Abstract

We determine within an accuracy of 10% the absolute magnitude of the quadratic effective coefficients of types I and II phase-matched second-harmonic generation from conversion efficiency measurements in a single nonlinear crystal cut as a sphere. The agreement is good with measurements performed in thin parallelepipedal samples. The material studied is KTiOPO4, for which improved Sellmeier equations are given.

© 1997 Optical Society of America

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References

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  1. F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, “KxRb1−xTiOPO4: a new nonlinear optical material,” J. Appl. Phys. 47, 4980–4985 (1976).
    [CrossRef]
  2. R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
    [CrossRef]
  3. B. Boulanger, J. P. Fève, G. Marnier, B. Ménaert, X. Cabirol, P. Villeval, and C. Bonnin, “Relative sign and absolute magnitude of d(2) nonlinear coefficients of KTP from second-harmonic-generation measurements,” J. Opt. Soc. Am. B 11, 750–757 (1994).
    [CrossRef]
  4. E. C. Cheung, K. Koch, G. T. Moore, and J. M. Liu, “Measurement of second-order nonlinear optical coefficients from spectral brightness of parametric fluorescence,” Opt. Lett. 19, 168–170 (1994).
    [CrossRef]
  5. S. X. Dou, M. H. Jiang, Z. S. Shao, and X. T. Tao, “Maker fringes in biaxial crystals and the nonlinear optical coefficients of thiosemicarbazide cadmium chloride monohydrate,” Appl. Phys. Lett. 54, 1101–1103 (1989).
    [CrossRef]
  6. J. W. Perry, in Materials for Nonlinear Optics, Chemical Perspectives, S. R. Marder, J. E. Sohn, and G. D. Stucky, eds., ACS Symp. Ser. 455 (1991), Chap. 4.
    [CrossRef]
  7. R. C. Eckardt and R. L. Byer, “Measurement of nonlinear optical coefficients by phase-matched harmonic generation,” in Inorganic Crystals for Optics, Electro-Optics, and Frequency Conversion, P. F. Bordui, ed., Proc. SPIE 1561, 119–127 (1991).
    [CrossRef]
  8. S. P. Velsko, “Direct measurements of phase-matching properties in small crystals of new nonlinear materials,” Opt. Eng. 28, 76–84 (1989).
    [CrossRef]
  9. G. Marnier and B. Boulanger, “The sphere method: a new technique in linear and nonlinear crystalline optical studies,” Opt. Commun. 72, 139–143 (1989).
    [CrossRef]
  10. J. J. Zondy, “Comparative theory of walk-off limited type II versus type I second harmonic generation with Gaussian beams,” Opt. Commun. 81, 427–440 (1991).
    [CrossRef]
  11. J. J. Zondy, M. Abed, and A. Clairon, “Type II frequency doubling at λ=1.30 μm and λ=2.53 μm in flux-grown potassium titanyl phosphate,” J. Opt. Soc. Am. B 11, 2004–2015 (1994).
    [CrossRef]
  12. G. Marnier, “Process for the flux synthesis of crystals of the KTiOPO4, potassium titanyl monophosphate type,” U.S. patent 4, 746, 396 (May 24, 1988).
  13. B. Boulanger, “Synthèse en flux et étude des propriétés optiques cristallines linéaires et non linéaires par la méthode de la sphère de KTiOPO4 et des nouveaux composés isotypes et solutions solides de formule générale (K, Rb, Cs)TiO(P, As)O4,” Ph.D. dissertation (Université de Nancy I, Vandoeuvre-lès-Nancy, France, 1989).
  14. J. P. Fève, “Existence et symétrie des interactions à 3 et 4 photons dans les cristaux anisotropes. Méthodes de mesure des paramétres affectant les couplages à 3 ondes: étude de KTP et isotypes,” Ph.D. dissertation (Université de Nancy I, Vandoeuvre-lès-Nancy, France, 1994).
  15. B. Boulanger, G. Marnier, B. Ménaert, X. Cabirol, J. P. Fève, C. Bonnin, and P. Villeval, “Collinear type II phase-matching for SHG in KTiOAsO4: demonstration of its impossibility at 1.064 μm and first experiment at 1.32 μm. Comparison with KTiOPO4,” Nonlin. Opt. 4, 133–142 (1993).
  16. J. P. Fève, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refraction in KTP,” Opt. Commun. 105, 243–252 (1994).
    [CrossRef]
  17. J. P. Fève, B. Boulanger, X. Cabirol, B. Ménaert, G. Marnier, C. Bonnin, and P. Villeval, “Non-critically phase-matched cascaded THG at 440 nm in KTiOP1−yAsyO4 crystals,” Opt. Commun. 115, 323–326 (1994).
    [CrossRef]
  18. See, for example, A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 2, pp. 33–36.
  19. J. P. Fève, B. Boulanger, and G. Marnier, “Experimental study of walk-off attenuation for type II second-harmonic-generation in KTP,” IEEE J. Quantum Electron. 31, 1569–1571 (1995).
    [CrossRef]
  20. J. P. Fève, B. Boulanger, and G. Marnier, “Determination of the longitudinal profile of a focused Nd:YAG Gaussian beam from second-harmonic-generation in a thin KTP crystal,” Appl. Opt. 33, 3169–3174 (1994).
    [CrossRef]
  21. K. Kato, “Parametric oscillation at 3.2 μm in KTP pumped at 1.064 μm,” IEEE J. Quantum Electron. 27, 1137–1140 (1991).
    [CrossRef]
  22. S. C. Mehendale and P. K. Gupta, “Effect of double refraction on type II phase-matched second harmonic generation,” Opt. Commun. 68, 301–304 (1988).
    [CrossRef]
  23. B. Boulanger and G. Marnier, “Field factor calculation for the study of the relationships between all the 3-wave non-linear optical interactions in uniaxial and biaxial crystals,” J. Phys. Condens. Matter 3, 8327–8350 (1991).
    [CrossRef]

