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 MI TiOPO4avec MI= K, Rb et Ti,” Bull. Soc. Fr. Min. Cristallogr. 94, 437 (1971).
  2. I. Tordjman, R. Masse, and J.-C. Guitel, “Structure cristalline du monophosphate KTiO5,” Z. Kristallogr. 139, 103 (1974).
    [CrossRef]
  3. F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, “Kx Rb1−x TiOPO4: 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 μ m 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 KTiOPO4,” 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 μ m in KTP pumped at 1.064 μ m,” 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. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, “A CO2to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2laser,” Opt. Commun. 97, 29 (1993).
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    [CrossRef]
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  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:LiNbO3and KTP measured by phase-matched second harmonic generation,” IEEE J. Quantum Electron. 26, 922 (1990).
    [CrossRef]
  20. R. W. P. Drever, J. l. 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).
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  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:YALO3laser in flux grown KTiOPO4crystal,” 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-1-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, LiIO3and 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 χ(2) coefficients of KTP by SHG measurements,” J. Opt. Soc. Am. B11, 750–757 (1994).
    [CrossRef]
  36. H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “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.

1993 (2)

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, “A CO2to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2laser,” Opt. Commun. 97, 29 (1993).
[CrossRef]

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

1992 (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]

K. Asaumi, “Second harmonic generation of KTiOPO4with double refraction,” Appl. Phys. B 54, 265 (1992).
[CrossRef]

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

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

K. Kato and M. Masutani, “Widely tunable 90° phase-matched KTP parametric oscillator,” Opt. Lett. 17, 178 (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:YALO3laser in flux grown KTiOPO4crystal,” IEEE J. Quantum Electron. 28, 48 (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]

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]

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]

1991 (4)

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]

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-1-oxide,” J. Opt. Soc. Am. B 8, 1732 (1991).
[CrossRef]

K. Kato, “Parametric oscillation at 3.2 μ m in KTP pumped at 1.064 μ m,” IEEE J. Quantum Electron. 27, 1137 (1991).
[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]

1990 (3)

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:LiNbO3and KTP measured by phase-matched second harmonic generation,” IEEE J. Quantum Electron. 26, 922 (1990).
[CrossRef]

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

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

1989 (4)

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

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]

T. Nishikawa and N. Uesugi, “Angle tuning characteristics of second-harmonic generation in KTiOPO4,” Appl. Phys. Lett. 55, 1943 (1989).
[CrossRef]

1988 (3)

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]

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]

D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, “Some optical properties of KTP, LiIO3and LiNbO3,” IEEE J. Quantum Electron. 24, 2231 (1988).
[CrossRef]

1987 (2)

1985 (1)

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 (1)

R. W. P. Drever, J. l. 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 (1)

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, “Kx Rb1−x TiOPO4: a new nonlinear optical material,” J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

1974 (1)

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

1971 (1)

R. Masse and J.-C. Grenier, “Etude des monophosphates du type MI TiOPO4avec MI= K, Rb et Ti,” Bull. Soc. Fr. Min. Cristallogr. 94, 437 (1971).

1968 (1)

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

1964 (1)

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

Abed, M.

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, “A CO2to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2laser,” Opt. Commun. 97, 29 (1993).
[CrossRef]

Acef, O.

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, “A CO2to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2laser,” 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 KTiOPO4with 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. Lagendijk, “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, LiIO3and 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.

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]

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 χ(2) coefficients of KTP by SHG measurements,” J. Opt. Soc. Am. B11, 750–757 (1994).
[CrossRef]

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:LiNbO3and 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.

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 χ(2) coefficients of KTP by SHG measurements,” J. Opt. Soc. Am. B11, 750–757 (1994).
[CrossRef]

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. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, “A CO2to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2laser,” 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. l. 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:LiNbO3and 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:LiNbO3and 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.

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 χ(2) coefficients of KTP by SHG measurements,” J. Opt. Soc. Am. B11, 750–757 (1994).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. l. 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. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, “A CO2to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2laser,” 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, LiIO3and LiNbO3,” IEEE J. Quantum Electron. 24, 2231 (1988).
[CrossRef]

Gier, T. E.

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, “Kx Rb1−x TiOPO4: 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 MI TiOPO4avec MI= 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 cristalline 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. l.

R. W. P. Drever, J. l. 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, LiIO3and LiNbO3,” IEEE J. Quantum Electron. 24, 2231 (1988).
[CrossRef]

Hierle, R.

Hough, J.

