Anti-Symmetric Medium Chirality Leading to Symmetric Field Helicity in Response to a Pair of Circularly Polarized Plane Waves in Counter-Propagating Configuration

Abstract

We examine how a chiral medium responds to a pair of plane waves of circular polarizations. To this goal, we assume the chiral medium to be spatially homogeneous for simplicity. By assuming the medium to be a lossless, we provide analytic formulas of key bilinear parameters such as the pair of electromagnetic and reactive Poynting vectors in addition to the pair of electromagnetic and reactive helicities. By examining two obliquely colliding plane waves, we learned that most of those key parameters are asymmetric with respect to the medium chirality. Only for a counter-propagating pair, some of those key parameters are found to exhibit symmetry with respect to the medium chirality. We will discuss the implications of those asymmetries and symmetries from the viewpoints of typical applications in optics and physics.

Spin-Orbital Coupling and Conservation Laws in Electromagnetic Waves Propagating through Chiral Media

“…for the chiral case with 0   . It is well-founded that compressible inviscid fluid flows admit bicharacteristics that consist of the reference sound speed plus and minus the fluid speed [8,19,20]. In this respect, it is illustrative to draw an analogy between our chiral case and our earlier work on fluid mechanics [21].…”

“…QQ , and (iii) the Helmholtz equations [3] and Supplementary Material of [8] for details. In this regard, it is often overlooked that  …”

“…for the Faraday and Ampère law in Equation ( 3). Taking the difference and the sum of the resulting two relations, we obtain the following pair of energy conservation laws [8].…”

“…In the first pair of Equation ( 14), 0 → = P is the familiar energy conservation law. In comparison, 20 avg J → +  = P has been explicitly derived in [8] for the first time, although its variants have been presented elsewhere [15]. Meanwhile, the second pair of Equation ( 14) is trivially satisfied.…”

“…For instance, the scattering coefficients obtained for the Mie scattering represent essentially the Poynting vector [3,6]. Additional aspects of chiral media are discussed by us [8] with recent references.…”