1995 (1)

J. P. Fève, B. Boulanger, and G. Marnier, “Experimental study of walk-off attenuation for type II second-harmonic-generation in KTP,” IEEE J. Quantum Electron. 31, 1569–1571 (1995).
[CrossRef]

1994 (6)

1991 (5)

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

J. W. Perry, in Materials for Nonlinear Optics, Chemical Perspectives, S. R. Marder, J. E. Sohn, and G. D. Stucky, eds., ACS Symp. Ser. 455 (1991), Chap. 4.
[CrossRef]

R. C. Eckardt and R. L. Byer, “Measurement of nonlinear optical coefficients by phase-matched harmonic generation,” in Inorganic Crystals for Optics, Electro-Optics, and Frequency Conversion, P. F. Bordui, ed., Proc. SPIE 1561, 119–127 (1991).
[CrossRef]

J. J. Zondy, “Comparative theory of walk-off limited type II versus type I second harmonic generation with Gaussian beams,” Opt. Commun. 81, 427–440 (1991).
[CrossRef]

B. Boulanger and G. Marnier, “Field factor calculation for the study of the relationships between all the 3-wave non-linear optical interactions in uniaxial and biaxial crystals,” J. Phys. Condens. Matter 3, 8327–8350 (1991).
[CrossRef]

1990 (1)

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[CrossRef]

1989 (3)

S. X. Dou, M. H. Jiang, Z. S. Shao, and X. T. Tao, “Maker fringes in biaxial crystals and the nonlinear optical coefficients of thiosemicarbazide cadmium chloride monohydrate,” Appl. Phys. Lett. 54, 1101–1103 (1989).
[CrossRef]

S. P. Velsko, “Direct measurements of phase-matching properties in small crystals of new nonlinear materials,” Opt. Eng. 28, 76–84 (1989).
[CrossRef]

G. Marnier and B. Boulanger, “The sphere method: a new technique in linear and nonlinear crystalline optical studies,” Opt. Commun. 72, 139–143 (1989).
[CrossRef]

1988 (1)

S. C. Mehendale and P. K. Gupta, “Effect of double refraction on type II phase-matched second harmonic generation,” Opt. Commun. 68, 301–304 (1988).
[CrossRef]

1976 (1)

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, “KxRb1−xTiOPO4: a new nonlinear optical material,” J. Appl. Phys. 47, 4980–4985 (1976).
[CrossRef]

Abed, M.

