Defect engineering in infrared photonic bandgap structures

A photonic crystal offers periodic potential because of its lattice of macroscopic dielectric media. When there is sufficient contrast between the materials' dielectric constants and minimal light absorption, the scattering at the interfaces can produce many of the same phenomena for photons as the atomic potential does for electrons in traditional crystals. In these cases, it is possible to design and construct photonic band gaps that prevent propagation of light in certain directions with specified energies.¹

Theoretical and experimental approaches to two-dimensional (2D) systems were reported in the early 1990s, which included systematic treatments of square lattices including dielectric rods and veins as well as square and triangular lattices made up of columns. At that time, scientists predicted² that a three-dimensional (3D) photonic crystal would have a complete band gap. Research later identified the complete band gap in crystals with a diamond lattice of spheres, as long as an appropriate sphere radius was chosen (this was regardless of whether the dielectric spheres were embedded in air or air was embedded in the spheres within a dielectric medium). The first 3D photonic crystal with a complete band gap was built on a microwave length scale by Yablonovitch et al.^3,4 This crystal (named Yablonovite) consisted of a dielectric medium that had been drilled along three of the axes of the diamond lattice.

A defect (anything that breaks the periodicity) in a photonic crystal can be used to localize light modes, making it possible to confine light to a single defect plane in 1D, localize light at a linear defect in 2D, or perturb a single lattice site in 3D. Point defects can create resonant cavities, and line defects can result in waveguides. In all of these cases, a defect can support modes that lay inside the band gap of the bulk crystal that are localized in the near vicinity.⁵

At Pacific Northwest National Laboratory (PNNL), we have been developing quantum cascade lasers (QCL) that are tunable from 3.5–16μm, chalcogenide glasses, and other components that support an integrated approach to chemical sensing. We have made significant progress in modeling and fabricating 2D infrared photonic band gap (PBG) materials and structures with specific defect configurations. In our research, we used the finite difference time domain method and the FullWAVE™ design tool from RSoft Design Group Inc. to compute transmission spectra and the plane wave expansion method and RSoft's BandSOLVE™ for band gaps. The hexagonal lattice of our model for As₂S₃, including parameters and illumination, is shown in Figure 1.

In this study, we modeled twelve different defect configurations. Note that in the RSoft software transverse-electric (TE) polarization corresponds to the electric field pointing out of the 2D plane and the magnetic field lying within the plane. For transverse-magnetic (TM) polarization, the magnetic field points out of the plane. The best resulting defect configuration is shown in Figure 2.

With this optimized defect configuration (see Figure 2), a hole diameter of 2μm resulted in 11.1% more output power than an example reported in literature with a larger hole, and demonstrated 76.7% more output power than one with no hole at the bend. The time lapse of TM propagation in this configuration is shown in Figure 3.

As a result of our research, we have concluded that, for best results, the light must be TM polarized to the lattice of holes. Careful design of the coupling between the initial waveguide and slanted waveguide is necessary to achieve good light efficiency. Yet, even when using the best configurations, we found that only approximately 25% of the energy propagates through the crystal. Our research has shown that much of the light is reflected at the bend, and adding a small hole there helps to match impedance and improve power throughput (see Figure 2).

Future work is required in the area of plane scatter. In addition, a more lengthy modeling effort and a full 3D simulation should be performed.