Consider the scalar optical field of the following form propagating in a (2) nonlinear medium: E(t) =

• Consider the scalar optical field of the following form propagating in a χ(2) nonlinear medium: E(t) = A exp(−iω1t) + B exp(−iω2t) + C exp(−i(ω1 + δ)t) + D exp(−i(ω2 − δ)t) + c.c. Calculate the second-order nonlinear polarization oscillating at frequencies (ω1+ω2) and (ω1−ω2). Think about what the δ-term signifies with respect to the second-order nonlinear polarization of the nonlinear medium (e.g. if δ is very small compared to ω1 and ω2)? Plot the polarization over time for a very small δ-value such that its effect becomes visible