Bierlein, J. D.

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, “KxRb1−xTiOPO4: a new nonlinear optical material,” J. Appl. Phys. 47, 4980–4985 (1976).
[CrossRef]

Bonnin, C.

B. Boulanger, J. P. Fève, G. Marnier, B. Ménaert, X. Cabirol, P. Villeval, and C. Bonnin, “Relative sign and absolute magnitude of d(2) nonlinear coefficients of KTP from second-harmonic-generation measurements,” J. Opt. Soc. Am. B 11, 750–757 (1994).
[CrossRef]

J. P. Fève, B. Boulanger, X. Cabirol, B. Ménaert, G. Marnier, C. Bonnin, and P. Villeval, “Non-critically phase-matched cascaded THG at 440 nm in KTiOP1−yAsyO4 crystals,” Opt. Commun. 115, 323–326 (1994).
[CrossRef]

Boulanger, B.

J. P. Fève, B. Boulanger, and G. Marnier, “Experimental study of walk-off attenuation for type II second-harmonic-generation in KTP,” IEEE J. Quantum Electron. 31, 1569–1571 (1995).
[CrossRef]

J. P. Fève, B. Boulanger, X. Cabirol, B. Ménaert, G. Marnier, C. Bonnin, and P. Villeval, “Non-critically phase-matched cascaded THG at 440 nm in KTiOP1−yAsyO4 crystals,” Opt. Commun. 115, 323–326 (1994).
[CrossRef]

J. P. Fève, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refraction in KTP,” Opt. Commun. 105, 243–252 (1994).
[CrossRef]

B. Boulanger, J. P. Fève, G. Marnier, B. Ménaert, X. Cabirol, P. Villeval, and C. Bonnin, “Relative sign and absolute magnitude of d(2) nonlinear coefficients of KTP from second-harmonic-generation measurements,” J. Opt. Soc. Am. B 11, 750–757 (1994).
[CrossRef]

J. P. Fève, B. Boulanger, and G. Marnier, “Determination of the longitudinal profile of a focused Nd:YAG Gaussian beam from second-harmonic-generation in a thin KTP crystal,” Appl. Opt. 33, 3169–3174 (1994).
[CrossRef]

B. Boulanger and G. Marnier, “Field factor calculation for the study of the relationships between all the 3-wave non-linear optical interactions in uniaxial and biaxial crystals,” J. Phys. Condens. Matter 3, 8327–8350 (1991).
[CrossRef]

G. Marnier and B. Boulanger, “The sphere method: a new technique in linear and nonlinear crystalline optical studies,” Opt. Commun. 72, 139–143 (1989).
[CrossRef]

Byer, R. L.

R. C. Eckardt and R. L. Byer, “Measurement of nonlinear optical coefficients by phase-matched harmonic generation,” in Inorganic Crystals for Optics, Electro-Optics, and Frequency Conversion, P. F. Bordui, ed., Proc. SPIE 1561, 119–127 (1991).
[CrossRef]

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[CrossRef]

Cabirol, X.

J. P. Fève, B. Boulanger, X. Cabirol, B. Ménaert, G. Marnier, C. Bonnin, and P. Villeval, “Non-critically phase-matched cascaded THG at 440 nm in KTiOP1−yAsyO4 crystals,” Opt. Commun. 115, 323–326 (1994).
[CrossRef]

B. Boulanger, J. P. Fève, G. Marnier, B. Ménaert, X. Cabirol, P. Villeval, and C. Bonnin, “Relative sign and absolute magnitude of d(2) nonlinear coefficients of KTP from second-harmonic-generation measurements,” J. Opt. Soc. Am. B 11, 750–757 (1994).
[CrossRef]

Cheung, E. C.

Clairon, A.

Dou, S. X.

