Waves Seminar Series

Department of Mathematical Sciences and Center for Applied Mathematics and Statistics

New Jersey Institute of Technology

Spring 2009

Talks in this series are held Wednesdays in Cullimore 611 at 2:45 pm unless noted otherwise. If you have any questions about a particular colloquium, please contact the person hosting the speaker. For general questions about the seminar schedule, please contact Roy Goodman.

Date

Speaker and title

Host

3/4

Mark Hoefer, Columbia University, Hydrodynamics in the Small Dispersion Limit (abstract)

Roy Goodman

4/1 (note 3:45 pm start)

Mikael Rechtsman, Courant Institute, Upper Bounds on Photonic Bandgaps (abstract)

Roy Goodman

March 4, Mark Hoefer, Columbia University, Hydrodynamics in the Small Dispersion Limit

In contrast to the well known theory of compressible gas dynamics where dissipation plays the dominant role in regularizing the solution, the propagation of waves through a nonlinear medium with small dispersion and negligible dissipation requires a wholly different regularization mechanism. This talk will focus on a dispersive regularization for hydrodynamic models--the nonlinear Schrodinger and Korteweg-deVries equations in the small dispersion limit--where shock wave structures arise. A collection of physically relevant hydrodynamic problems will be solved asymptotically including, as time permits, blast waves, nonlinear wave interactions, and driven dynamics. Comparisons with experiments in nonlinear, defocusing photonics and Bose-Einstein condensation will be presented.

April 1, Mikael Rechtsman, Courant Institute, Upper Bounds on Photonic Bandgaps

A 20-year search has been on to find photonic crystals (periodic dielectric structures) with the largest possible full photonic bandgaps. A large, robust bandgap is key to the many applications of these materials, which include near-lossless waveguiding, optical filtering, optical computing, and others. A number of three-dimensional structures with large gaps have been proposed (e.g., a diamond lattice of spheres, [1] the “Woodpile” structure [2] ), and in two dimensions, structural optimizations to find the largest-bandgap structure have been performed, (e.g., in refs. [3] and [4]). So far, however, there has been no work on finding rigorous limits on how high the bandgap may be. In this talk, I present upper bounds on the bandgaps of one and two dimensional photonic crystals.

References

  1. Phys. Rev. Lett. 65, 3152 (1990)
  2. J. Mod. Opt. 41, 231 (1994)
  3. Appl. Phys. B. 81, 235 (2005)
  4. Phys. Rev. Lett. 101, 073902 (2008)


Links to Old Seminar Schedules

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