Abstract

Achromatic phase matching (APM) involves dispersing the light entering a nonlinear optical crystal so that a wide range of wavelengths is simultaneously phase matched. We constructed an APM apparatus consisting of six prisms, the final dispersion angle of which was optimized to match to second order in wavelength the type I phase-matching angle of β barium borate (BBO). With this apparatus, we doubled tunable fundamental light from 620 to 700 nm in wavelength using a 4-mm-long BBO crystal. An analogous set of six prisms after the BBO crystal, optimized to second order in second-harmonic wavelength, realigned the output second-harmonic beams. Computer simulations predict that adjustment of a single prism can compensate angular misalignment of any or all the prisms before the crystal, and similarly for the prisms after the crystal. We demonstrated such compensation with the experimental device. The simulations also indicate that the phase-matching wavelength band can be shifted and optimized for different crystal lengths.

© 1999 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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1998 (1)

1997 (3)

1993 (1)

P. Tournois, “New diffraction grating pair with very linear dispersion for laser pulse compression,” Electron. Lett. 29, 1414–1415 (1993).
[CrossRef]

1990 (2)

G. Szabo, Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990).
[CrossRef]

R. W. Short, S. Skupsky, “Frequency conversion of broad-bandwidth laser light,” IEEE J. Quantum Electron. 26, 580–588 (1990).
[CrossRef]

1989 (1)

O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25, 2464–2468 (1989).
[CrossRef]

1985 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–679 (1983).
[CrossRef] [PubMed]

1979 (1)

1976 (1)

V. D. Volosov, E. V. Goryachkina, “Compensation of phase-matching dispersion in generation of nonmonochromatic radiation harmonics. I. Doubling of neodymium-glass radiation frequency under free-oscillation conditions,” Sov. J. Quantum Electron. 6, 854–857 (1976).
[CrossRef]

Bisson, S. E.

Bor, Z.

G. Szabo, Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990).
[CrossRef]

Boyd, R. D.

Britten, J. A.

Bryan, S. J.

Dmitriev, V. G.

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).
[CrossRef]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–679 (1983).
[CrossRef] [PubMed]

Goryachkina, E. V.

V. D. Volosov, E. V. Goryachkina, “Compensation of phase-matching dispersion in generation of nonmonochromatic radiation harmonics. I. Doubling of neodymium-glass radiation frequency under free-oscillation conditions,” Sov. J. Quantum Electron. 6, 854–857 (1976).
[CrossRef]

Gurzadyan, G. G.

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).
[CrossRef]

Jacobson, A.

Kane, S.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–679 (1983).
[CrossRef] [PubMed]

Martinez, O. E.

O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25, 2464–2468 (1989).
[CrossRef]

Mitchell, M. G.

Nguyen, H. T.

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).
[CrossRef]

Ouw, D.

Perry, M. D.

Richman, B. A.

Saikan, S.

Schäfer, F. P.

Shore, B. W.

Short, R. W.

R. W. Short, S. Skupsky, “Frequency conversion of broad-bandwidth laser light,” IEEE J. Quantum Electron. 26, 580–588 (1990).
[CrossRef]

Sidick, E.

Skupsky, S.

R. W. Short, S. Skupsky, “Frequency conversion of broad-bandwidth laser light,” IEEE J. Quantum Electron. 26, 580–588 (1990).
[CrossRef]

Squier, J.

Szabo, G.

G. Szabo, Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990).
[CrossRef]

Tournois, P.

P. Tournois, “New diffraction grating pair with very linear dispersion for laser pulse compression,” Electron. Lett. 29, 1414–1415 (1993).
[CrossRef]

Trebino, R.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–679 (1983).
[CrossRef] [PubMed]

Volosov, V. D.

