Two plane waves oscillating at the same frequency but propagating in opposite directions through a third-order nonlinear material. The third-order nonlinear susceptibility and the linear index of refraction of the material are assumed to be real quantities, neglect second-order nonlinearity. Both waves have large amplitudes. a) Calculate the third-order nonlinear polarizations that contribute to the fields associated with the two waves. b) Calculate the effective refractive index experienced by each of the interacting waves. c) How must the intensities of the fields be related so that one of the fields suffers 1.5 times the phase shift of the other in the nonlinear medium?