"Directed Energy Weapons" refer to any number of types of unconventional and exotic weaponry.
The full range of these weapons is classified information, so no attempts will be made to distinguish between categories within the realm of energy weapons, as doing so would imply specific knowledge of all that are available.
In addition, no claim is be made about whether the directed energy weapon operates from a space-, air-, or ground-based platform, nor are any claims made about whether or not it involves sound waves, antimatter weapons, scalar weapons, a facility like HAARP, etc.
However, the evidence appears consistent with the use of energy weapons that go well beyond the capabilities of conventional explosives.
Wikipedia article on Directed-Energy Weapons
Although speculation about DEWs on 9/11 began shortly after the event, one of the first scientists with relevant credentials to publicly propose the DEW hypothesis was Dr. Judy Wood, a former professor of mechanical engineering.
The following material is largely from her book Where Did the Towers Go?, as well as from her old and new websites.
Where Did the Towers Go?
I. 9/11 Enigmas
II. New Nomenclature
Everyone knows the towers fell off the edge of the Earth