2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/84730We present an algorithm for the maximization of photonic bandgaps in two-dimensional crystals. Once the translational symmetries of the underlying structure have been imposed, our algorithm finds a global maximal (and complete, if one exists) bandgap. Additionally, we prove two remarkable results related to maximal bandgaps: the so-called `maximum contrast' rule, and about the location in the Brillouin zone of band edges.4 pagesOpticstext