S. X. Dou, M. H. Jiang, Z. S. Shao, and X. T. Tao, “Maker fringes in biaxial crystals and the nonlinear optical coefficients of thiosemicarbazide cadmium chloride monohydrate,” Appl. Phys. Lett. 54, 1101–1103 (1989).
[CrossRef]

Eckardt, R. C.

R. C. Eckardt and R. L. Byer, “Measurement of nonlinear optical coefficients by phase-matched harmonic generation,” in Inorganic Crystals for Optics, Electro-Optics, and Frequency Conversion, P. F. Bordui, ed., Proc. SPIE 1561, 119–127 (1991).
[CrossRef]

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[CrossRef]

Fan, Y. X.

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[CrossRef]

Fève, J. P.

J. P. Fève, B. Boulanger, and G. Marnier, “Experimental study of walk-off attenuation for type II second-harmonic-generation in KTP,” IEEE J. Quantum Electron. 31, 1569–1571 (1995).
[CrossRef]

J. P. Fève, B. Boulanger, X. Cabirol, B. Ménaert, G. Marnier, C. Bonnin, and P. Villeval, “Non-critically phase-matched cascaded THG at 440 nm in KTiOP1−yAsyO4 crystals,” Opt. Commun. 115, 323–326 (1994).
[CrossRef]

J. P. Fève, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refraction in KTP,” Opt. Commun. 105, 243–252 (1994).
[CrossRef]

B. Boulanger, J. P. Fève, G. Marnier, B. Ménaert, X. Cabirol, P. Villeval, and C. Bonnin, “Relative sign and absolute magnitude of d(2) nonlinear coefficients of KTP from second-harmonic-generation measurements,” J. Opt. Soc. Am. B 11, 750–757 (1994).
[CrossRef]

J. P. Fève, B. Boulanger, and G. Marnier, “Determination of the longitudinal profile of a focused Nd:YAG Gaussian beam from second-harmonic-generation in a thin KTP crystal,” Appl. Opt. 33, 3169–3174 (1994).
[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, 4980–4985 (1976).
[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, 301–304 (1988).
[CrossRef]

Jiang, M. H.

S. X. Dou, M. H. Jiang, Z. S. Shao, and X. T. Tao, “Maker fringes in biaxial crystals and the nonlinear optical coefficients of thiosemicarbazide cadmium chloride monohydrate,” Appl. Phys. Lett. 54, 1101–1103 (1989).
[CrossRef]

Kato, K.

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

Koch, K.

Liu, J. M.

Marnier, G.

J. P. Fève, B. Boulanger, and G. Marnier, “Experimental study of walk-off attenuation for type II second-harmonic-generation in KTP,” IEEE J. Quantum Electron. 31, 1569–1571 (1995).
[CrossRef]

J. P. Fève, B. Boulanger, X. Cabirol, B. Ménaert, G. Marnier, C. Bonnin, and P. Villeval, “Non-critically phase-matched cascaded THG at 440 nm in KTiOP1−yAsyO4 crystals,” Opt. Commun. 115, 323–326 (1994).
[CrossRef]

J. P. Fève, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refraction in KTP,” Opt. Commun. 105, 243–252 (1994).
[CrossRef]

B. Boulanger, J. P. Fève, G. Marnier, B. Ménaert, X. Cabirol, P. Villeval, and C. Bonnin, “Relative sign and absolute magnitude of d(2) nonlinear coefficients of KTP from second-harmonic-generation measurements,” J. Opt. Soc. Am. B 11, 750–757 (1994).
[CrossRef]

J. P. Fève, B. Boulanger, and G. Marnier, “Determination of the longitudinal profile of a focused Nd:YAG Gaussian beam from second-harmonic-generation in a thin KTP crystal,” Appl. Opt. 33, 3169–3174 (1994).
[CrossRef]

B. Boulanger and G. Marnier, “Field factor calculation for the study of the relationships between all the 3-wave non-linear optical interactions in uniaxial and biaxial crystals,” J. Phys. Condens. Matter 3, 8327–8350 (1991).
[CrossRef]

G. Marnier and B. Boulanger, “The sphere method: a new technique in linear and nonlinear crystalline optical studies,” Opt. Commun. 72, 139–143 (1989).
[CrossRef]

Masuda, H.

