Abstract

The second-order nonlinear-optical coefficients of β-BaB2O4 have been absolutely determined for visible to ultraviolet second-harmonic wavelengths: The fundamental wavelengths used were 0.532, 0.852, 1.064, and 1.313 µm. The following values were obtained by use of the wedge technique: d22=2.6 pm/V at 0.532 µm; d22=2.3 pm/V at 0.852 µm; d22=2.2 pm/V, d33=0.04 pm/V, d31=0.04 pm/V, and d15=0.03pm/V at 1.064 µm; and d22=1.9 pm/V at 1.313 µm.

© 1999 Optical Society of America

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  1. C. Zimmermann, V. Vuletic, A. Hemmerich, and T. W. Hänsch, “All solid state laser source for tunable blue and ultraviolet radiation,” Appl. Phys. Lett. 66, 2318–2320 (1995).
    [CrossRef]
  2. M. Oka, L. Y. Liu, W. Wiechmann, Y. Taguchi, H. Wada, T. Okamoto, H. Suganuma, and S. Kubota, “Progress in all-solid-state deep-ultraviolet coherent light sources,” in Nonlinear Frequency Generation and Conversion, M. C. Gupta, W. J. Kozlovsky, and D. C. MacPherson, eds., Proc. SPIE 2700, 302–310 (1996); K. Kondo, M. Oka, H. Wada, T. Fukui, N. Umezu, K. Tatsuki, and S. Kubota, “Demonstration of long-term reliability of a 266-nm, continuous-wave, frequency-quadrupled solid-state laser using β-BaB2O4,” Opt. Lett. 23, 195–197 (1998).
    [CrossRef]
  3. Y. X. Fan, R. C. Eckardt, R. L. Byer, J. Nolting, and R. Wallenstein, “Visible BaB2O4 optical parametric oscillator pumped at 355 nm by a single-axial-mode pulsed source,” Appl. Phys. Lett. 53, 2014–2016 (1988).
    [CrossRef]
  4. S. Wu, G. A. Blake, Z. Sun, and J. Ling, “Simple, high-performance type II β-BaB2O4 optical parametric oscillator,” Appl. Opt. 36, 5898–5901 (1997).
    [CrossRef] [PubMed]
  5. C. Chen, B. Wu, A. Jiang, and G. You, “A new-type ultraviolet SHG crystal—β-BaB2O4,” Sci. Sin. Ser. B 28, 235–243 (1985).
  6. 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]
  7. C.-T. Chen, Y. X. Fan, R. C. Eckardt, and R. L. Byer, “Recent developments in barium borate,” in Laser and Nonlinear Optical Materials, L. G. De Shazer, ed., Proc. SPIE 681, 12–19 (1986).
    [CrossRef]
  8. D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
    [CrossRef]
  9. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14, 2268–2294 (1997).
    [CrossRef]
  10. R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
    [CrossRef]
  11. S. Kubota, M. Oka, L. Y. Liu, T. Okamoto, M. Watanabe, Y. Taguchi, H. Masuda, T. Fukui, W. Wiechmann, H. Kikuchi, and A. Godil, “Recent progress in the quality of KTiOPO4 and β-BaB2O4 crystals used for the mi-green SHG laser and 1.5 W of cw 266 nm generation, ' in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 228–234 (1995).
    [CrossRef]

1997 (2)

1995 (2)

C. Zimmermann, V. Vuletic, A. Hemmerich, and T. W. Hänsch, “All solid state laser source for tunable blue and ultraviolet radiation,” Appl. Phys. Lett. 66, 2318–2320 (1995).
[CrossRef]

S. Kubota, M. Oka, L. Y. Liu, T. Okamoto, M. Watanabe, Y. Taguchi, H. Masuda, T. Fukui, W. Wiechmann, H. Kikuchi, and A. Godil, “Recent progress in the quality of KTiOPO4 and β-BaB2O4 crystals used for the mi-green SHG laser and 1.5 W of cw 266 nm generation, ' in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 228–234 (1995).
[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]

