In Stable One-Dimensional Dissipative Solitons in Complex Cubic-Quintic Ginzburg-Landau Equation you will a study on a pulse propagating in a medium.One can measure some pulse parameters presented therein and finding their alternation conclude particular changes.

I think is a rather challenging task with a not so accurate outcome. First of all you should know all the components of your OPA (which I believe is what you are using). Normally you generate white light (supercontinuum generation), then you have a first opa interaction with fundamental in a noncollinear arrangement and then usually a second opa interaction with some more fundamental light. For all of this, you have normally a saphire plate, two nonlinear crystals, some ND filters and a lot of lenses and mirrors. You should know all the properties of all of this elements. For propagation in linear media you can have an estimation by fourier transform the pulse at the entrance and calculating E(x_0+Dx,omega)=E(x_0,omega)exp(i*k(omega)*Dx), and inverse fourier transform the results (where k=n(omega)omega/c). Basically k(omega)*Dx is a spectral phase accumulated by each monochromatic wave during propagation. This spectral phase is normally approximated by a Taylor expansion around the pulse carrier frequency w for which the first terms are normally called group delay (GD), group delay dispersion(GDD) and third order dispersion (TOD), which you can normally find for each material. For all nonlinear interactions is a little harder, because you need to know how the phase mismatch depends on omega. On a first order approximation, this is proportional to the group velocity mismatch, GVM=(1/v_g1-1/v_g2). From here you can calculate bandwidth and using the time-bandwidth product estimate a lower bound to the pulse width. I think is easier to buy/build and autocorrelator, for example an interferometric one. I hope this helps, and best luck.

I agree with the answer provided by Luis Domenianni . What I would add is that pulses with spectra centred near 1600 nm don't experience a huge amount of dispersion in fused silica and related glasses, so the pulse won't be stretched too much, depending on how many of the optics in your OPA are transmission and not reflecting elements. For that reason the pulse duration will depend more on the phasematching bandwidth of the BBO crystals since this is an important factor which determines in the bandwidth of the OPA signal (and idler) beam(s). Given that you are interested in the SWIR output from the OPA, you can be reasonably confident that the SWIR pulse duration will be longer than the pulse duration of the pump, unless you play some tricks with the non-colinearity or non-linearity in the set-up.