V. D. Volosov, E. V. Goryachkina, “Compensation of phase-matching dispersion in generation of nonmonochromatic radiation harmonics. I. Doubling of neodymium-glass radiation frequency under free-oscillation conditions,” Sov. J. Quantum Electron. 6, 854–857 (1976).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

G. Szabo, Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990).
[CrossRef]

Electron. Lett. (1)

P. Tournois, “New diffraction grating pair with very linear dispersion for laser pulse compression,” Electron. Lett. 29, 1414–1415 (1993).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. W. Short, S. Skupsky, “Frequency conversion of broad-bandwidth laser light,” IEEE J. Quantum Electron. 26, 580–588 (1990).
[CrossRef]

O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25, 2464–2468 (1989).
[CrossRef]

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

Opt. Lett. (3)

Science (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–679 (1983).
[CrossRef] [PubMed]

Sov. J. Quantum Electron. (1)

V. D. Volosov, E. V. Goryachkina, “Compensation of phase-matching dispersion in generation of nonmonochromatic radiation harmonics. I. Doubling of neodymium-glass radiation frequency under free-oscillation conditions,” Sov. J. Quantum Electron. 6, 854–857 (1976).
[CrossRef]

Other (1)

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic of the APM device (not to scale). The first two prisms serve to disperse the fundamental beam spatially (but not angularly) so that the rest of the prisms cause all beams to converge in the crystal. The first two prisms also demagnify the monochromatic beam divergence so that the divergence at the crystal is less than the crystal angular acceptance. The fourth, fifth, and sixth prisms are Littrow (30° apex angle), with near-normal incidence and near 60° exit angles. They magnify and add to the dispersion of the third prism. The output APM system is qualitatively the reverse of the input, but the prisms are of a different material and at different angles from the input.

Fig. 2
Fig. 2

(a) Comparison of the predicted differences between the cumulative dispersion angle of the input prisms and the exact phase-matching angle of the BBO crystal as a function of fundamental wavelength: solid curve, original prism angles optimized for a 4-mm-long BBO crystal; dashed curve, prism 3 incident angle adjusted to provide equivalent phase matching for a 16-mm-long crystal; and dotted curve, a 1-mm-long crystal. Note that the acceptance angle (horizontal lines in inset) and thus the bandwidth vary inversely with the crystal length. (b) Comparison as in (a) showing shifting of the bandwidth by simultaneous adjustment of prisms 5 and 6: solid curve, original prism angles; dashed curve, adjustment to shift bandwidth -20 nm; and dotted curve, +20 nm.

Fig. 3
Fig. 3

(a) Comparison of the predicted differences between the cumulative dispersion angle of the input prisms and the exact phase-matching angle of the BBO crystal as a function of fundamental wavelength: solid curve, original optimized prism angles; dashed curve, misaligned prisms; dotted curve, fifth prism reoptimized. (b) Comparison of the predicted output angles from the cumulative dispersion of the output prisms as a function of second-harmonic wavelength: solid curve, original optimized prism angles; dashed curve, misaligned prisms; dotted curve, last output prism reoptimized.

Fig. 4
Fig. 4

Contour plot of the experimentally measured relative second-harmonic conversion efficiency versus wavelength and crystal angle. The theoretically predicted difference between the dispersion and exact phase-matching angles [from Fig. 2(a)] is shown for comparison (solid curve). The point spacing is 5 nm × 100 µrad.

Fig. 5
Fig. 5

Experimentally measured second-harmonic beam (a) position and (b) angle as functions of second-harmonic wavelength. The squares correspond to the plane of dispersion (horizontal) and the triangles to out of the plane of dispersion (vertical). The theoretically predicted output angle in the dispersion plane is shown for comparison [solid curve in (b)].

Tables (1)

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Table 1 Prism Materials and Angles for the APM Devicea

Equations (8)

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2 500 μrad2 mrad/nm=0.5 nm.
2500 μrad5 μrad/nm21/2=20 nm,
dθdλ, d2θdλ2,
dθoutdλ=θoutθindθindλ+θoutλ,
d2θoutdλ2=θoutθind2θindλ2+2θoutλ2+2θoutθin2dθindλ2+2 2θoutλθindθindλ,
E= θλ-θλ0-ϕλϕλ2dλ,
βjm=βjm-1+rand,
P=1+expEm-1-EmT-1,

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