Prescribing a Finite Contrast Ratio for Opening Band-Gaps in 2-dimensional Periodic Media
Tuesday, September 27, 2016 - 11:00am - 12:00pm
High-contrast photonic crystals have been a topic of intense study by both mathematicians and physicists for the past several decades. A highly desirable quality of these crystals is the existence of band gaps in the frequency spectrum, that is, bands of frequencies which are not permitted to propagate through the medium. Band gaps have been proven to exist in the high-contrast limit since at least the turn of the millennium, but explicit calculation of the magnitude of contrast necessary to open band gaps has remained a somewhat elusive problem in an abstract mathematical setting. In this talk, a method for prescribing a finite contrast ratio necessary to open band gaps for 2-dimensional periodic media, as well as the location and estimates on the length of these gaps, will be uncovered, using only information regarding the geometry of the periodic structure itself.