You have posed a very interesting query. Going by your words, the two situations are totally different. If you look minutely, the interchange is not recommendable. However, for your own analysis, you can proceed and compare the results. As I can see, you are more interested in getting variations in frequencies. When the question of replacement comes, you can not rule out the coherence length. In case of fiber lasers, it is different from that of non-linear crystal. Another point is that modulator dimension (NL crystal and fiber ) will also have an impact on the out put. Anyways, best wishes for your endeavor and I will be glad to see them.

Optical pump or laser can be feed the fibers (such as EDFA, etc) to trigger different levels of energy. In this way, change of output wavelength is raised from electron transition among the levels.

In nonlinear crystals such as photonic crystals, light can be manipulated and propagated in desired paths according to light intensity or wavelength. So, in this media the used mechanism can be all optical and differs from the last mechanism in the fiber.

For nonlinear material, one can employ other mechanisms such as temperature, electric field, etc for changing the refractive index of media. This issue can help one to change output wavelength.

I see...

since we always have at least a triple level interaction , i.e. pump->lase_high->ground I cannot assume that the phase of the pump has any fixed relation to the output, since it isn't maintained from pump to lase_high.

Basically, because the transition from pump->lase_high is a purely statistical process and not induced, thus decoupling everything (which is actually the only way pumping works in the first place, duh...). Thanks I should have seen this before.

Great help!

I'm happy to talk to you

First of all, we must pay attention to the fact that

The structure of optical fiber is different with the structure of nonlinear crystals

When a fiber laser (wavelength specified) as secondary fiber laser pumping units used

The secondary system emits wavelength that are more than pumping wavelengths

Note, If the material active length in the secondary system not suitable

For example, it is shorter than the Optimum length

In the output we will see two wavelengths

The wavelength of the pump is not absorbed and the laser wavelength is emitted

Any kind of the lasers can be seen as a frequency converter, obviously, either up shifting or down shifting, depending on the active ion feature in the gain medium.

The frequency convertion or multiplying could be realized by the laser cavity design associating with the gain medium, or by the parametric oscillation.

If the parametric oscillation is employed in order to obtain the new frequency, so that the fiber acts as a nonlinear crystal, instead of the conventional gain medium where the lasing is driven by the upper-level conversion.

Therefore, your assumption could be taken under certain conditions.