Derive the Manley-Rowe relation for the process of the second harmonics generation.
Manley-Rowe relation: ~ The Manley-Rowe relations are mathematical expressions developed originally for electrical engineers to predict the amount of energy in a wave that has multiple frequencies.
Second-harmonic generation: ~ Second harmonic generation (SHG); also called frequency doubling; is a nonlinear optical process, in which photons interacting with a nonlinear material are effectively “combined” to form new photons with twice the energy, and therefore twice the frequency and half the wavelength of the initial photons. It is example of nonlinear phenomena (I, 3). In the SHG process, the intense wave at the frequency $\omega$ propagates in the medium with second-order nonlinearity ( VI, 1).