We present a closed-form solution for the two-wave coupling process, resulting in a periodic solution with respect to time that describes a moving grating. In the photorefractive medium, it has been shown that a moving grating will produce in a phase shift in the coupling constant. To our knowledge, this has not been derived directly from the grating dynamic equations. We will also show that the temporal dynamics does not have any asymptotically stable equilibrium points of an exponential form. As an example, we have developed resonance conditions resulting in a new expression for the frequency detuning of a resonator with photorefractive gain medium.
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