Near-Field Behaviors of Internal Energy Flows of Free-Space Electromagnetic Waves Induced by Electric Point Dipoles

Abstract

Both orbital and spin energy fluxes constitute the internal flows decomposed from a Poynting vector. For generic electromagnetic waves propagating through source-free media, these energy fluxes are quadratic in field variables so that their properties are not easily predictable. Notwithstanding, their near-field behaviors play important roles in nanoscale photonics. For time-oscillatory fields, we found two hitherto-overlooked distinctions between the two internal flows. The first is an unequal level between them because the vorticity of an orbital energy flux plays a role comparable to a spin energy flux itself. The second is regarding the electric-magnetic dual symmetry in handling the two internal flows, whence the reactive helicity plays a role as important as the electromagnetic helicity. By helicity conservation, an inter-electric-magnetic transport is possible for the spin angular momentum density, while the electric and magnetic constituents of orbital energy fluxes admit only respective intra-electric and intra-magnetic transports. We have tested the validities of all these claims by exemplarily taking the electromagnetic fields induced by an electric point dipole, either a linear or a circular one. We have thus made new contributions not only in deriving explicit forms of the internal energy flows but also in revealing the magnetic activities hidden under the electromagnetic waves induced by electric point dipoles.

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

“…This relation is reduced to M O S now occupy the same hierarchy or level. This hierarchy issue has been discussed in our recent paper [12] for achiral medium. We have thus extended this hierarchy structure to the chiral case in this study, thereby constituting another key contribution of this study.…”

“…has been fully discussed with a proper example with the EM fields induced by electric point dipoles [12]. Notice hence that Equation (15) holds true not only to a achiral case but also to a chiral case.…”

“…Therefore, the active and reactive Poynting vectors is completely separable into its spin and orbital portions. Such an achiral case has already been investigated for the freespace EM fields induced by electric point dipoles [12]…”

“…Based on the variables of electric and magnetic fields of a certain EM wave, several key parameters can be formed for further analysis. Such a bilinear parameter can be formed either for an electric field or for a magnetic field [12]. To be fair, an average parameter can be further constructed based an electric-magnetic duality [13][14][15].…”

“…with counter-propagating waves in[8]. It is noteworthy that   , even for achiral cases as we have recently examined in[7] and[12]. Consequently, each wave configuration needs to be closely investigated for the behaviors of   ,…”