Gain saturation of fiber optic parametric amplification has frequently been studied by considering the reduction of signal gain with pump depletion in a moderately saturated system. But once the pump is considerably depleted, the reverse process occurs where sidebands tend to provide power back to the pump and then pump power increases as a result. But this can lead to a back and forth process when we consider an infinitely long fiber and somehow comes to a steady state. But I have doubts on how Fermi-Pasta-Recurrence can be incorporated into this to explain this behavior under highly gain saturated conditions.. Specially the occurence of multiple saturation cycles with decreasing amplitudes to finally attain a steady state.. What is the determinig factor for Fermi-Pasta recurrence to disappear after a certain fiber length?
Preston Guynn I'll definitely look into it. Thank you for the answer. Anyway, MI is considered in temporal domain if I'm not wrong. My concern is how this can be applied in spatial domain.. Maybe I might find a clue in the paper.
I think its worthwhile to take a look at the paper, "Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects" by G. Capellini and S. Trillo 1991. They have conducted a spatial instability analysis to demonstrate the pump power variation and found out that the pump power change is not always periodic but depends on the input relative phase between the interacting waves. The analysis is very descriptive and have addressed for different phase matching conditions.
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