I still don't understand it, though. A force is needed for compression, and forces work because of repulsion (e.g., electrostatic repulsion when a hand squeezes a tennis ball.) But photons don't have any type of charge for a repulsion?
The simplest way to understand it is to assume all the light (of any frequency) is instantly absorbed by the outer layer of matter. This would then instantly flash into a high temp plasma, rocketing radially outwards at very high speed. Momentum conservation requires what is left of the capsule to move in the opposite direction, or radially inwards toward the center. This implosion effect is what they will do with NIF to create conditions suitable for fusion breakeven. The NIF's light (UV) is converted to x-rays to make the illumination more uniform.