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How can one explain prism dispersion by using nonlinear optics?

We all know, that prism disperses white light. We also can obtain mathematical relation between wavelength and deflection angle by using simple linear optics. But I recently heard that the prism itself somehow affects the way light travels through it and that is the question of nonlinear optics. So how can one explain this effect by using nonlinear optics?

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1. In linear optics, the medium is essentially a fixed quantity. That is, the strength of the light beam's electric field is very low, and essentially has no effect on the medium's response to the light. In nonlinear optics, the light beam's electric field is strong enough that it actually affects how the medium responds to the light. Hence nonlinear, because the light affects the medium which affects the light. These effects only occur in normal materials with very intense light, or in certain special materials which can usually be easily polarized. As a conceptual example, I'll use nonlinear sound waves in water: For a sound wave of normal intensity, the water molecules are locally slightly compressed and slightly expanded as the wave passes. The dispersion only depends on the density of the water and its compressibility. For an ultra-intense sound wave, when the crest passes, the molecules are compressed so tightly that they heat up (absorbing energy from the wave). When the trough comes, the superheated water vaporizes and forms air pockets. This changes the density of the water, and significantly alters the speed of the wave. It is no longer sufficient to know only the density and compressibility to know how fast the wave will travel, as we now need to know about water's thermal properties as well.