1988 (1)

Y. X. Fan, R. C. Eckardt, R. L. Byer, J. Nolting, and R. Wallenstein, “Visible BaB2O4 optical parametric oscillator pumped at 355 nm by a single-axial-mode pulsed source,” Appl. Phys. Lett. 53, 2014–2016 (1988).
[CrossRef]

1987 (1)

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

1986 (1)

C.-T. Chen, Y. X. Fan, R. C. Eckardt, and R. L. Byer, “Recent developments in barium borate,” in Laser and Nonlinear Optical Materials, L. G. De Shazer, ed., Proc. SPIE 681, 12–19 (1986).
[CrossRef]

1985 (1)

C. Chen, B. Wu, A. Jiang, and G. You, “A new-type ultraviolet SHG crystal—β-BaB2O4,” Sci. Sin. Ser. B 28, 235–243 (1985).

1964 (1)

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[CrossRef]

Blake, G. A.

Byer, R. L.

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]

Y. X. Fan, R. C. Eckardt, R. L. Byer, J. Nolting, and R. Wallenstein, “Visible BaB2O4 optical parametric oscillator pumped at 355 nm by a single-axial-mode pulsed source,” Appl. Phys. Lett. 53, 2014–2016 (1988).
[CrossRef]

C.-T. Chen, Y. X. Fan, R. C. Eckardt, and R. L. Byer, “Recent developments in barium borate,” in Laser and Nonlinear Optical Materials, L. G. De Shazer, ed., Proc. SPIE 681, 12–19 (1986).
[CrossRef]

Chen, C.

C. Chen, B. Wu, A. Jiang, and G. You, “A new-type ultraviolet SHG crystal—β-BaB2O4,” Sci. Sin. Ser. B 28, 235–243 (1985).

Chen, C.-T.

C.-T. Chen, Y. X. Fan, R. C. Eckardt, and R. L. Byer, “Recent developments in barium borate,” in Laser and Nonlinear Optical Materials, L. G. De Shazer, ed., Proc. SPIE 681, 12–19 (1986).
[CrossRef]

Davis, L.

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Eckardt, R. C.

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]

Y. X. Fan, R. C. Eckardt, R. L. Byer, J. Nolting, and R. Wallenstein, “Visible BaB2O4 optical parametric oscillator pumped at 355 nm by a single-axial-mode pulsed source,” Appl. Phys. Lett. 53, 2014–2016 (1988).
[CrossRef]

C.-T. Chen, Y. X. Fan, R. C. Eckardt, and R. L. Byer, “Recent developments in barium borate,” in Laser and Nonlinear Optical Materials, L. G. De Shazer, ed., Proc. SPIE 681, 12–19 (1986).
[CrossRef]

Eimerl, D.

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[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]

Y. X. Fan, R. C. Eckardt, R. L. Byer, J. Nolting, and R. Wallenstein, “Visible BaB2O4 optical parametric oscillator pumped at 355 nm by a single-axial-mode pulsed source,” Appl. Phys. Lett. 53, 2014–2016 (1988).
[CrossRef]

C.-T. Chen, Y. X. Fan, R. C. Eckardt, and R. L. Byer, “Recent developments in barium borate,” in Laser and Nonlinear Optical Materials, L. G. De Shazer, ed., Proc. SPIE 681, 12–19 (1986).
[CrossRef]

Fukui, T.

S. Kubota, M. Oka, L. Y. Liu, T. Okamoto, M. Watanabe, Y. Taguchi, H. Masuda, T. Fukui, W. Wiechmann, H. Kikuchi, and A. Godil, “Recent progress in the quality of KTiOPO4 and β-BaB2O4 crystals used for the mi-green SHG laser and 1.5 W of cw 266 nm generation, ' in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 228–234 (1995).
[CrossRef]

Godil, A.

