My femtosecond system is down for two weeks while waiting on a replacement module. If it were up, I'd just try it.
I'd have to run the pump beam into a doubler first, we use near and mid IR Ti-Saph. Our lab has a metric ton of leftover dyes, this is one problem I could answer quickly.
Depending on your dye laser's cavity length, you might get self modelocking or other nasties.
If your Femto laser pumps in the middle of the dye laser's adsorption band, you've got a good shot, provided your focus into the medium is not so sharp.
Ie use a linear focus from a cylindrical lens, not focus to a point.
What whacks me out about the internet is the huge amount of dis-information out there, which leads people to do things that won't work. Things like using 445 nm diode lasers to try to pump dyes that only adsorp in the green etc. However, this question is one that we will actually have to try, to answer it well.
OK, I let my fingers do the walking on Sci-Finder Scholar. The answer is yes, a few groups have pumped dye with compressed pulses. They end up with lengthened, but very sharp, dye laser pulses. The pulses are short, so the average energy is low, and they tend to self modelock, as expected. They get decent tuning, on the order of 250 nm range with a green pump:
There are a FEW, and I mean just a FEW papers on the subject:
See:
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Tunable femtosecond dye laser synchronously pumped by the compressed second harmonic of Nd:YAG
A. M. Johnson and W. M. Simpson »View Author Affiliations
JOSA B, Vol. 2, Issue 4, pp. 619-625 (1985)
http://dx.doi.org/10.1364/JOSAB.2.000619
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Steve