Designing low-loss cavities across the band-gap of photonic crystal slabs

Abstract: Photonic crystal cavities (PCCs) are defects in host photonic crystals (PCs) which create bound states in the PC band gap. These bound states are resonant states of the electromagnetic field with a complex resonance frequency and can have very small mode volumes. PCCs are attractive for a variety of applications, from cavity quantum electrodynamics to biosensing. A PC slab geometry is advantageous given its superior manufacturability compared to three-dimensional crystals, and the accessibility of the surface allows sensing and coupling. However, the emission into the half spaces above and below the slab limits the bound state lifetime. Controlling this emission is thus crucial for applications, most of which benefiting from a long lifetime. A range of methods to find defect geometries suppressing the emission to increase the lifetime have been demonstrated in the past. However, they do not cater for a designed resonant frequency covering a wide addressable range, as needed for multiplexed devices. Here, we demonstrate a design method controlling both resonance frequency and emission, by minimising a cost function including both losses and target frequency. We show applications on PCCs in GaAs PC slabs immersed in water, relevant for biosensing. The reduced refractive index contrast in these structures compared to previously studied PCCs embedded in vacuum renders the emission suppression more challenging. We optimize the quality factor of a standard L3 cavity from 1000 to 10^4-10^5, with an addressable resonance frequency range covering 12% relative bandwidth, spanning more than half of the band gap. We furthermore report optimised structures of H1 cavities, and provide the optimisation code for widespread use.