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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'