Photonic band structure in a one-dimensional distributed Bragg reflector pillar

Abstract

This paper aims to calculate the photonic band structure in a distributed Bragg reflector pillar. The one-dimensional periodic photonic pillar consists of alternating layers of GaAs and air. We consider the dependence of the GaAs dielectric constant on the hydrostatic pressure at a fixed temperature value. The guided-mode expansion method is employed in the case of the photonic pillar; on expanding the magnetic field of the pillar into the basis of guided modes of a homogeneous waveguide, a linear eigenvalue problem is obtained. It is observed that the photonic band structure consists of true-guided modes outside the light dispersion in the effective core, and the radiative modes are located above the light dispersion. When the pressure is increased at a given temperature, the dielectric band exhibits a shift to higher frequencies, while the air band exhibits a slight shift to lower frequencies, resulting in a decrease in the width of the photonic band gap. The calculation of the photonic pillar fundamental mode did not yield a cutoff frequency.