I have been making a simulation of light traveling in medium from classical physics perspective and while trying to makes sence of a traveling wave packet i realized i don't understand something very fundamental.
Left side of the image:
Nothing to it, we know which way a light ray will refract/reflect from Snell's law and Fresnel's equations, both of which we can get from Maxwell's equations and border conditions.
Right side of the image:
Googling about ultra short laser pulses I've read that dispersion becomes a big problem. A short pulse of light is by it's definition made of different frequencies, so no problem there, the medium "will do" a Fourier analysis of the light and send them in different directions.
This means, that a short pulse of light will refract in different directions but a long pulse of light (which are basically a bunch of short pulses one after another) will not. How does the medium know how long the pulse will be?
If it's a short pulse of light it seems to disperse it, but if it's long it just sends it in one direction. How does the medium/light "know" what to do?