Effect of optical nonreciprocity in crystals

Abstract

The property of a material medium to provide different conditions for light propagation in the opposite directions is usually called optical nonreciprocity. This nonreciprocity can be related to the phase (propagation velocity), amplitude, and polarization of an electromagnetic wave. This work is focused on the optical nonreciprocity in phase, which is caused by different propagation velocities of the electromagnetic wave in the opposite directions. The optical nonreciprocity of a substance is usually manifested only when it is exposed to various external fields. However, from the general theoretical standpoint, the natural optical nonreciprocity in certain crystals may exist in the absence of any external fields. In my opinion, the existence of an intracrystalline electromagnetic field is one of the causes responsible for the natural optical nonreciprocity of a crystal. In this case, the preferential direction along which the optical nonreciprocity is maximal is determined by the vector product of intracrystalline electric and magnetic fields averaged over physically infinitesimal volumes. If the average value of this product in a crystal is nonzero, then the optical nonreciprocity can arise due to the nonlinearity of vacuum electrodynamics. As is well known [1], recent experiments at the Stanford accelerator confirmed that vacuum electrodynamics is nonlinear theory. Therefore, the propagation of electromagnetic waves in external electromagnetic fields differs from that in vacuum. In particular, as was shown in [2, 3], the propagation velocity of electromagnetic waves in the direction of the vector product of the external electric and magnetic fields differs from that in the opposite direction. It is worth noting that, in addition to the intracrystalline electromagnetic field, other causes can be responsible for the natural optical nonreciprocity in crystals. Therefore, one of the urgent problems of crystal optics is the theoretical study of various mechanisms responsible for the optical nonreciprocity and investigation of laws governing the propagation of electromagnetic waves in nonreciprocal crystals. The search for experimental methods for studying this phenomenon and experimental verification of its various possible mechanisms are also very important. Below, ignoring the details of various mechanisms that provide the natural optical nonreciprocity in crystals, we analyze basic laws governing the propagation of electromagnetic waves in them. In order to solve the posed problem, it is convenient to write the coupling equations in the form D = D ( B , E ), H = H ( B , E ) . This study is focused on the analysis of phenomena in anisotropic media in the presence of relatively weak electromagnetic fields, when nonlinear effects can be neglected. In this case, the coupling equations can be written as