Abstract
We investigate light spins for cylindrical electromagnetic waves on resonance. To this goal, we consider both a dielectric cylinder of infinite length immersed in vacuum and a cylindrical hole punched through a dense dielectric medium. In order for waves of constant frequencies to be established through lossless media, energy absorption is allowed in the surrounding medium to compensate for radiation loss. The dispersion relation is then numerically solved for an asymmetry parameter implying a balance in energy exchange. Numerical studies are performed by varying parameters of refractive index contrast, azimuthal mode index, and size parameter of a cylindrical object. The resulting data is presented mostly in terms of a specific spin, defined as light spin per energy density. This specific spin is found to be bounded in its magnitude, with its maximum associated with either optical vortices or large rotations. Depending on parametric combinations, the specific spin could not only undergo finite jumps across the material interface but also exhibit limit behaviors.
Highlights
Among various measures characterizing electromagnetic (EM) waves, energy density is the most fundamental one, but it is scalar
The orbital angular momentum (AM) is extrinsic, since it depends on the distance vector between a coordinate center and the point of application
( ) that nin, nex = (2,1) on (a) and (b) for solid ( ) cylinders, whereas nin, nex = (1, 2) on (c) and (d) for cylindrical holes; q = 2π of larger radius for (a) and (c); q = 0.2π of smaller radius for (b) and (d). It is obvious from figure 6(a) and (b) that ∆σ z = 0 or the specific spin is continuous across the material interface for a particular combination of system parameters
Summary
Among various measures characterizing electromagnetic (EM) waves, energy density is the most fundamental one, but it is scalar. As a conjugate configuration to the solid cylinder, we consider a cylindrical hole with its interior having a smaller dielectric constant than that of its exterior In this study, both dielectric media are assumed lossless for the sake of simplicity of analysis. The effects of the cylinder’s size with respect to the wavelength will be investigated By this way, the jumps in the specific spin across the cylindrical dielectric-dielectric interface will be illustrated with varying parameters. In all our results to be presented, the rotational speed represented by the azimuthal mode indices is found to play a pivotal role in revealing distinct features of the specific spin By this way, we will be naturally led to the concept of singularity and optical vortices [25]. Since Maxwell’s equations are linear, the magnetic field can assume the following normalized forms respectively in the interior and exterior. When A ≠ 0 , A denotes the deviation from a perfect balance between outgoing and incoming wave [17]
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