OK.
So the other direction, lasers can now blast an incoming missile by heat and energy input ..... 8<)
Heat is energy. But, IIRC, some of the damage mechanism for short pulse lasers is due to momentum transfer. Short of like pounding on the missile with a ball peen hammer, only much harder.
But other lasers, such as the one on the ABL 747, do there thing by energy deposition.