In this Letter, we investigate a magnetic field induced by guiding plasmonic modes in graphene-coated nanowire via an inverse Faraday effect. Magnetic field distribution for different plasmonic modes has been calculated. It has been shown that a magnetic field has a vortex-like distribution for some plasmonic modes. The possibility of producing magnetic field distribution that rotates along the nanowire axis and periodically depends on azimuthal angle has been demonstrated.

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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.

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We examine the conservation of electromagnetic energy for systems involving metal-like constituents, not only for continuous waves with real frequencies but also for temporally attenuated waves with complex frequencies. For this purpose, we derive a generic conservation law in terms of attenuated time-harmonic waves, thereby identifying the dual role played by the material loss on the dissipation and conserved energy. As the simplest example, we analyze absorption spectra for single-interface plasmon resonances along with energy flows through the bounding surfaces. By these formulations, we could infer basic working principles of both metal wire photonic crystals and the optical vortices.