1. Consider the scalar optical field of the form propagating in a x2) nonlinear medium: [10] E(t) = A exp(-iwit) + B exp(-iwzt) + C'exp(-i(wi + 8)t) + Dexp(-i(w2 6)t) + c.c. Calculate the second-order nonlinear polarization oscillating at frequencies (wi+w2) and (w1-w2). Think about what the 8-term signifies with respect to the second-order nonlinear polarization of the nonlinear medium (e.g. if d is very small compared to wi and w2)? Plot the polarization over time for a very small d-value such that its effect becomes visible!