Abstract

Measurements of the conversion efficiency of second-harmonic generation in KTP (KTiOPO4) by the use of type I phase matching for different fundamental wavelengths of a mode-locked picosecond Ti:sapphire laser are presented. The observed phase matching angles are in agreement with the calculated phase matching curves. At a fundamental wavelength of 834 nm and an intensity of 100 MW/cm2 the conversion efficiency is 4% at maximum, and the corresponding effective nonlinear coefficient d eff is equal to 0.32 pm/V. The experimental values of d eff are related to d 11 (= 0.46 pm/V) of quartz and are in line with the predictions.

© 1995 Optical Society of America

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References

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  1. F. C. Zumsteg, J. D. Bierlein, T. E. Gier, “KxRb1−xTiOPO4: a new nonlinear material,” J. Appl. Phys. 47, 4980–4985 (1976).
    [CrossRef]
  2. D. W. Anthon, C. D. Crowder, “Wavelength dependent phase matching in KTP,” Appl. Opt. 27, 2650–2652 (1988).
    [CrossRef] [PubMed]
  3. J. Q. Yao, T. S. Fahlen, “Calculation of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
    [CrossRef]
  4. M. H. van der Mooren, Th. Rasing, H. J. A. Bluyssen, “Second harmonic generation of blue light in bulk KTP by type I phase matching,” in Proceedings of the International Conference on Lasers ’92, C. P. Wang, ed. (STS, McLean, Va., 1993), pp. 264–267.
  5. H. Ito, H. Naito, H. Inaba, “Generalized study on angular dependence of induced second order nonlinear optical polarizations and phase matching in biaxial crystals,” J. Appl. Phys. 46, 3992–3998 (1975).
    [CrossRef]
  6. R. J. Bolt, M. H. van der Mooren, H. de Haas, “Growth of KTiOPO4 (KTP) single crystals by means of phosphate and phosphate/sulfate fluxes out of a three-zone furnace,” J. Cryst. Growth 114, 141–152 (1991).
    [CrossRef]
  7. T. Y. Fan, C. E. Huang, B. Q. Hu, R. C. Eckardt, Y. X. Fan, R. L. Byer, R. S. Feigelson, “Second harmonic generation and accurate index of refraction measurements in flux-grown KTiOPO4,” Appl. Opt. 26, 2390–2394 (1987).
    [CrossRef] [PubMed]
  8. H. Vanherzeele, J. D. Bierlein, “Magnitude of the nonlinear-optical coefficients of KTiOPO4,” Opt. Lett. 17, 982–984 (1992).
    [CrossRef] [PubMed]
  9. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chap. 16, pp. 416 and 431.
  10. J. Yao, W. Sheng, W. Shi, “Accurate calculation of the optimum phase-matching parameters in three-wave interactions with biaxial nonlinear-optical crystals,” J. Opt. Soc. Am. B 9, 891–902 (1992).
    [CrossRef]

1992 (2)

1991 (1)

R. J. Bolt, M. H. van der Mooren, H. de Haas, “Growth of KTiOPO4 (KTP) single crystals by means of phosphate and phosphate/sulfate fluxes out of a three-zone furnace,” J. Cryst. Growth 114, 141–152 (1991).
[CrossRef]

1988 (1)

1987 (1)

1984 (1)

J. Q. Yao, T. S. Fahlen, “Calculation of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
[CrossRef]

1976 (1)

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

1975 (1)

H. Ito, H. Naito, H. Inaba, “Generalized study on angular dependence of induced second order nonlinear optical polarizations and phase matching in biaxial crystals,” J. Appl. Phys. 46, 3992–3998 (1975).
[CrossRef]

Anthon, D. W.

Bierlein, J. D.

H. Vanherzeele, J. D. Bierlein, “Magnitude of the nonlinear-optical coefficients of KTiOPO4,” Opt. Lett. 17, 982–984 (1992).
[CrossRef] [PubMed]

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

Bluyssen, H. J. A.

M. H. van der Mooren, Th. Rasing, H. J. A. Bluyssen, “Second harmonic generation of blue light in bulk KTP by type I phase matching,” in Proceedings of the International Conference on Lasers ’92, C. P. Wang, ed. (STS, McLean, Va., 1993), pp. 264–267.

Bolt, R. J.

R. J. Bolt, M. H. van der Mooren, H. de Haas, “Growth of KTiOPO4 (KTP) single crystals by means of phosphate and phosphate/sulfate fluxes out of a three-zone furnace,” J. Cryst. Growth 114, 141–152 (1991).
[CrossRef]

Byer, R. L.

Crowder, C. D.

de Haas, H.

R. J. Bolt, M. H. van der Mooren, H. de Haas, “Growth of KTiOPO4 (KTP) single crystals by means of phosphate and phosphate/sulfate fluxes out of a three-zone furnace,” J. Cryst. Growth 114, 141–152 (1991).
[CrossRef]

Eckardt, R. C.

Fahlen, T. S.

J. Q. Yao, T. S. Fahlen, “Calculation of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
[CrossRef]

Fan, T. Y.

Fan, Y. X.

Feigelson, R. S.

Gier, T. E.

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

Hu, B. Q.

