Define what is meant by the nonlinear electrical polarization of an optical medium.
The electrical polarization for a general optical medium is given by
Explain how can this expression be modified for amorphous (i.e., isotropic) media, and give reasons for the validity of the modification. Show how the expression for P can lead to the generation of the second harmonic of an optical wave propagating in the medium, and discuss the conditions which affect the efficiency with which this harmonic is generated. Why is such generation (apparently) only possible in a crystalline medium?