Abstract

In recent years there have been many theoretical studies of one-dimensional (1-D) quasi periodic structures realizing Fibonacci^1,2 or Cantor sequences, obtained by alternating layers of GaAs and AlAs. More recently interesting experimental works have been done studying optical absorption, luminescence, excitation spectra, and electron-hole recombination dynamics. The interesting properties of the structures studied in Refs. 1-2 are linked to the properties of self-similar spaces. Because of its generality it is possible to apply the treatment to the case of any kind of waves propagating in a self-similar medium. In the present paper we study the optical transmission properties, for normal incidence, of a 1-D dielectric integrated resonator, realized by a refractive index distribution that follows the triadic Cantor sequence. Consider two dielectric layers of linear refractive index n₂ and with n₂ > n₁. It is useful to choose the thickness of the two layers such that their linear optical path is the same. The initiator is the layer of refractive index n₂. If L is the optical path of the initiator, the generator is obtained substituting the central part of the initiator having an optical path of L/3 with the layer of refractive index n₁ and thickness such that the optical path is L/3 again. The resonator is obtained iterating the operation on the left and right third optical path, and stopping the iteration at the Nth step. We consider the resonator embedded between two equal semi-infinite layers of refractive index n less than n₂ and n₂.³ We have studied the output versus input intensity behaviour when one of the two layers is a third order nonlinear material, at a given e.m. frequency.

© 1994 IEEE