Abstract
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.
Highlights
Cylindrical electromagnetic waves around a cylindrical obstacle have been investigated for a long time [15]
Prompted by the upper bound on |sz| defined through both Eqs. (6.6) and (6.7), we introduce two additional degrees of polarization Πrθ,1 and Πrθz
In summary, we have revisited the plasmonic resonances around a metallic nanowire, but in the presence of both energy absorption and energy radiation
Summary
Cylindrical electromagnetic waves around a cylindrical obstacle have been investigated for a long time [15]. The collective electronic motions in metals are in resonance with electromagnetic waves [10, 28], which are called plasmonic waves [29] Through this example of plasmonic waves, we are here to explain several consequences resulting from the energy balance between the radiating outgoing waves and the absorptive incoming waves. Since Maxwell’s equations are linear, the magnetic field can assume the following normalized forms respectively in the interior and exterior [17, 18, 36]. The residual function RD for the exterior is defined as follows with the help of GDm;AðqÞ defined previously in Eq (1.1) Notice that both RM and RD arise essentially from the respective field profiles given in Eq (2.7). To the best of the author’s knowledge, the particular dispersion relation RM 1⁄4 RD in Eq (2.10) is derived here for the first time in the presence of both energy radiation and absorption
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