensity pattern at λ/2 = 1.265 μm taken 1 m away from the crystal. The circles are experimental data for the transverse section in the (ac) plane; the crossed data refer to the perpendicular section. The solid curves are obtained from fits of the data to a Gaussian pattern.

Fig. 9
Fig. 9

Conversion efficiency versus pump wavelength (lc = 6 mm, w0 = 140 μm) showing an impurity (water) absorption near 2.8 μm. Note that this absorption does not induce any anomalous dispersion. The dashed line is the Miller-rule prediction corrected for effective walk-off that is due to the oblique incidence. The solid curve is a least-squares fit to an OH Gaussian absorption profile centered at 2.8 μm. The residual absorption at 2.53 μm deduced from the fitted parameters is 0.6% cm−1.

Tables (2)

Tables Icon

Table 1 Experimentally Measured PM angles [θPM(exp)] Compared with Calculated Onesa

Tables Icon

Table 2 Nonlinear Coefficient d24 Measured by SHG at λ = 1.30 μm and λ = 2.532 μm and Related Beam Parameters and Conversion Efficienciesa

Equations (26)

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

n e - 2 ( θ 2 , ω ) = sin 2 ( θ 2 ) n c 2 ( ω ) + cos 2 ( θ 2 ) n a 2 ( ω ) ,
n b 2 ( ω ) + n e 2 ( θ 2 , ω ) + 2 n b ( ω ) n e ( θ 2 , ω ) cos ( θ 2 - θ 1 ) = [ 2 n b ( 2 ω ) ] 2 ,
sin i = n b ( ω ) sin r o = n e ( θ 2 , ω ) sin r e ,
θ PM ( i , ω ) = θ cut + r o ρ 1 - 3 = θ cut + r e ± ρ 2 - 3 ,
ρ 1 - 3 = arcos { [ 2 n b ( 2 ω ) ] 2 + n b 2 ( ω ) - n e 2 ( θ 2 , ω ) 2 [ 2 n b ( 2 ω ) ] n b ( ω ) } .
B 1 2 - B 2 2 + 2 α 2 + 2 [ ( B 1 2 - α 2 ) ( x 2 - α 2 ) ] 1 / 2 + x 2 = 0 ,
tan ρ = n e 2 ( θ 2 , ω ) 2 [ n c - 2 ( ω ) - n a - 2 ( ω ) ] sin ( 2 θ 2 ) ,
2 α ( B 1 2 - α 2 ) 1 / 2 - ( x 2 - α 2 ) 1 / 2 B 2 2 - B 1 2 - x 2 = [ ( A 1 2 - x 2 ) ( x 2 - C 1 2 ) ] 1 / 2 A 1 C 1 ,
Γ SH ( t , ) = P ( 2 ω ) / [ P ( ω ) ] 2 = K t 2 exp ( - α 2 ω l ) G ( t , ) / ρ 2 ,
G ( t , ) = π t - 2 0 t d x [ erf ( t - x 2 + λ ) - erf ( x 2 + λ ) ] × exp ( - x 2 2 ) [ cos ( x ) - x β sin ( x ) ] .
d 24 ( λ / 2 ) d 24 ( λ 0 / 2 ) = [ n b 2 ( λ / 2 ) - 1 ] [ n b 2 ( λ ) - 1 ] [ n c 2 ( λ ) - 1 ] [ n b 2 ( λ 0 / 2 ) - 1 ] [ n b 2 ( λ 0 ) - 1 ] [ n c 2 ( λ 0 ) - 1 ] ,
d M M d i = ( n 1 + n 2 ) n 2 tan ρ 2 n 3 d r 2 d i + n 1 n 2 sin ( r 1 - r 2 ) 2 n 3 ( d r 2 d i - d r 1 d i ) ,
d r 1 d i = cos i n 1 cos r 1 ,
d r 2 d i = cos i n 2 cos r 2 + n 2 tan ρ sin r 2 .
h m ( B ) = 0.27163 1 + 0.339 B + 1.0517 1 + 1.00008 B 2 - 0.25563 1 + 0.59847 B 3 ,
l opt ( B ) = 2.7517 + 0.62204 1 + 0.39218 B + 2.49362 1 + 3.2012 B 2 ;
h m ( B ) = 1.067699 1 + 3.0942 B 2 ,
l opt ( B ) = - 0.15267 + 3.0150 1 + 1.3475 B + 2.7751 1 + 3.2421 B 2 .
G ( t , ) = t - 2 0 t 0 t d y d y × [ cos ( y - y ) - y - y β sin ( y - y ) ] × exp [ - b ( y - y ) - c ( y 2 + y 2 ) - λ ( y + y ) ] .
I ( t ) = 0 t d y 0 t d y f ( y , y ) = 0 t d y F ( y , t ) .
d I d τ = 2 0 τ f ( y , τ ) d y = 2 [ I ˜ ( , τ ) + 1 β I ˜ ( , τ ) ] ,
I ˜ ( , τ ) = 0 τ d y cos ( τ - y ) exp [ - b ( τ - y ) 2 - c ( τ 2 + y 2 ) - λ ( τ + y ) ] .
H ˜ ( λ , τ , γ , ) = J ˜ + i K ˜ = 0 τ d x exp ( λ x - γ 2 x 2 - i x ) ,
2 γ 2 J ˜ ˙ = - J ˜ + λ K ˜ + sin ( τ ) × exp ( λ τ - γ 2 τ 2 ) , 2 γ 2 K ˜ ˙ = - λ J ˜ - K ˜ + cos ( τ ) × exp ( λ τ - γ 2 τ 2 ) - 1.
d I d τ = [ 2 - β ( b + c ) ] J + 2 c τ + λ β ( b + c ) K + sin τ β ( b + c ) × exp [ - ( b + c ) τ 2 - λ τ ] , d J d τ = - ( 2 b + c b + c ) ( 2 c τ + λ ) J + c b + c K + b cos τ b + c × exp [ - ( b + c ) τ 2 - λ τ ] + c b + c exp ( - 2 c τ 2 - 2 λ τ ) , d K d τ = - ( 2 b + c b + c ) ( 2 c τ + λ ) K - c b + c J - b sin τ b + c × exp [ - ( b + c ) τ 2 - λ τ ] .
H ¯ ( λ , τ , γ , ) = J + i K = exp ( - 2 c τ 2 - 2 λ τ ) × 0 τ d x exp [ - ( b + c ) x 2 + ( 2 c τ + λ ) x - i x ] .

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