Upper bounds on photonic bandgaps

Mikael Rechtsman

Courant Institute, NYU

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. [3-4]). 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.


  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)

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