Consider the problem of degenerate three-wave mixing, where the nonlinear interaction is between the frequencies and 2. The field at 2 is very intense and can be considered undepleted. In this case, one can write A_2(z) = A(0), so that the evolution of the fundamental field () is described solely by Eq* .

Solve Eq* for the fundamental field assuming perfect phase-matching and A_2(0) = iE_2, with E_2 purely real. b) Plot A_1(z) for the case where A_1(0) is i) in phase and ii) out of phase with A2(0) using the software of your preference. What is the difference between the two cases and how do you interpret this result?