In mode-locked Ti:sapphire lasers, positive dispersion is caused mainly by the crystal. A prism pair placed in the laser resonator can compensate for some of the dispersion by introducing negative group velocity dispersion.
My questions are:
1) How are positive and negative dispersion caused in the crystal and prism pair, respectively?
2) How is the distance between the prism pair determined?
Positive dispersion means that the lower frequencies are ahead of the higher frequencies in time, and this is caused by the fact that the crystal's group index (derivative of refractive index) is smaller for lower frequencies, giving them faster group velocity going through the crystal. To compensate, the pair of prisms gets the higher frequencies to catch up just by making the lower frequencies go through a longer path length. As the prisms separate the frequencies spatially through refraction, the lower frequencies take the more outside path so that they have to travel a slightly longer distance.
The correct distance between prisms is that which puts all frequencies back on top of each other. This is usually adjustable in Ti:Sapphire lasers, so that you don't really have to precisely calculate it before hand. The way to find the optimum is by measuring the pulse width - the shortest pulse width is the point where dispersion is compensated, and it is here that the pulse is called "transform-limited".
