Abstract
The natural and technological worlds operate by employing waves of all sorts: electron, electromagnetic, acoustic and so on. These waves can be manipulated by blocking their propagation in certain frequency regions called gaps, while allowing the propagation in other regions called bands. Semiconductor technology, for example, is based on electron-wave propagation in the so-called conduction and valence bands. And a new technology is emerging based on periodic structures that have bands and gaps for electromagnetic waves.