The thermal effects on the photonic band gaps of the two-dimensional SiO2-Si hexagonal photonic crystal

In this study, we investigate the thermal effects on the photonic band gaps of a two-dimensional SiO₂-Si hexagonal photonic crystal composed of a silicon dioxide (SiO₂) substrate with an array of silicon-filled holes. The photonic band structures of the transverse electric (TE) mode are calculated using the plane wave expansion method, and the thermal effects on the photonic band gaps are analyzed. Two temperature-dependent refractive-index models, namely the Ghosh model and the Sellmeier equation, are used to calculate the refractive indices of silicon dioxide. In addition, a temperature-dependent refractive-index function for silicon reported by H. H. Li is adopted at the target telecommunication wavelength of 1.55 μm, without considering the absorption coefficient. Using these experimentally based material parameters, well-converged numerical results are obtained. Eight photonic band gaps are initially identified below the normalized frequency ωa / 2 πc = 1.1 over the temperature range from 200 K to 600 K. However, the sixth gap remains close to zero width and is excluded from the quantitative discussion because it is extremely narrow and may be affected by numerical convergence. Therefore, the remaining seven reliable photonic band gaps are analyzed in detail. The results show that lower-order band gaps exhibit relatively weak temperature dependence, whereas some higher-order band gaps show more pronounced thermal variation. These numerical results provide useful theoretical guidance for the development and optimization of future silicon photonic devices, such as waveguides and optical filters.