Cylindrical electromagnetic waves with radiation and absorption of energy

Cylindrical electromagnetic waves have been examined mostly with a radiation condition applied at the radial far field. In modern optical technology, there are however growing number of applications where both radiation and absorption of energy should be taken into account. In order to illustrate the ramifications of such energy balance, we take plasmonic waves propagating around a metallic nanowire as an example. Hence, we provide both key mathematical formulas and corresponding numerical results for the collective electronic motions in resonance with electromagnetic waves. Firstly, we show theoretically why a net Poynting energy flow is directed inward to the cylindrical axis. Secondly, we invoke a Cauchy-Schwarz inequality for complex variables in deriving an upper bound on the specific transverse light spin along the axial direction. Thirdly, we could identify both first- and second-order polarizations. Overall, loss-induced and gain-compensated characteristics are illustrated for a dissipative system. In addition, the stability of neutral states are examined by relaxing the angular periodicity.