Third-harmonic generation. Assuming the condition of perfect phase matching, derive and solve exactly the coupled-amplitude equations describing third-harmonic generation. You may assume that the nonlinear optical material is lossless. Include in your analysis the processes described by the two susceptibility elements χ(3) (3ω;ω,ω,ω) and χ(3) (ω; 3ω,-ω,-ω). Calculate the intensity of the third harmonic wave as a function of the length of the interaction region for the following two situations: (a) In the limit in which the undepleted pump approximation is valid. (b) For the general case in which the pump intensity cannot be assumed to remain constant