Tailoring Light with Photonic Crystal Slabs : From Directional Emission to Topological Half Charges

Photonic crystal slabs are a versatile and important platform for molding the flow of light. In this thesis, we consider ways to control the emission of light from photonic crystal slab structures, specifically focusing on directional, asymmetric emission, and on emitting light with interesting topological features. First, we develop a general coupled-mode theory formalism to derive bounds on the asymmetric decay rates to top and bottom of a photonic crystal slab, for a resonance with arbitrary in-plane wavevector. We then employ this formalism to inversionsymmetric structures, and show through numerical simulations that asymmetries of top-down decay rates exceeding 104 can be achieved by tuning the resonance frequency to coincide with the perfectly transmitting Fabry-Perot frequency. The emission direction can also be rapidly switched from top to bottom by tuning the wavevector or frequency. We then consider the generation of Mobius strips of light polarization, i.e. vector beams with half-integer polarization winding, from photonic crystal slabs. We show that a quadratic degeneracy formed by symmetry considerations can be split into a pair of Dirac points, which can be further split into four exceptional points. Through calculations of an analytical two-band model and numerical simulations of two-dimensional photonic crystals and photonic crystal slabs, we demonstrate the existence of isofrequency contours encircling two exceptional points, and show the half-integer polarization winding along these isofrequency contours. We further propose a realistic photonic crystal slab structure and experimental setup to verify the existence of such Mobius strips of light polarization. Thesis Supervisor: Marin Solja-id Title: Professor of Physics and MacArthur Fellow