Effective magnetic field for photons based on the magneto-optical effect

We propose to create an effective magnetic field for photons in photonic crystal resonator lattices using the magneto-optical effect. The inter-resonator coupling is mediated by magneto-optical waveguides or magneto-optical resonators, and thus the coupling between the nearest-neighbor photonic crystal resonators acquire a direction-dependent phase. The effective magnetic field can be realized with a proper choice of the spatial distribution of such a direction-dependent phase.

Figure 1

A scheme of photonic resonator lattice with uniform effective magnetic field. The direction-dependent coupling phases (along positive $x$) on the $x$ bonds are labeled and on the $y$ bonds are zero.

Figure 2

(a) Three-dimensional view (left) and top view (right) of a magneto-optical photonic crystal waveguide. The magnetization $M$ is along $y$ axis. Inset is a schematic plot of dispersion splitting of the forward and backward propagating waveguide modes. (b) Three-dimensional view (left) and top view (right) of two photonic crystal resonators coupled through an intermediate magneto-optical waveguide. (c) Top view of a square lattice of photonic crystal resonators with magneto-optical waveguide-mediated coupling along $x$ axis and nonmagneto-optical waveguide-mediated coupling along $x$ axis.

Figure 3

(a) A photonic crystal resonator which supports two degenerate even and odd dipolar modes (schematic) bonded with magneto-optical material (blue). (b) Light transmission through a photonic crystal waveguide side-coupled to a magneto-optical resonator (blue). The magnetization $M$ is along $z$ axis. (c) A square lattice of photonic crystal resonators (red) with magneto-optical resonator-mediated coupling along $x$ axis.