Two-dimensional Magneto-photonic Crystal Circulators

Abstract

ABSTRACTPrevious research has demonstrated enhanced Faraday rotation in one-dimensional magnetic photonic crystals, where nonreciprocity in magneto-optical cavities is resonantly enhanced to provide optical isolation in optical paths on the scale of a few microns. In this paper, we study the nonreciprocity of two-dimensional magnetic photonic crystal resonators to allow further miniaturization and monolithic in-plane integration with current integrated optical devices. The nonreciprocal magnetic resonators are constructed by alternating the magnetization directions of the ferromagnetic domains in cavities side-coupled to photonic crystal waveguides. We show analytically that the gyrotropic splitting and the strength of the magnetic hybridization of the cavity modes are determined by the overlap integral between the domain magnetization vector and the modal cross product. With a large overlap obtained from optimizing the domain structures, we circularly hybridize two nearly degenerate modes to form a pair of counter-rotating whispering-gallery like modes, oscillating at different frequencies. As a physical realization, we synthesize two singly-degenerate circularly-hybridized modes in a two-dimensional crystal formed of a triangular air hole lattice in bismuth iron garnet with a TE bandgap. We tune the magnetic splitting and the decay constants of the rotating modes to demonstrate numerically a three-port optical circulator with a 30dB extinction bandwidth of 35GHz at 1550nm. An alternative implementation of a four-port circulator is achieved by side-coupling a point defect to two parallel waveguides. Our numerical experiments are performed with finite-difference time-domain simulations and agree well with the analytical coupled-mode theory predictions.