If yes, then what is the cause of this and under what conditions we can observe this?
Nonlinear polarization induced in nonlinear medium contains components oscillating (and radiating) at all three interacting frequencies. In case of perfect phase matching signal and idler waves produced all over the medium interfere constructively, and these waves grow, with no back conversion. Naturally, perfect PM is an ideal case, and in any real situation it is not fulfilled completely, e.g., in all parts of diverging beam, in case of imperfect angular positioning of a crystal and so on. Back conversion in these cases is a cause of limitation of efficiency or direct conversion. Directly back conversion can be observed if we put second crystal after first converter and carefully adjust phases of waves so that polarization in the second crystal would produce signal and idler in opposite phase to that of input waves/ But I do not advice to prove this experimentally, it will require lot of work on adjustment.
Yes. Back conversion happens all the time in nonlinear three wave mixing processes. There are 6 equations governing three wave mixing processes like SHG, THG, and OPA. Really there are three equations but they also have imaginary components and can be written in real form to produce 6 equations that carry phase information as well as intensity information. Most three wave mixing processes are done with pulsed laser beams since the intensity required is usually quite high for efficient operation. Even if one assumes perfect phase matching for a nonlinear crystal (which is almost never the case), there are parts of the pulsed laser beam which are more intense than others both in time and spatial coordinates. Therefore once parts of the laser beam become efficiently converted to the other wavelengths, then the phase information changes sign and that part of the beam starts to "back convert" to the original pump beam. This happens at different lengths down the crystal in time and space for the beam and as such it is impossible to get 100% conversion efficiency. Often laser manufacturers will compromise and give specifications of like 40-45% for an SHG component rather than optimize their nonlinear crystals for higher conversion efficiencies that could be realized ( 60-70% is certainly possible in some cases). As the previous author has mentioned you can back convert most of the beam using a second crystal. I have done this myself and was able to "undo" a 40% SHG process back to about 8% total conversion efficiency using a second crystal. Having studied and modeled these processes for over 10 years, there are many aspects of these processes which are not readily appreciated and have caused many people to waste money on a "shotgun" approach for specifying nonlinear crystals. A good freeware program which can help is SNLO.
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