Photonic band structure in a two-dimensional photonic crystal with a Sierpinski triangle structure

Abstract

The plane wave expansion method was used to calculate the photonic band structure of a hexagonal lattice in which the triangular GaAs scatterers have a Sierpinski structure. In triangles with lengths of less than 0.6 a, in the photonic band structure for low frequencies, the photonic band gaps appear mainly in the transverse-magnetic polarization, as shown by the results. Nevertheless, when the size of triangles increases above 0.8 a, an overlap of the photonic band gap in the transverse-electric and transverse-magnetic polarizations occurs. Hence, a complete photonic band gap is produced, where the photonic modes cannot propagate in either direction. In addition, we detected that another optimal condition for creating a complete photonic band gap is that the dielectric contrast should be greater than 12. Likewise, the pressure and temperature dependence of the GaAs dielectric constant are considered, detecting a higher frequency shift of the photonic band structure, when the temperature remains constant at 4 K and the pressure increases from 0 to 70 kbar.