S. Kubota, M. Oka, L. Y. Liu, T. Okamoto, M. Watanabe, Y. Taguchi, H. Masuda, T. Fukui, W. Wiechmann, H. Kikuchi, and A. Godil, “Recent progress in the quality of KTiOPO4 and β-BaB2O4 crystals used for the mi-green SHG laser and 1.5 W of cw 266 nm generation, ' in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 228–234 (1995).
[CrossRef]

Graham, E. K.

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Hänsch, T. W.

C. Zimmermann, V. Vuletic, A. Hemmerich, and T. W. Hänsch, “All solid state laser source for tunable blue and ultraviolet radiation,” Appl. Phys. Lett. 66, 2318–2320 (1995).
[CrossRef]

Hemmerich, A.

C. Zimmermann, V. Vuletic, A. Hemmerich, and T. W. Hänsch, “All solid state laser source for tunable blue and ultraviolet radiation,” Appl. Phys. Lett. 66, 2318–2320 (1995).
[CrossRef]

Ito, R.

Jiang, A.

C. Chen, B. Wu, A. Jiang, and G. You, “A new-type ultraviolet SHG crystal—β-BaB2O4,” Sci. Sin. Ser. B 28, 235–243 (1985).

Kikuchi, H.

S. Kubota, M. Oka, L. Y. Liu, T. Okamoto, M. Watanabe, Y. Taguchi, H. Masuda, T. Fukui, W. Wiechmann, H. Kikuchi, and A. Godil, “Recent progress in the quality of KTiOPO4 and β-BaB2O4 crystals used for the mi-green SHG laser and 1.5 W of cw 266 nm generation, ' in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 228–234 (1995).
[CrossRef]

Kitamoto, A.

Kondo, T.

Kubota, S.

S. Kubota, M. Oka, L. Y. Liu, T. Okamoto, M. Watanabe, Y. Taguchi, H. Masuda, T. Fukui, W. Wiechmann, H. Kikuchi, and A. Godil, “Recent progress in the quality of KTiOPO4 and β-BaB2O4 crystals used for the mi-green SHG laser and 1.5 W of cw 266 nm generation, ' in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 228–234 (1995).
[CrossRef]

Ling, J.

Liu, L. Y.

S. Kubota, M. Oka, L. Y. Liu, T. Okamoto, M. Watanabe, Y. Taguchi, H. Masuda, T. Fukui, W. Wiechmann, H. Kikuchi, and A. Godil, “Recent progress in the quality of KTiOPO4 and β-BaB2O4 crystals used for the mi-green SHG laser and 1.5 W of cw 266 nm generation, ' in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 228–234 (1995).
[CrossRef]

Masuda, H.

S. Kubota, M. Oka, L. Y. Liu, T. Okamoto, M. Watanabe, Y. Taguchi, H. Masuda, T. Fukui, W. Wiechmann, H. Kikuchi, and A. Godil, “Recent progress in the quality of KTiOPO4 and β-BaB2O4 crystals used for the mi-green SHG laser and 1.5 W of cw 266 nm generation, ' in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 228–234 (1995).
[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]

Miller, R. C.

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[CrossRef]

Nolting, J.

Y. X. Fan, R. C. Eckardt, R. L. Byer, J. Nolting, and R. Wallenstein, “Visible BaB2O4 optical parametric oscillator pumped at 355 nm by a single-axial-mode pulsed source,” Appl. Phys. Lett. 53, 2014–2016 (1988).
[CrossRef]

Oka, M.

S. Kubota, M. Oka, L. Y. Liu, T. Okamoto, M. Watanabe, Y. Taguchi, H. Masuda, T. Fukui, W. Wiechmann, H. Kikuchi, and A. Godil, “Recent progress in the quality of KTiOPO4 and β-BaB2O4 crystals used for the mi-green SHG laser and 1.5 W of cw 266 nm generation, ' in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 228–234 (1995).
[CrossRef]

Okamoto, T.

