Temperature tuning of two-dimensional photonic crystals in the presence of phonons and a plasma of electrons and holes

Abstract

We have theoretically studied the electromagnetic transmittance in finite samples of InSb-based two-dimensional photonic crystals. The cases of both $E$ and $H$ polarization were considered. Due to the temperature dependence of the intrinsic carrier concentration in the semiconductor, our square arrays of parallel InSb cylinders in air\char22{}or vice versa, parallel hollow cylinders in InSb\char22{}give rise to tunable transmission spectra. As the temperature increases from $200\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}290\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, we find that the midgap frequencies move up in frequency while the widths of the gaps diminish, in agreement with the bulk band structure [see Halevi and Ramos-Mendieta, Phys. Rev. Lett. 85, 1875 (2000)]. The wave transmittance was calculated taking into account the dispersion due to phonons, as well as free charge carriers; absorptive mechanisms due to phonons, holes and electrons were also considered. We find that absorption affects considerably the transmittance intensity. In order to achieve significant tuning of the transmission, appropriate structural parameters and spectral regions are proposed. For select values of the frequency, even switching is possible, namely, the transmittance is finite for some value of the temperature and vanishes (or is very small) for a different value. We also proved that, for the plasma model with a background dielectric constant (as appropriate for a polar semiconductor), the band structure is determined by a standard eigenvalue problem. Application to hollow cylinders, forming a hexagonal lattice in InSb background, demonstrates the existence of a complete photonic gap\char22{}for both $E$ and $H$ polarizations\char22{}in a wide range of temperatures.