= G. Jonušauskas
{c}
\b[G. Jonušauskas] coauthored the 1992 <beta barium borate> experiment with <A. Dubietis> and <A. Piskarskas>, demonstrating parametric amplification of chirped and stretched femtosecond pulses.<Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal by A. Dubietis and others>[published byline and Abstract]{ref}
An <optical parametric amplifier> must satisfy both frequency relations and <phase matching>. For a pump, signal and idler with angular frequencies $\omega_p,\omega_s,\omega_i$, the three-wave process obeys $\omega_p=\omega_s+\omega_i$. Coherent buildup also depends on their wavevectors: ideally $\mathbf k_p=\mathbf k_s+\mathbf k_i$. Matching frequencies alone does not ensure that fields generated at different positions add constructively.
For an original undepleted-pump, weak-conversion illustration, suppose the driving amplitude is uniform along a crystal of length $L$. A scalar phase mismatch $\Delta k$ makes the generated field proportional to
$$
\int_0^L e^{i\Delta k z}\,dz
=L e^{i\Delta kL/2}\operatorname{sinc}(\Delta kL/2),
\qquad \operatorname{sinc}u=\frac{\sin u}u.
$$
At exact <phase matching> the limiting amplitude is proportional to $L$. At $\Delta kL=2\pi$ the idealized integral is zero because contributions cancel. This elementary coherent-sum model explains the need to control crystal orientation and optical frequencies; it is not the full high-gain solution or a reported setting from Jonušauskas's experiment.
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