Say one had three intense laser pulses and one weak reference pulse coming together on the surface of a thin nonlinear medium as if coming from the corners of a square. The three intense laser pulses mix, and there will be the third order mixing k1+k2-k3 or k1-k2+k3 or whatever coming out in the same direction as the weak reference pulse. Here's my question: If this nonlinear medium isn't thin, there will be nonlinear refraction from higher order terms in the expansion of the refractive index. Will the nonlinear mixing signal refract approximately the same amount as the reference pulse? And another question: If one were to look at the reflected light, would the nonlinear mixing reflection change direction as the higher order terms of the refractive index become stronger/weaker if all of the three excitation pulses are shifted to be more in/out-of phase? I guess this amounts to 'does the law of reflection hold for intense light at interfaces with nonlinear media'