1. Just going through some material about parametric amplifiers but I have difficulties to see where the solution comes in given text. In equations it is assumed undepleted pump wave and in equations there is loss caused by linear absorption for signal and idler. 2. p.s. There is a typo on the equation 2.7. With alpha and gamma it should be i instead of s. And in equation 2.8 the matrix element on the left and down should be E_p* instead of just E_p. 3. For some reason I just don't get it how get from 2.8 to 2.9. Till 2.8 it was all clear. This is just bugging me badly.