The almost-wrong simplification is that a nonlinear medium changes the wavelength of the light that passes through it.
If you can control the nonlinearity, you can control the wavelength change and so change properties such as the angle of refraction to change where the light goes (like in a rainbow/a prism, where the red light refracts more).
If you can control the nonlinearity, you can control the wavelength change and so change properties such as the angle of refraction to change where the light goes (like in a rainbow/a prism, where the red light refracts more).