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[CrossRef]

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, 301–304 (1988).
[CrossRef]

Ménaert, B.

B. Boulanger, J. P. Fève, G. Marnier, B. Ménaert, X. Cabirol, P. Villeval, and C. Bonnin, “Relative sign and absolute magnitude of d(2) nonlinear coefficients of KTP from second-harmonic-generation measurements,” J. Opt. Soc. Am. B 11, 750–757 (1994).
[CrossRef]

J. P. Fève, B. Boulanger, X. Cabirol, B. Ménaert, G. Marnier, C. Bonnin, and P. Villeval, “Non-critically phase-matched cascaded THG at 440 nm in KTiOP1−yAsyO4 crystals,” Opt. Commun. 115, 323–326 (1994).
[CrossRef]

Moore, G. T.

Perry, J. W.

J. W. Perry, in Materials for Nonlinear Optics, Chemical Perspectives, S. R. Marder, J. E. Sohn, and G. D. Stucky, eds., ACS Symp. Ser. 455 (1991), Chap. 4.
[CrossRef]

Shao, Z. S.

S. X. Dou, M. H. Jiang, Z. S. Shao, and X. T. Tao, “Maker fringes in biaxial crystals and the nonlinear optical coefficients of thiosemicarbazide cadmium chloride monohydrate,” Appl. Phys. Lett. 54, 1101–1103 (1989).
[CrossRef]

Tao, X. T.

S. X. Dou, M. H. Jiang, Z. S. Shao, and X. T. Tao, “Maker fringes in biaxial crystals and the nonlinear optical coefficients of thiosemicarbazide cadmium chloride monohydrate,” Appl. Phys. Lett. 54, 1101–1103 (1989).
[CrossRef]

Velsko, S. P.

S. P. Velsko, “Direct measurements of phase-matching properties in small crystals of new nonlinear materials,” Opt. Eng. 28, 76–84 (1989).
[CrossRef]

Villeval, P.

J. P. Fève, B. Boulanger, X. Cabirol, B. Ménaert, G. Marnier, C. Bonnin, and P. Villeval, “Non-critically phase-matched cascaded THG at 440 nm in KTiOP1−yAsyO4 crystals,” Opt. Commun. 115, 323–326 (1994).
[CrossRef]

B. Boulanger, J. P. Fève, G. Marnier, B. Ménaert, X. Cabirol, P. Villeval, and C. Bonnin, “Relative sign and absolute magnitude of d(2) nonlinear coefficients of KTP from second-harmonic-generation measurements,” J. Opt. Soc. Am. B 11, 750–757 (1994).
[CrossRef]

Zondy, J. J.

J. J. Zondy, M. Abed, and A. Clairon, “Type II frequency doubling at λ=1.30 μm and λ=2.53 μm in flux-grown potassium titanyl phosphate,” J. Opt. Soc. Am. B 11, 2004–2015 (1994).
[CrossRef]

J. J. Zondy, “Comparative theory of walk-off limited type II versus type I second harmonic generation with Gaussian beams,” Opt. Commun. 81, 427–440 (1991).
[CrossRef]

Zumsteg, F. C.

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, “KxRb1−xTiOPO4: a new nonlinear optical material,” J. Appl. Phys. 47, 4980–4985 (1976).
[CrossRef]

ACS Symp. Ser. (1)

J. W. Perry, in Materials for Nonlinear Optics, Chemical Perspectives, S. R. Marder, J. E. Sohn, and G. D. Stucky, eds., ACS Symp. Ser. 455 (1991), Chap. 4.
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. X. Dou, M. H. Jiang, Z. S. Shao, and X. T. Tao, “Maker fringes in biaxial crystals and the nonlinear optical coefficients of thiosemicarbazide cadmium chloride monohydrate,” Appl. Phys. Lett. 54, 1101–1103 (1989).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. P. Fève, B. Boulanger, and G. Marnier, “Experimental study of walk-off attenuation for type II second-harmonic-generation in KTP,” IEEE J. Quantum Electron. 31, 1569–1571 (1995).
[CrossRef]

