Enhanced design strategy for Mesoscopic Self-Collimation

Abstract

Mesoscopic photonic crystals (MPhC) are composed of alternating photonic crystal slabs (PhC) and homogeneous material. MPhC structures combine PhC dispersive properties (self-collimation and slow light, among others) with reflectivity control (Bragg mirrors). One of the most studied properties of MPhC is mesoscopic selfcollimation (MSC). MSC occurs when PhC dispersion properties compensate the natural divergence of light in homogeneous material [1]. However, MSC is only visible if the energy properly propagates throughout the structure, it is thus crucial to control undesirable reflections at each interface. Different methods, relying on complex Fourier modal analysis [2], allow reflectivity control using an impedance-based approach such as half-holes or comet-like holes between each interface. These methods have fabrication limitations (not circular holes) and may need long and complex calculations. We propose a method based on a fast and simple multiscale approach. In constrast to [3] we prioritize perfect antireflection at the different interfaces, instead of perfect self-collimation. At the µm-scale, we first model the MPhC as a multilayer Bragg structure. By solving simple Bragg equations we determine a first set of parameters ensuring perfect antireflection. At the nm-scale, we then take into account the PhC dispersion properties to search for MSC solutions within the first set of parameters. With this approach, we obtain a complete set of MPhC geometries that ensures reflectivity control and correct MSC (i.e. low beam divergence), without the need for long numerical simulations. To validate our model, we use FDTD [4] simulations to study light propagation through the previously determined MPhC (Figures 1b, 1c, 1d).