for correct answer you need to determine pump pulse duration. Energy would be good also. Formally you are limited by two parameters: surface damage and superfluorescence. With femtosecond pump you can reach gain 10^5-10^6 in single pass and superfluorescence is limiting because there is no reason to amplify more because of rising noise. With 100ps - ns pump limiting factor is surface damage. You can reach 10^3-10^4 in single pass. For ns short cavity is often used with final gain 10^6 or even more (for oscillators - unseeded).
Thanks, I've recently found a paper (attached) with 104-105 gain for picosecond pump and up to 107-108 gain for femtosecond pump, with the second BBO crystal bringing it up to 1010. Do you think it would be much worse in waveguides?
have no experience with waveguides. Formally, if you reach pump intensity and phase matching is OK, gain values should be similar to one obtained in the free-space setup. Should be no difference is there waveguide or not. Except damage threshold. I expect that waveguide is kind of defect or inclusion what may drastically decrease material damage threshold. Sometimes waveguides are much longer as bulk crystals with expectation that higher gain can be obtained in longer material with lower intensity, but often Raman starts and four-wave-mixing flows energy to frequency sidebands. As result pump intensity is clamped and (or) energy of the signal do not increase. And I believe you will not get the same... but almost.
For the multi-cascaded OPA you can do what you want. Formally there is no limit how much you can amplify. For example with gain 10^10 you can get ~1.6nJ from a single photon. nJ is huge energy but energy and time profile contrast will be extremely bad because of amplified "quantum noise" and Poissonian statistics of single photon seed source. Therefore main questions are how much your seed is larger compared to quantum noise (in the time frame of pump pulse and spatial and frequency bandwidth of OPA) and how you will perform cleaning of the resulting signal. For the best result you need to filter wavelength (frequency) to time limited by the pulse duration and do spatial filtering down to single mode.
Therefore in huge OPA systems with multi-mili-Joule output main question is where to get seed signal strong enough to be 6-8 orders stronger compared to quantum noise level. But not how to get proper gain. In the article you send noise is 20% what is really bad for most practical applications. In the article authors claim that contrast can be easily increased by use of "color" filter. However it is not demonstrated that "easily".