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From periodic to random inhomogeneities along optical waveguidesI will focus on describing qualitatively and quantitatively the propagation of light through waveguides with reoccurring defects. Depending on how the defects repeat the waveguide can exhibit anything from periodic to almost periodic to random inhomogeneities along its axis. Their mathematical description can be mapped to discrete rotations on the unit circle where the angle of rotation changes under certain rules. Once the inhomogeneities are well understood, we can rigorously study the energy transfer they induce among propagating and radiative modes of the waveguide. I will rely on the recently developed time dependent resonance theory for perturbed dispersive Hamiltonian systems. This is joint work with Michael I. Weinstein. 

VIGRE Steering Committee Department of Mathematics University of Utah 155 South 1400 East; Room 233 Salt Lake City, UT 84112 email: viscom@math.utah.edu 