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DD12.9.1

Two-dimensional Magneto-photonic Crystal Circulators Zheng Wang1, Shanhui Fan Department of Electrical Engineering, Stanford University, Stanford, CA 94305 1 Department of Applied Physics, Stanford University, Stanford, CA 94305-4090 ABSTRACT Previous 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 counterrotating whispering-gallery like modes, oscillating at different frequencies. As a physical realization, we synthesize two singly-degenerate circularly-hybridized modes in a twodimensional 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 sidecoupling 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.

INTRODUCTION Integrated non-reciprocal optical devices, such as optical isolators and circulators, can play very important roles in densely integrated optical circuits. Besides their usual application in eliminating the detrimental reflections to laser sources, integrated non-reciprocal devices also simplify the design of large scale optical circuits by suppressing multiple reflections between components, and thereby improving tolerance with respect to fabrication imperfections and environmental fluctuations. Enhanced Faraday rotation in one-dimensional magneto-optical photonic crystal (PC) cavities has attracted much research attention recently [1]. Here we explore nonreciprocal resonators in two-dimensional photonic crystals. Such resonators are of great advantages in onchip circuits, due to their strong field confinement and fabrication compatibility. We numerically demonstrate a broadband three-port circulator in two-dimensional PCs, where the domain

DD12.9.2

structures of the ferromagnetic material in the resonator are sp