Abstract

We present studies of the optical properties of the new nonlinear material BiB3O6 for second harmonic generation from the visible to infrared. We have determined the phase-matching conditions and effective nonlinear coefficients in the three principal optical planes, acceptance bandwidths, spatial and temporal walkoff, group velocity dispersion and double phase-matching behaviour. We also report on experimental studies in this material, where efficient, high-average-power second harmonic generation of femtosecond pulses into the blue is demonstrated. Using 130-fs fundamental pulses at 76 MHz, single-pass second harmonic average powers as much as 830 mW at greater than 50% conversion efficiency have been generated over a tunable range of 375–435 nm. Using cross-correlation measurements in a 100-µm β-BaB2O4 crystal second harmonic pulse durations of 220 fs are obtained. Our theoretical findings are verified by experimental data, where excellent agreement between the calculations and measurements is obtained. Direct comparison of BiB3O6 with β-BaB2O4 also confirms improved performance of this new material for second harmonic generation of femtosecond pulses.

© 2004 Optical Society of America

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References

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  1. H. Hellwig, J. Liebertz, L. Bohaty, �??Exceptional large nonlinear optical coefficients in the monoclinic bismuth borate BiB3O6 (BIBO),�?? Solid State Commun. 109. 249, (1999).
    [CrossRef]
  2. H. Hellwig, J. Liebertz, and L. Bohaty, �??Linear optical properties of the monoclinic bismuth borate BiB3O6,�?? J. Appl. Phys. 88, 240-244 (2000).
    [CrossRef]
  3. C. Du, Z. Wang, J. Liu, X. Xu, B. Teng, K. Fu, J. Wang, Y. Liu, and Z. Shao, �??Efficient intracavity second harmonic generation at 1.06 μm in a BiB3O6 (BIBO) crystal,�?? Appl. Phys. B 73, 215-217 (2001).
    [CrossRef]
  4. Z. Wang, B. Teng, K. Fu, X. Xu, R. Song, C. Du, H. Jiang, J. Wang, Y. Liu, Z. Shao, �??Efficient second-harmonic generation of pulsed laser radiation in BiB3O6 (BIBO) crystal with different phase matching directions,�?? Opt. Commun. 202, 217-220 (2002).
    [CrossRef]
  5. C. Du, B. Teng, Z. Wang, J. Liu, X. Xu, G. Xu, K. Fu, J. Wang, Y. Liu, Z. Shao, �??Actively Q-switched intracavity second-harmonic generation of 1.06 µm in BiB3O6 crystal,�?? Optics & Laser Technology 34, 343-346 (2002).
    [CrossRef]
  6. C. Czeranowsky, E. Heumann, and G. Huber, �??All-solid-state continuous-wave frequency-doubled Nd:YAG-BiBO laser with 2.8 W output power at 473 nm,�?? Opt. Lett. 28, 432-434 (2003).
    [CrossRef] [PubMed]
  7. I.V. Kityk, W. Imiolek, A. Majchrowski, E. Michalski, �??Photoinduced second harmonic generation in partially crystallized BiB3O6 glass,�?? Opt. Commun. 19, 219, 421-426 (2003).
    [CrossRef]
  8. M. Ghotbi, M. Ebrahim-Zadeh, A. Majchrowski, E. Michalski, I. V. Kityk, �??High-average-power femtosecond pulse generation in the blue using BiB3O6,�?? Opt. Lett. 29, 2530-2532 (2004).
    [CrossRef] [PubMed]
  9. J. Yao, W. Sheng, and 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]
  10. In our earlier work [8], the horizontal axis of Fig. 3 was erroneously labelled as the external angle, which we hereby correct to the internal angle.
  11. S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

Appl. Phys. B (1)

C. Du, Z. Wang, J. Liu, X. Xu, B. Teng, K. Fu, J. Wang, Y. Liu, and Z. Shao, �??Efficient intracavity second harmonic generation at 1.06 μm in a BiB3O6 (BIBO) crystal,�?? Appl. Phys. B 73, 215-217 (2001).
[CrossRef]

J. Appl. Phys. (1)

H. Hellwig, J. Liebertz, and L. Bohaty, �??Linear optical properties of the monoclinic bismuth borate BiB3O6,�?? J. Appl. Phys. 88, 240-244 (2000).
[CrossRef]

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

Opt. Commun. (2)

I.V. Kityk, W. Imiolek, A. Majchrowski, E. Michalski, �??Photoinduced second harmonic generation in partially crystallized BiB3O6 glass,�?? Opt. Commun. 19, 219, 421-426 (2003).
[CrossRef]

Z. Wang, B. Teng, K. Fu, X. Xu, R. Song, C. Du, H. Jiang, J. Wang, Y. Liu, Z. Shao, �??Efficient second-harmonic generation of pulsed laser radiation in BiB3O6 (BIBO) crystal with different phase matching directions,�?? Opt. Commun. 202, 217-220 (2002).
[CrossRef]

Opt. Lett. (2)

Optics & Laser Technology (1)

C. Du, B. Teng, Z. Wang, J. Liu, X. Xu, G. Xu, K. Fu, J. Wang, Y. Liu, Z. Shao, �??Actively Q-switched intracavity second-harmonic generation of 1.06 µm in BiB3O6 crystal,�?? Optics & Laser Technology 34, 343-346 (2002).
[CrossRef]

Solid State Commun. (1)

H. Hellwig, J. Liebertz, L. Bohaty, �??Exceptional large nonlinear optical coefficients in the monoclinic bismuth borate BiB3O6 (BIBO),�?? Solid State Commun. 109. 249, (1999).
[CrossRef]

Other (2)

In our earlier work [8], the horizontal axis of Fig. 3 was erroneously labelled as the external angle, which we hereby correct to the internal angle.

