Electric field propagation from a meta-surface using ray optics and Fourier optics

Understanding how meta-surfaces generate far field intensity distributions is key for real-world applications such as remote sensing and for designing experimental setups. The electric field distribution generated by a meta-surface consisting of Germanium crosses deposited on a calcium fluoride substrate was simulated using the Finite Difference Time Domain (FDTD) method. The electric field was then analyzed to find the component which propagates to a detector at a distance of 100 mm from the meta-surface. To simulate far field propagation using ray optics, a ray diagram was made to approximate the square magnitude of the electric field. This was done using weighted Voronoi cells, where the density of rays corresponds to the magnitude squared of the electric field. The gradient of the wavefront was used to determine the propagation direction of each ray. The meta-surface was resonant at a wavelength of 4 μm and off resonant at 3.05 μm. At both wavelengths, the beam focused to a central spot at the detector plane. This was also confirmed by Fourier optics. When resonant, the transmission to the detector was reduced.