S. Kubota, M. Oka, L. Y. Liu, T. Okamoto, M. Watanabe, Y. Taguchi, H. Masuda, T. Fukui, W. Wiechmann, H. Kikuchi, and A. Godil, “Recent progress in the quality of KTiOPO4 and β-BaB2O4 crystals used for the mi-green SHG laser and 1.5 W of cw 266 nm generation, ' in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 228–234 (1995).
[CrossRef]

Shirane, M.

Shoji, I.

Sun, Z.

Taguchi, Y.

S. Kubota, M. Oka, L. Y. Liu, T. Okamoto, M. Watanabe, Y. Taguchi, H. Masuda, T. Fukui, W. Wiechmann, H. Kikuchi, and A. Godil, “Recent progress in the quality of KTiOPO4 and β-BaB2O4 crystals used for the mi-green SHG laser and 1.5 W of cw 266 nm generation, ' in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 228–234 (1995).
[CrossRef]

Velsko, S.

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Vuletic, V.

C. Zimmermann, V. Vuletic, A. Hemmerich, and T. W. Hänsch, “All solid state laser source for tunable blue and ultraviolet radiation,” Appl. Phys. Lett. 66, 2318–2320 (1995).
[CrossRef]

Wallenstein, R.

Y. X. Fan, R. C. Eckardt, R. L. Byer, J. Nolting, and R. Wallenstein, “Visible BaB2O4 optical parametric oscillator pumped at 355 nm by a single-axial-mode pulsed source,” Appl. Phys. Lett. 53, 2014–2016 (1988).
[CrossRef]

Watanabe, M.

S. Kubota, M. Oka, L. Y. Liu, T. Okamoto, M. Watanabe, Y. Taguchi, H. Masuda, T. Fukui, W. Wiechmann, H. Kikuchi, and A. Godil, “Recent progress in the quality of KTiOPO4 and β-BaB2O4 crystals used for the mi-green SHG laser and 1.5 W of cw 266 nm generation, ' in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 228–234 (1995).
[CrossRef]

Wiechmann, W.

S. Kubota, M. Oka, L. Y. Liu, T. Okamoto, M. Watanabe, Y. Taguchi, H. Masuda, T. Fukui, W. Wiechmann, H. Kikuchi, and A. Godil, “Recent progress in the quality of KTiOPO4 and β-BaB2O4 crystals used for the mi-green SHG laser and 1.5 W of cw 266 nm generation, ' in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 228–234 (1995).
[CrossRef]

Wu, B.

C. Chen, B. Wu, A. Jiang, and G. You, “A new-type ultraviolet SHG crystal—β-BaB2O4,” Sci. Sin. Ser. B 28, 235–243 (1985).

Wu, S.

You, G.

C. Chen, B. Wu, A. Jiang, and G. You, “A new-type ultraviolet SHG crystal—β-BaB2O4,” Sci. Sin. Ser. B 28, 235–243 (1985).

Zalkin, A.

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Zimmermann, C.

C. Zimmermann, V. Vuletic, A. Hemmerich, and T. W. Hänsch, “All solid state laser source for tunable blue and ultraviolet radiation,” Appl. Phys. Lett. 66, 2318–2320 (1995).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

C. Zimmermann, V. Vuletic, A. Hemmerich, and T. W. Hänsch, “All solid state laser source for tunable blue and ultraviolet radiation,” Appl. Phys. Lett. 66, 2318–2320 (1995).
[CrossRef]

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[CrossRef]

Y. X. Fan, R. C. Eckardt, R. L. Byer, J. Nolting, and R. Wallenstein, “Visible BaB2O4 optical parametric oscillator pumped at 355 nm by a single-axial-mode pulsed source,” Appl. Phys. Lett. 53, 2014–2016 (1988).
[CrossRef]

IEEE J. Quantum Electron. (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]

J. Appl. Phys. (1)

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

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

Proc. SPIE (2)

C.-T. Chen, Y. X. Fan, R. C. Eckardt, and R. L. Byer, “Recent developments in barium borate,” in Laser and Nonlinear Optical Materials, L. G. De Shazer, ed., Proc. SPIE 681, 12–19 (1986).
[CrossRef]

