Nonreciprocal optical Bloch oscillations in garnet/silicon-on-insulator waveguide arrays
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Nonreciprocal optical Bloch oscillations in garnet/silicon-on-insulator waveguide arrays Pradeep Kumar and Miguel Levy Department of Physics, Michigan Technological University, Houghton MI 49931 U.S.A. ABSTRACT We show that nonreciprocal Bloch-like oscillations can emerge in passive optical waveguide arrays with linearly growing effective index in the absence of loss or gain. Spectral asymmetry, a difference in propagation constants and Bloch oscillation periods in opposite propagation directions, are established by imposing different vertical spatial index gradients at the substrate/core, and core/cover interfaces in the presence of transverse magnetization. A model system consisting of an array of transversely magnetized asymmetric garnet/silicon-on-insulator waveguides is presented. INTRODUCTION In the present paper we propose and examine a mechanism for the generation of nonreciprocal optical Bloch oscillations (BO) in a silicon based waveguide array system. Bloch oscillatory motion is a remarkable phenomenon first predicted by F. Bloch and C. Zener in the 1930’s [1] consisting of oscillatory trajectories for particles subject to a constant force in periodic potentials. In optical systems this constant force is replicated by designing into the array a constant difference in waveguide mode index between adjacent waveguides [2-4]. Unequal propagation constants (spectral asymmetry) and different Bloch oscillatory periods in opposite propagation directions are predicted for in-plane transversely-magnetized optical lattices with linearly growing effective index. Upon transverse magnetization in magneto-optic waveguides an interesting phenomenon arises, known as the nonreciprocal phase shift effect [5, 6]. This effect is due to light confinement in magnetized asymmetric waveguides lacking in spatial inversion symmetry. It critically depends on the introduction of unequal spatial gradients in the gyrotropy parameter or refractive index across dissimilar waveguide interfaces. In recent years silicon optics has gained more attention over its ability to provide dense onchip integration of electronic and optic devices. In particular silicon-on-insulator (SOI) with high index contrast offers an excellent platform for micron scale ultra fast electro-optic devices, and hence serves as a motivation to identify useful optical structures based on this material system [7, 8]. The structure we propose consists of a silicon core layer over a silicon dioxide substrate, typical of a silicon-on-insulator (SOI) waveguide structure readily available commercially. The structure has a magneto-optic garnet cover layer, with parameters typical for bismuth-substituted yttrium iron garnet (Bi: YIG) films, such cover layers could be bonded or sputter-deposited over the silicon core [8]. In the present work we model an asymmetric array system of garnet/SOI waveguides; and by imposing a uniform propagation-constant step between adjacent waveguides we make contact with Bloch oscillations and extend previous treatments to passive nonreciprocal sys
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