Vortex Phase Singularities in Multiple Slit Interference Patterns in Chaotic Metamaterial Billiards

A wide range of diffractive wave interference patters have been produced by using different planar slit configurations. In particular, situations have been recently studied having more than two slits to test the validity of the superposition principle in wave and quantum mechanics. Here we study the presence of vortex or phase singular fluctuations produced by interference patterns in chaotic billiards with a variable number of diffraction slits. We report numerical wave simulation results of integrable and non-integrable D-shape billiards, having a variable number of slit type configurations. Embedded in this D-shaped chaotic billiards we considere different combinations of positive (PIM) and negative index of refraction (NIM) materials. We compare the topological charge in the phase singularities and their correlations in the different interference pattern configurations produced. We studied closed and open billiards. We found different types of topological charge properties directly related on the geometry, the number of slits as well as the different embedded PIM and NIM configurations. The properties of the vortex pattern configurations and their correlations change dramatically as a function of the geometry of the cavity and he number of slit configurations.