Nonreciprocity in photonic crystals: indirect photonic band gaps, unidirectional superprisms, and negative refraction

Abstract

We have theoretically investigated wave propagation in nonreciprocal photonic crystals (PC), which break simultaneously space-inversion and time-reversal symmetries. We identify a remarkable set of properties that are consequences of simply imposing the two symmetry constraints (independent of material choices, dimensionality, etc.). The model material system that we have investigated is a 1D periodic, lossless dielectric helical medium with magnetooptic activity for which we obtained both analytic and numerical solutions of the dispersion relations. We show that nonreciprocal PC display indirect photonic band gaps (band edges are not aligned in k-space, by analogy with the electronic case) even in the 1D case. Furthermore, we find that these PC support backward wave eigenmodes (opposite group and phase velocities). By analyzing the isofrequency contour diagrams, we show that it is also possible to obtain negative refraction at the interface between air and the photonic crystal, that nonlinearities of the photonic bands allow for superprism effects which differ from the known case by being unidirectional (i.e. not present if the light path is reversed), and that the propagation direction of light waves inside the nonreciprocal PC can be laterally deflected by perpendicular magnetic fields.