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

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[CrossRef]

J. Appl. Phys. (1)

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, “KxRb1−xTiOPO4: a new nonlinear optical material,” J. Appl. Phys. 47, 4980–4985 (1976).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. Condens. Matter (1)

B. Boulanger and G. Marnier, “Field factor calculation for the study of the relationships between all the 3-wave non-linear optical interactions in uniaxial and biaxial crystals,” J. Phys. Condens. Matter 3, 8327–8350 (1991).
[CrossRef]

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, 301–304 (1988).
[CrossRef]

J. P. Fève, B. Boulanger, and G. Marnier, “Experimental study of internal and external conical refraction in KTP,” Opt. Commun. 105, 243–252 (1994).
[CrossRef]

J. P. Fève, B. Boulanger, X. Cabirol, B. Ménaert, G. Marnier, C. Bonnin, and P. Villeval, “Non-critically phase-matched cascaded THG at 440 nm in KTiOP1−yAsyO4 crystals,” Opt. Commun. 115, 323–326 (1994).
[CrossRef]

G. Marnier and B. Boulanger, “The sphere method: a new technique in linear and nonlinear crystalline optical studies,” Opt. Commun. 72, 139–143 (1989).
[CrossRef]

J. J. Zondy, “Comparative theory of walk-off limited type II versus type I second harmonic generation with Gaussian beams,” Opt. Commun. 81, 427–440 (1991).
[CrossRef]

Opt. Eng. (1)

S. P. Velsko, “Direct measurements of phase-matching properties in small crystals of new nonlinear materials,” Opt. Eng. 28, 76–84 (1989).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

R. C. Eckardt and R. L. Byer, “Measurement of nonlinear optical coefficients by phase-matched harmonic generation,” in Inorganic Crystals for Optics, Electro-Optics, and Frequency Conversion, P. F. Bordui, ed., Proc. SPIE 1561, 119–127 (1991).
[CrossRef]

Other (5)

G. Marnier, “Process for the flux synthesis of crystals of the KTiOPO4, potassium titanyl monophosphate type,” U.S. patent 4, 746, 396 (May 24, 1988).

B. Boulanger, “Synthèse en flux et étude des propriétés optiques cristallines linéaires et non linéaires par la méthode de la sphère de KTiOPO4 et des nouveaux composés isotypes et solutions solides de formule générale (K, Rb, Cs)TiO(P, As)O4,” Ph.D. dissertation (Université de Nancy I, Vandoeuvre-lès-Nancy, France, 1989).

J. P. Fève, “Existence et symétrie des interactions à 3 et 4 photons dans les cristaux anisotropes. Méthodes de mesure des paramétres affectant les couplages à 3 ondes: étude de KTP et isotypes,” Ph.D. dissertation (Université de Nancy I, Vandoeuvre-lès-Nancy, France, 1994).

B. Boulanger, G. Marnier, B. Ménaert, X. Cabirol, J. P. Fève, C. Bonnin, and P. Villeval, “Collinear type II phase-matching for SHG in KTiOAsO4: demonstration of its impossibility at 1.064 μm and first experiment at 1.32 μm. Comparison with KTiOPO4,” Nonlin. Opt. 4, 133–142 (1993).

See, for example, A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 2, pp. 33–36.

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Figures (6)

Fig. 1
Fig. 1

Incident (wo, d) and refracted (wo, d) Gaussian beam parameters. D is the sphere diameter. The origin of the d, d axis is taken as the entrance surface of the sphere.

Fig. 2
Fig. 2

Refracted Gaussian beam parameters in the sphere (wo, d) calculated for incident beam radius w0=31.6 µm. d=0 corresponds to an incident beam waist located at the sphere entrance. The focusing parameter is f=d/D, so the refracted beam waist is at the sphere entrance for f=0 and at the exit for f=1.

Fig. 3
Fig. 3

Type II phase-matched SHG conversion efficiency at the sphere exit as a function of the focusing conditions for an incident power of 648±30 mW at 1.32 µm.

Fig. 4
Fig. 4

Type I phase-matched SHG conversion efficiency at the sphere exit as a function of the focusing conditions for an incident power of 613±30 mW at 1.32 µm.

