Waveguides in two-dimensional photonic band gap structures

I. El-Kady, M.M. Sigalas, R. Biswas, K.M. Ho, and C. M. Soukoulis

Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011

One of the most promising applications of photonic band gap (PBG) structures today is their use in the guiding and controlling of light. One such structure uses a two-dimensional PBG with a layered waveguide in the third direction. In typical structures [1], [2] the photonic crystal consists of air holes etched into a semiconductor slab waveguide, well into the bottom of the cladding. However, the air holes scatter light out of the waveguide plane, either into the air or into the substrate. It is very interesting to investigate the dependence of such losses on the refractive index contrast between the waveguide core and the cladding [3], [4] and the geometry of the guide.

To study this phenomenon, we use the finite difference time domain (FDTD) method. A two-dimensional hexagonal lattice of air holes is fabricated in a multi-layer structure consisting of a high dielectric GaAs layer (e=12.5) surrounded by two lower, (air (e=1) for one case and Ga0.2Al0.8As (e=9.5) for the other case), dielectric layers. The guiding properties will be presented as a function of frequency and filling ratio of the 2D lattice. The concept of light cone as a criterion for fully guiding and controlling light will also be investigated. Optimum geometries will be discussed.

[1] D. Labilloy et al., Phys. Rev. Lett. 79, 4147 (1997).
[2] D`Urso et al., J. Opt. Soc. Am. B 15, 1155 (1998).
[3] H. Benisty et al., Appl. Phys. Lett. 76, 532 (2000).
[4] I. El-Kady et al., J. Lightwave Technol., 17, 2042 (1999).