Series: Mathematics Colloquium

Date: Thursday, February 5, 2004

Time: 4:00 - 5:00 PM

Place: 102 McAllister Building

Host: Spyridon Kamvissis

Refreshments: 3:15 - 4:00 PM, in 212 McAllister

Speaker: Stefanos Venakides, Duke University

Title: Boundary States and Resonances in Photonic Crystals

Abstract:  

  We begin with a comprehensive introduction to the theory of
  propagation in photonic crystals, in particular Bloch waves, and the
  formation of photonic bandgaps. We then describe our numerical
  experiments on photonic crystal slabs.  We finally present a precise
  theoretical explanation of certain resonant peaks and dips in the
  electromagnetic transmission coefficient of periodically structured
  slabs in the presence of guided slab modes.  The theory applies to
  very general geometries of the unit cell and is based on
  boundary-integral representations of the electromagnetic
  fields. These depend on the frequency and Bloch wavevector and
  provide a complex-analytic connection in these parameters between
  generalized scattering states and guided slab modes. The coincidence
  and perturbation of three zeros, those of the dispersion relation
  for slab modes, the reflection constant, and the transmission
  constant, are central to calculating transmission anomalies both for
  lossless dielectric materials and for perfect metals. Collaborators:
  Stephen Shipman, LSU, Mansoor Haider, NCSU.