Fig. 5
Fig. 5

Angular variation of type II SHG conversion efficiency near a phase-matching direction with a walk-off angle of 0.23°.

Fig. 6
Fig. 6

Angular variation of type II SHG conversion efficiency near a phase-matching direction with a walk-off angle of 1.81°.

Tables (4)

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Table 1 Calculated Refractive Indices (ni) Total Transmission Coefficient (T), Walk-Off Angle (ρ), Field Factors (Fij), and Aperture Functions (hopt) Corresponding to the Phase-Matching Directions Studied (θ, ϕ)a

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Table 2 Comparison of Effective Coefficients Determined by Sphere and Parallelepiped Experiments, deffsphere/deffparallelepiped

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Table 3 Fundamental (Pω) and Harmonic (P2ω) Powers of Three 1.32-µm SHG Experiments Performed in Spheres and Parallelepipeds

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Table 4 Absolute Effective Coefficients and dij Coefficients Measured from Sphere and Parallelepiped Experiments

Equations (29)

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11-nnR01n,
wo=wonE2+F2,d=-dE-Fπwo2λ(E2+F2),
E=1n+1-nnRd,F=1-nnRπwo2λ,
ηSHG(L)=P2ω(L)Pω(0)=CLPω(0)h(L, wo, ρ, f, Δk)cos2 ρ2ω,
nx2(λ)=2.1239+0.14274λ2λ2-18.477+0.87370λ2λ2-0.045906,
ny2(λ)=2.0649+0.15529λ2λ2-19.373+0.95463λ2λ2-0.045505,
nz2(λ)=1.6539+0.34767λ2λ2-29.378+1.6482λ2λ2-0.038825.
d24=deffacII/F24acII,
d15=deffbcII/F15bcII,
d33=deffI-d15(F15I+F31I)-d24(F24I+F32I)F33I.
n±=2-B(B2-4C)1/21/2,
B=-ux2(b+c)-uy2(a+c)-uz2(a+b),
C=ux2bc+uy2ac+uz2ab,
a=nx-2(ω),b=ny-2(ω),c=nz-2(ω),
ux=cos ϕ sin θ,uy=sin ϕ sin θ,uz=cos θ.
C=5.95×10-22N-1Ndeff2λω3n1ω+n2ω2T32ωT1ωT2ωn32ωn1ωn2ω
(perwattmeter).
h(L, wo, ρ, f, Δk)=2zoπL-+|H(a)|2×exp(-4a2)da,
H(a)=12π-fL/zoL(1-f)/zodτ1+iτ×exp-γ2τ+fLzo2-iστ.
F15I(θ, ϕ)=2ex-(2ω, θ, ϕ)ex+(ω, θ, ϕ)ez+(ω, θ, ϕ),
F24I(θ, ϕ)=2ey-(2ω, θ, ϕ)ey+(ω, θ, ϕ)ez+(ω, θ, ϕ),
F31I(θ, ϕ)=ez-(2ω, θ, ϕ)[ex+(ω, θ, ϕ)]2,
F32I(θ, ϕ)=ez-(2ω, θ, ϕ)[ey+(ω, θ, ϕ)]2,
F33I(θ, ϕ)=ez-(2ω, θ, ϕ)[ez+(ω, θ, ϕ)]2,
F15II(θ, ϕ)=ex-(2ω, θ, ϕ)[ex+(ω, θ, ϕ)ez-(ω, θ, ϕ)+ex-(ω, θ, ϕ)ez+(ω, θ, ϕ)],
F24II(θ, ϕ)=ey-(2ω, θ, ϕ)[ey+(ω, θ, ϕ)ez-(ω, θ, ϕ)+ey-(ω, θ, ϕ)ez+(ω, θ, ϕ)],
(n±)2[ep±-up(uxex±+uyey±+uzez±)]=(np)2ep±,
(p=x, y, z),(ex±)2+(ey±)2+(ez±)2=1.
ρ±(ω)=ε arccos[eˆ±(ω)·uˆ(ω)]-ε(π/2),

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