S. Kubota, M. Oka, L. Y. Liu, T. Okamoto, M. Watanabe, Y. Taguchi, H. Masuda, T. Fukui, W. Wiechmann, H. Kikuchi, and A. Godil, “Recent progress in the quality of KTiOPO4 and β-BaB2O4 crystals used for the mi-green SHG laser and 1.5 W of cw 266 nm generation, ' in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 228–234 (1995).
[CrossRef]

Sci. Sin. Ser. B (1)

C. Chen, B. Wu, A. Jiang, and G. You, “A new-type ultraviolet SHG crystal—β-BaB2O4,” Sci. Sin. Ser. B 28, 235–243 (1985).

Other (1)

M. Oka, L. Y. Liu, W. Wiechmann, Y. Taguchi, H. Wada, T. Okamoto, H. Suganuma, and S. Kubota, “Progress in all-solid-state deep-ultraviolet coherent light sources,” in Nonlinear Frequency Generation and Conversion, M. C. Gupta, W. J. Kozlovsky, and D. C. MacPherson, eds., Proc. SPIE 2700, 302–310 (1996); K. Kondo, M. Oka, H. Wada, T. Fukui, N. Umezu, K. Tatsuki, and S. Kubota, “Demonstration of long-term reliability of a 266-nm, continuous-wave, frequency-quadrupled solid-state laser using β-BaB2O4,” Opt. Lett. 23, 195–197 (1998).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Dependence of the SH power on sample thickness for d22 (BBO) at the fundamental wavelength of 0.532 µm. (b) Part of (a) around one of the Maker-fringe peaks plotted on an expanded horizontal scale. The fundamental power was 39.85 mW, and the fundamental beam radii wx and wy were 19.35 and 22.18 µm, respectively. Open squares, experimental data; solid curves, the theoretical fitting curve with Eq. (2).

Fig. 2
Fig. 2

Dependence of the SH power on sample thickness for d22 from the X-cut and d33, d31, and d15 from the Y-cut BBO wedge samples. The fundamental wavelength is 1.064 µm. The ordinates show relative SH power for those components. Open squares, experimental data; solid curves, the theoretical fitting curves with Eq. (2).

Tables (2)

Tables Icon

Table 1 Refractive Indices of BBO Used in the Data Analysis

Tables Icon

Table 2 Experimentally Determined Miller Δ and Effective Nonlinear-Optical Coefficients of BBO (pm/V)a

Equations (14)

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

Δijk=dijk(-2ω; ω, ω)[ni2(2ω)-1][nj2(ω)-1][nk2(ω)-1],
P2ω(L)=K(Pω)22L2π1/2wx2wy(ΔkL/2)2×- exp-4x2wx2F[l(x)]G[l(x)]dx,
K=2ω2d2π0c3nω2n2ω,
l(x)=L+x tan θ,
F(l)=1(1+F2ω sin2 k2ωl)(1+Fω sin2 kωl)2,
G(l)=116nω2n2ω3(nω+n2ω)2×C(1) sin2Δk2l-C(2) sin2k2ω+2kω2l+C(3) sin2 k2ωl+C(4) sin2 2kωl+C(5) sin2k2ω2l-C(6) sin2 kωl.
F2ω=(n2ω2-1)24n2ω2,
Fω=(nω2-1)24nω2,
C(1)=2nω2n2ω2[nωn2ω(nω2+3)(2n2ω2-nω2+3)+(3nω2+1)(4n2ω2-nω2+1)],
C(2)=2nω2n2ω2[nωn2ω(nω2+3)(2n2ω2-nω2+3)-(3nω2+1)(4n2ω2-nω2+1)],
C(3)=nω4(n2ω2-1)[(2n2ω2-nω2+1)2-4n2ω2],
C(4)=n2ω4(nω2-1)3,
C(5)=4nω2(nω2-1)(n2ω2-nω2)(4n2ω2-nω2+1),
C(6)=4n2ω2(nω2-1)(n2ω2-nω2)(3nω2+1).

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