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

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Figures (23)

Fig. 1. (a).
Fig. 1. (a).

Phase-matching angles and the corresponding magnitude of the effective nonlinear coefficient for type I (o+oe) SHG in xy plane as a function of fundamental wavelength.

Fig. 1. (b).
Fig. 1. (b).

Phase-matching angles and the corresponding magnitude of the effective nonlinear coefficient for type II (o+ee) SHG in xy plane as a function of fundamental wavelength.

Fig. 2.
Fig. 2.

(a)–(d). Phase-matching angles and the corresponding magnitude of effective nonlinear coefficient for type I (e+eo) SHG in the yz plane as a function of fundamental wavelength.

Fig. 3.
Fig. 3.

Phase-matching angles and the corresponding magnitude of the effective nonlinear coefficient for (a) type I (o+oe) SHG in the xz plane (b) type I (e+eo) SHG, and (c) type II (o+eo) SHG in the xz plane as a function of fundamental wavelength.

Fig. 4.
Fig. 4.

Continuity of type I phase-matching from the xz plane (o+oe) to the yz plane (e+eo) and the corresponding magnitude of the effective nonlinear coefficient as a function of fundamental wavelength.

Fig. 5.
Fig. 5.

Angle phase-matching range for type I (e+eo) SHG in the optical yz plane as a function of fundamental wavelength. The solid curve is the calculation and the data represent experimental measurements.

Fig. 6.
Fig. 6.

Variation of walkoff angle for type I (e+eo) phase-matching in yz plane as a function of fundamental wavelength.

Fig. 7.
Fig. 7.

Variation of walkoff angle for type I (o+oe) phase-matching in xz plane as a function of fundamental wavelength.

Fig. 8.
Fig. 8.

Second harmonic average power and conversion efficiency as functions of input fundamental power for a 1.4-mm crystal at 406 nm.

Fig. 9.
Fig. 9.

Comparison of the generated second harmonic power in BIBO and BBO as a function of input fundamental power at 406 nm.

Fig. 10.
Fig. 10.

Double phase-matching behaviour for type I (e+eo) SHG in BIBO arising from the monoclinic crystal symmetry.

Fig. 11.
Fig. 11.

Variation of the effective nonlinear coefficient in the two directions of double phase-matching for type I (e+eo) SHG in BIBO. The plots correspond to a fundamental wavelength of 812 nm.

Fig. 12.
Fig. 12.

Variation of SHG power as a function of fundamental power for two different phase-match directions in type I (e+eo) SHG in the yz plane (ϕ=90°) of BIBO. The data correspond to a crystal length of 1 mm and fundamental pulses of 130 fs at 812 nm.

Fig. 13.
Fig. 13.

Calculated FWHM angular acceptance for type I (e+eo) SHG in yz plane (ϕ=90°) as a function of fundamental wavelength.

Fig. 14.
Fig. 14.

Calculated FWHM angular acceptance for type I (o+oe) SHG in xz plane (ϕ=0°) as a function of fundamental wavelength.

Fig. 15.
Fig. 15.

Calculated and measured phase-matching angular acceptance for type I (e+eo) SHG in yz plane in a 1.4-mm crystal at a fundamental wavelength of 812 nm.

Fig. 16.
Fig. 16.

Calculated FWHM spectral acceptance for type I (e+eo) SHG in yz plane (ϕ=90°) as a function of fundamental wavelength.

Fig. 17.
Fig. 17.

Calculated FWHM spectral acceptance for type I (o+oe) SHG in xz plane (ϕ=0°) as a function of fundamental wavelength.

Fig. 18.
Fig. 18.

Calculated and measured phase-matching spectral acceptance for type I (e+e→o) SHG in a 1.4-mm crystal at a fundamental wavelength of 812 nm.

Fig. 19.
Fig. 19.

Group velocity walkoff between the fundamental and second harmonic pulses for type I (e+eo) SHG in yz plane and type I (o+o→e) SHG in xz plane of BIBO as a function of fundamental wavelength.

Fig. 20.
Fig. 20.

(a) Group velocity dispersion of fundamental pulses for type I (e+eo) SHG in yz plane and type I (o+oe) SHG in xz plane as a function of wavelength, (b) Group velocity dispersion of second harmonic pulses for type I (e+eo) SHG in yz plane and type I (o+oe) SHG in xz plane as a function of wavelength.

Fig. 21.
Fig. 21.

Cross-correlation intensity profiles of second harmonic pulses at 406 nm for the 0.4mm and 2-mm BIBO crystals.

Fig. 22.
Fig. 22.

Measured spectra of second harmonic pulses at 406 nm for the 0.4-mm and 2-mm BIBO crystals.

Tables (1)

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Table 1. Non-zero elements of the nonlinear coefficient tensor in BIBO in the xyz optical coordinates system.

Equations (6)

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d eff = d 133 sin ϕ
d eff = d 123 sin ϕ
d eff = d 122 cos 2 θ d 133 sin 2 θ + d 123 sin 2 θ
d eff = d 122 cos θ
d eff = d 213 sin 2 θ
d eff = d 212 cos θ

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