The Mid-Infrared (MIR) and TeraHertz (THz) regions of the electromagnetic spectrum have a vast range of potential applications. These include security (surveillance, detection of explosives), safety (gas sensing and detection of hazardous compounds) as well as a variety of scientific and industrial applications, such as chemical analysis, thermography, medical imaging, and non-destructive testing. Due to the long wavelength of the radiation, novel types of optical guides and resonators are commonly found in MIR and THz device designs, such as ring cavities, microdiscs, photonic crystals, supercrystals, and micro-antennas.
Of particular interest are Photonic Crystal (PHC) cavities. Propagation of light in a PHC is similar to propagation of electron waves in a crystal lattice. The electromagnetic waves can be separated into a plane wave and a periodic Bloch function. This allows investigating the properties of a large finite PHC based on the analysis of a single unit cell. This analysis is commonly done in Fourier space which can have one, two, or three dimensions implicitly assuming periodic boundary conditions around the unit cell. In our work, however, a real-space approach is used. The periodicity is explicitly ensured by connecting the mesh vertices that lie on opposite surfaces of the unit cell. Thus, the unit cell can be made periodic in certain spatial dimensions, while in the remaining dimensions different boundary conditions may be applied.
The real-space approach with mixed boundaries allows us to analyze PHC slabs. Such a slab might consist of a layer of silicon a few micrometers thick with holes arranged in a regular hexagonal pattern also a few microns apart. Light propagates in the horizontal plane as it would in a two-dimensional PHC, but part of it also radiates vertically into the spaces above and below the slab. To capture this radiative dissipation effect we apply periodic boundary conditions in the horizontal plane and absorbing boundary conditions below and above the slab. Doing so, we obtain a complex photonic band structure which contains wavevector-dependent information about radiative losses for every PHC mode.