Electric field intensity in a 2D photonic crystal waveguide. Top: Dielectric cladding in the z-direction. The photonic crystal is periodic in the x-y direction. The dielectric contrast between the core and the cladding is 12.5/9.5. Bottom: Air cladding in the z-direction. The dielectric contrast between the core and the cladding is 12.5/1.0. The higher contrast achieves better confinement of the wave in the core.

Bruce Harmon, Kai-Ming Ho, Costas Soukoulis, Rana Biswas, Ihab El-Kady, Dave Turner, and Mihail Sigalas, Ames Laboratory

Research Objectives
This research project has two concurrent thrusts: (1) The design and development of novel structures and photonic devices in the infrared and optical regimes with full 3D band gaps. This includes unusual colloidal crystals being fabricated by our collaborators here at Ames Laboratory, for photonic gaps at optical wavelengths. (2) Development of applications in the microwave and millimeter wave regime for existing 3D photonic band gap (PBG) crystals. These include novel waveguides that can bend electromagnetic waves with bending radii of the order of a single wavelength.

Computational Approach
(1) The transfer matrix method (TMM) is used to design and study PBG filters. Maxwell’s equations are solved to determine the reflection and transmission of electromagnetic waves from a finite thickness PBG material. The method can incorporate realistic absorption and frequency dependent dielectric functions.

(2) In the finite difference time domain (FDTD) method, Maxwell’s equations are discretized on a real-space grid. The time evolution of the electromagnetic fields is calculated by solving the time-dependent Maxwell’s equations. This code can simulate the radiation properties of antennas or the bending of light in a photonic crystal.

Accomplishments
In collaboration with Bilkent University, we fabricated an exceptionally directional antenna utilizing a Fabry-Perot cavity be-tween two photonic crystals. The beam had a half-power width of less than 10°. Very good agreement was achieved between experiment and the finite difference simulation.

We performed calculations to design a microcavity within a PBG crystal with a complete band gap in the infrared. The crystal has been fabricated at Sandia National Laboratories.

Finite-difference simulations were used to design a planar waveguide in the 3D layer-by-layer crystal with a 90° bend with 100% transmission through the bend. A similar L-shaped waveguide was also simulated in a metallic photonic crystal, and only three unit cells thickness were needed for 85% transmission efficiency. The performance of waveguides in 2D PBG structures has been simulated, and the guiding efficiency was optimized as a function of the structural parameters. Such structures are important in all-optical photonic crystal devices.

Significance
Computational simulation can rapidly test the electromagnetic behavior of new structures and then select the best performing ones for fabrication. Our approach led to novel photonic lattices fabricated at Sandia that can for the first time manipulate 1.5 micron wavelengths used for optical fibers.

Publications
B. Temelkuran, M. Bayindir, E. Ozbay, R. Biswas, G. Tuttle, M. M. Sigalas, and K.-M. Ho, “Photonic crystal based resonant antenna with a very high directivity,” Journal of Applied Physics 87, 603 (2000).

R. Biswas, M. M. Sigalas, G. Subramania, C. M. Soukoulis, and K.-M. Ho, “Photonic band gaps of porous solids,” Physical Review B 61, 4549 (2000).

I. El-Kady, M. M. Sigalas, R. Biswas, and K.-M. Ho, “Dielectric waveguides in two-dimensional photonic bandgap materials,” Journal of Lightwave Technology 17, 2042 (1999).