Large area photonic crystal cavities: A local density approach

Large area photonic crystal cavities are devices of interest for photovoltaics, optoelectronics, and solid-state lighting. However, depending on their dimensions they pose a large computational challenge. Here, we use a local density approach to avoid direct simulation of the device.We capture the effect of both ideal and distorted photonic crystals in an effective mass and an effective potential. We use these to map the problem of calculating the electromagnetic field modes to solving a simple time-independent Schrödinger equation. We show that, in the case that the hole radius varies quadratically as a function of position, the eigenmodes of the photonic crystals can be described by the corresponding eigenmodes of the quantum harmonic oscillator with typical agreements well above 90%.