Huang, C. E.

Inaba, H.

H. Ito, H. Naito, H. Inaba, “Generalized study on angular dependence of induced second order nonlinear optical polarizations and phase matching in biaxial crystals,” J. Appl. Phys. 46, 3992–3998 (1975).
[CrossRef]

Ito, H.

H. Ito, H. Naito, H. Inaba, “Generalized study on angular dependence of induced second order nonlinear optical polarizations and phase matching in biaxial crystals,” J. Appl. Phys. 46, 3992–3998 (1975).
[CrossRef]

Naito, H.

H. Ito, H. Naito, H. Inaba, “Generalized study on angular dependence of induced second order nonlinear optical polarizations and phase matching in biaxial crystals,” J. Appl. Phys. 46, 3992–3998 (1975).
[CrossRef]

Rasing, Th.

M. H. van der Mooren, Th. Rasing, H. J. A. Bluyssen, “Second harmonic generation of blue light in bulk KTP by type I phase matching,” in Proceedings of the International Conference on Lasers ’92, C. P. Wang, ed. (STS, McLean, Va., 1993), pp. 264–267.

Sheng, W.

Shi, W.

van der Mooren, M. H.

R. J. Bolt, M. H. van der Mooren, H. de Haas, “Growth of KTiOPO4 (KTP) single crystals by means of phosphate and phosphate/sulfate fluxes out of a three-zone furnace,” J. Cryst. Growth 114, 141–152 (1991).
[CrossRef]

M. H. van der Mooren, Th. Rasing, H. J. A. Bluyssen, “Second harmonic generation of blue light in bulk KTP by type I phase matching,” in Proceedings of the International Conference on Lasers ’92, C. P. Wang, ed. (STS, McLean, Va., 1993), pp. 264–267.

Vanherzeele, H.

Yao, J.

Yao, J. Q.

J. Q. Yao, T. S. Fahlen, “Calculation of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chap. 16, pp. 416 and 431.

Zumsteg, F. C.

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

Appl. Opt. (2)

J. Appl. Phys. (3)

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

J. Q. Yao, T. S. Fahlen, “Calculation of optimum phase match parameters for the biaxial crystal KTiOPO4,” J. Appl. Phys. 55, 65–68 (1984).
[CrossRef]

H. Ito, H. Naito, H. Inaba, “Generalized study on angular dependence of induced second order nonlinear optical polarizations and phase matching in biaxial crystals,” J. Appl. Phys. 46, 3992–3998 (1975).
[CrossRef]

J. Cryst. Growth (1)

R. J. Bolt, M. H. van der Mooren, H. de Haas, “Growth of KTiOPO4 (KTP) single crystals by means of phosphate and phosphate/sulfate fluxes out of a three-zone furnace,” J. Cryst. Growth 114, 141–152 (1991).
[CrossRef]

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

Opt. Lett. (1)

Other (2)

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chap. 16, pp. 416 and 431.

M. H. van der Mooren, Th. Rasing, H. J. A. Bluyssen, “Second harmonic generation of blue light in bulk KTP by type I phase matching,” in Proceedings of the International Conference on Lasers ’92, C. P. Wang, ed. (STS, McLean, Va., 1993), pp. 264–267.

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Figures (4)

Fig. 1
Fig. 1

KTP PM curves for type I second-harmonic generation.

Fig. 2
Fig. 2

Calculated (curves) and measured (dots) d eff as a function of the PM angle ϕ. Each value of ϕ corresponds to a particular θ value according to Fig. 1.

Fig. 3
Fig. 3

Laboratory frame u, v, w and angles α and β. Also shown are crystal axes x, y, z and angles ϕ and θ.

Fig. 4
Fig. 4

Experimentally determined conversion efficiency for different wavelengths as a function of the PM orientation.

Equations (7)

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d eff = 0.5 ( d 24 - d 15 ) sin 2 θ sin 2 ϕ ( 3 sin 2 δ - 1 ) cos δ + 3 ( d 15 cos 2 ϕ + d 24 sin 2 ϕ ) sin θ cos 2 θ sin δ cos 2 δ + ( d 15 sin 2 ϕ + d 24 cos 2 ϕ ) sin θ sin δ ( 3 sin 2 δ - 2 ) + d 33 sin 3 θ sin δ cos 2 δ ,
[ cos θ c 0 - sin θ c 0 1 0 sin θ c 0 cos θ c ] [ cos ϕ c sin ϕ c 0 - sin ϕ c cos ϕ c 0 0 0 1 ] ( 0 1 0 ) ,
i = [ cos β sin β 0 - sin β cos β 0 0 0 1 ] [ 1 0 0 0 cos α - sin α 0 sin α cos α ] ( 0 1 0 ) .
i = [ u x v x w x u y v y w y u z v z w z ] ( cos α sin β cos α cos β sin α ) .
r = arcsin { sin [ arccos ( i · v ) ] / n ( r ) } .
θ = arccos ( r z ) , ϕ = arctan ( r y / r x ) .
( cos θ cos ϕ cos δ - sin ϕ sin δ cos θ sin ϕ cos δ + cos ϕ sin δ - sin θ cos δ ) .

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