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

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 compared to three-dimensional crystals due to its superior manufacturability, 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 are 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 optimise the quality factor of a standard L3 cavity from 1000 to, with an addressable resonance frequency range covering about 10% relative bandwidth, spanning more than half of the band gap. For a H1 cavity starting from a quality factor of 127, optimisation achieves quality factors ofover 12% relative bandwidth.