Reversality of optical interactions in noncentrosymmetric media.

We revise the widely accepted belief that linear optical interactions obey time reversality. We have come to the conclusion that the analysis of light– matter interaction should be based on the validity of relativistic reversality, i.e., PT invariance (where T and P are time and space inversion operators), rather than on simple T invariance. Examples of the violation of microscopic reversality for scattering of electrons in a noncentrosymmetric potential were given by Belinicher and Sturman, and here we address the consequences of the lack of space-inversion symmetry on the reversality of optical interactions. All the results presented below are consequences of the propagating electromagnetic wave’s not having a defined parity with respect to space inversion or a defined symmetry with respect to time reversal (see, for example, Ref. 3). We found that the difference between T and PT invariance is significant when relativistic terms in light–matter interaction are taken into account in crystals lacking inversion centers. We show that T -odd interactions may emerge only in first-order spatial dispersion, i.e., wave-vector proportional phenomena, and that in some crystal structures they may be probed optically. This research has been stimulated by recent observations of the time-nonreversible optical phenomenon in noncentrosymmetric cubic crystals that was explained by use of a specific model for a direct-gap zinc blende semiconductor. Here we show that nonreversality is a general feature of nonlocal light–matter interactions in crystals that lack inversion centers and may be predicted without recourse to any particular material. Transformations of the molecular characteristics and electromagnetic fields under space and time inversion have been discussed by numerous sources. – 8 To summarize these results, under the parity operator P molecular characteristics transform as follows: coordinates of the elements of molecular structure r ) 2r, gradients of internal molecular characteristics = ) 2=; kinetic momenta of particles p ­ 2i"s≠y≠rd ) 2p; internal molecular electrostatic potential V srd ) V srd; angular and spin momenta of electrons L ) L; s ) s ; electric field strength Esr, td ) 2Es2r, td; magnetic induction Bsr, td ) Bs2r, td; and vector potential Asr, td ) 2As2r, td [for example, for an electromag-