R. W. P. Drever, J. l. 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:YALO3laser in flux grown KTiOPO4crystal,” 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:YALO3laser in flux grown KTiOPO4crystal,” 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:YALO3laser in flux grown KTiOPO4crystal,” IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

Josse, D.

Juncar, P.

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, “A CO2to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2laser,” 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 μ m in KTP pumped at 1.064 μ m,” 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. l. 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. Lagendijk, “Phase modulation in second-order nonlinear-optical processes,” Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

Lagendijk, A.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “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. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, “A CO2to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2laser,” 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 confocale,” Thèse 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:YALO3laser in flux grown KTiOPO4crystal,” 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, LiIO3and 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.

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]

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 χ(2) coefficients of KTP by SHG measurements,” J. Opt. Soc. Am. B11, 750–757 (1994).
[CrossRef]

Masse, R.

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

R. Masse and J.-C. Grenier, “Etude des monophosphates du type MI TiOPO4avec MI= 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:LiNbO3and 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.

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 χ(2) coefficients of KTP by SHG measurements,” J. Opt. Soc. Am. B11, 750–757 (1994).
[CrossRef]

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. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, “A CO2to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2laser,” Opt. Commun. 97, 29 (1993).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. l. 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 μ m 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 KTiOPO4,” Appl. Phys. Lett. 55, 1943 (1989).
[CrossRef]

Ohtsu, M.

W. Wang, K. Nakagawa, Y. Toda, and M. Ohtsu, “1.5 μ m 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. Lagendijk, “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. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, “A CO2to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2laser,” 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:YALO3laser in flux grown KTiOPO4crystal,” 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:YALO3laser in flux grown KTiOPO4crystal,” 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 μ m 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 cristalline du monophosphate KTiO5,” Z. Kristallogr. 139, 103 (1974).
[CrossRef]

Uesugi, N.

T. Nishikawa and N. Uesugi, “Angle tuning characteristics of second-harmonic generation in KTiOPO4,” Appl. Phys. Lett. 55, 1943 (1989).
[CrossRef]

Van Stryland, E. W.

Vanherzeele, H.

Velsko, S. P.

Wang, W.

W. Wang, K. Nakagawa, Y. Toda, and M. Ohtsu, “1.5 μ m 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. l. 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:YALO3laser in flux grown KTiOPO4crystal,” 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:YALO3laser in flux grown KTiOPO4crystal,” 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:YALO3laser in flux grown KTiOPO4crystal,” 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:YALO3laser in flux grown KTiOPO4crystal,” IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

Zondy, J.-J.

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, “A CO2to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2laser,” 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.

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]

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, “Kx Rb1−x TiOPO4: a new nonlinear optical material,” J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

Zyss, J.

Appl. Opt. (2)

Appl. Phys. B (2)

K. Asaumi, “Second harmonic generation of KTiOPO4with double refraction,” Appl. Phys. B 54, 265 (1992).
[CrossRef]

R. W. P. Drever, J. l. 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. (3)

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

W. Wang, K. Nakagawa, Y. Toda, and M. Ohtsu, “1.5 μ m 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 KTiOPO4,” Appl. Phys. Lett. 55, 1943 (1989).
[CrossRef]

Bull. Soc. Fr. Min. Cristallogr. (1)

R. Masse and J.-C. Grenier, “Etude des monophosphates du type MI TiOPO4avec MI= K, Rb et Ti,” Bull. Soc. Fr. Min. Cristallogr. 94, 437 (1971).

IEEE J. Quantum Electron. (5)

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

D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, “Some optical properties of KTP, LiIO3and LiNbO3,” IEEE J. Quantum Electron. 24, 2231 (1988).
[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:LiNbO3and 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:YALO3laser in flux grown KTiOPO4crystal,” IEEE J. Quantum Electron. 28, 48 (1992).
[CrossRef]

J. Appl. Phys. (2)

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, “Kx Rb1−x TiOPO4: a new nonlinear optical material,” J. Appl. Phys. 47, 4980 (1976).
[CrossRef]

J. Opt. Soc. Am. B (6)

Laser Focus (1)

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. (5)

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]

O. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, “A CO2to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2laser,” Opt. Commun. 97, 29 (1993).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

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

Phys. Status Solidi A (1)

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

Z. Kristallogr. (1)

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

Other (4)

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.

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 χ(2) coefficients of KTP by SHG measurements,” J. Opt. Soc. Am. B11, 750–757 (1994).
[CrossRef]

Ph. Laurent, “Stabilization en fréquence de diodes laser par couplage optique résonant sur une cavité Fabry–Pérot confocale,” Thèse 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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