Abstract

Angular dispersion of the signal beam inside the nonlinear media is introduced to improve the non-collinear phase-matching range. Simulations run for BBO crystals predict that bandwidth increase is possible for most of the application spectral range and that it can surpass one order of magnitude in some particular configurations.

© 2004 Optical Society of America

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References

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Appl. Opt. (2)

Appl. Phys. B (1)

G. Szabó and Zs. Bor, ???Frequency conversion of ultrashort pulses,??? Appl. Phys. B 58, 237-241 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

O. E. Martínez, ???Achromatic phase matching for second harmonic generation of femtosecond pulses,??? IEEE J. Quantum Electron. 25, 2464-2468 (1989).
[CrossRef]

J. Appl. Phys. (1)

I. Jovanovic, B. J. Comaskey, and D. M. Pennington, ???Angular effects and beam quality in optical parametric amplification,??? J. Appl. Phys. 90, 4328-4337 (2001)
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (3)

S. Saikan, ???Automatically tunable second harmonic generation of dye lasers,??? Opt. Commun. 18, 439-443 (1976).
[CrossRef]

J. A. Fülöp, A. P. Kovács, and Z. Bor, ???Broadband dispersion-compensated two-pass second harmonic generation of femtosecond pulses,??? Opt. Commun. 188, 365-370 (2001).
[CrossRef]

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley and J. L. Collier, ???The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplifiers,??? Opt. Commun. 144, 125-133 (1997).
[CrossRef]

Opt. Express (1)

Rev. Sci. Instrum. (1)

G. Cerullo and S. De Silvestri, ???Review article - Ultrafast optical parametric amplifiers,??? Rev. Sci. Instrum. 74, 1-18 (2003).
[CrossRef]

Other (1)

Sandia National Laboratories, <a href= "http://www.sandia.gov/imrl/X1118/xxtal.htm">http://www.sandia.gov/imrl/X1118/xxtal.htm</a>

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Figures (7)

Fig. 1.
Fig. 1.

Dependence of the ideal non-collinear angle with the signal wavelength for some phase-matching angles, using a 532nm pump for a BBO crystal. The dots mark stationary points.

Fig. 2.
Fig. 2.

Definition of the angles used in the simulation and wave vector matching. The idler gets dispersed in both directions.

Fig. 3.
Fig. 3.

(a) Spectral gain profile vs. λ s0 for an 8.7 mm long BBO crystal without dispersion. Pump is λ p=532 nm, I p=1 GW.cm-2. Some pixelation results from the step used in the simulation. (b) Similar to (a), but with optimised signal angular dispersion. The dashed line marks a turn point for abscissa counting and also signals the configuration detailed in Fig. 4 (c) Full width half maximum bandwidth of (a) and (b) in dotted and solid curves, respectively. Abscissas for the dotted line are as usual in literature, but for the solid line they are the effective central wavelengths for the gain bandwidth, not λ s0, because of the greater gain asymmetry around it.

Fig. 4.
Fig. 4.

Calculated gain (solid) and phase (dotted) for an 8.73 mm long BBO crystal, pumped by 1 GW.cm-2 at 532 nm; λ 0=1060 nm. The FWHM bandwidth is 724 nm, centred at 1170 nm.

Fig. 5.
Fig. 5.

BBO wavelength-dependence of the phase-matching angle (left), non-collinear angle (centre), and dispersion (right). The configurations with the flattest gain and phase for wavelengths near λ 0 are shown dotted; dispersion given by Eq. (9) is applied to flatten these curves up to second order. Solid lines show the optimised parameters to allow extended bandwidth.

Fig. 6.
Fig. 6.

(a) BBO’s spectral gain distribution using the parameters of the dotted curves in Fig. 5. (b), (c), (d), (e) Gain changes induced by perturbation of the critical parameters. Blue and yellow graphs show the effects of negative and positive deltas, respectively. They are presented colour-wise summed: white means both of them overlap, indicating the configurations with better error tolerance.

Fig. 7.
Fig. 7.

(a) BBO’s spectral gain distribution using the optimised parameters of the solid curves in Fig. 5. (b), (c), (d), (e) Gain changes induced by perturbation of the critical parameters. Colours are as in Fig. 6.

Equations (9)

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G = 1 + ( γ L ) 2 ( sinh B B ) 2
φ = tan 1 B sin A cosh B A cos A sinh B B cos A cosh B A sin A sinh B
A = Δ kL 2
B = [ ( γ L ) 2 ( Δ kL 2 ) 2 ] 1 2
γ = 4 π d eff ( I p 2 ε 0 n p n s n i c λ s λ i ) 1 2
Δ kL = ( k p k s k i ) L
cos ( θ NC , ideal ) = k p 2 + k s 2 k i 2 2 k p k s
θ NC , aprox 2 ( λ s ) = θ NC 2 ( λ s 0 ) + [ θ disp ( λ s λ s 0 ) ] 2
θ disp = { [ θ NC , ideal ( λ s 0 ) . θ NC , ideal ( λ s 0 ) ] 1 2 if θ NC , ideal ( λ s 0 ) > 0 θ NC , ideal ( λ s 0 ± δ λ s ) if θ NC , ideal ( λ s 0 ) = 0

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