Electromagnetic dynamical characteristics of a surface plasmon-polariton

Abstract

We consider an electromagnetic field near the interface between two media with arbitrary real frequency-dependent permittivities and permeabilities, under conditions supporting the surface plasmon-polariton (SPP) propagation. The dispersion of the electric and magnetic properties is taken into account based on the recent approach for description of the spin and momentum of electromagnetic field in complex media [Phys. Rev. Lett. 119, 073901 (2017); New J. Phys., 19, 123014 (2017)]. It involves the Minkowski momentum decomposition into spin and orbital parts with the dispersion-modified permittivities and permeabilities. Explicit expressions are derived for spatial densities of the energy, energy flow, spin and orbital momenta and angular momenta of the transverse-magnetic (TM) SPP field. The expressions are free from nonphysical singularities; the only singular contribution describes a strictly localized surface part of the spin momentum that can be associated with the magnetization current in the conductive component of the SPP-supporting structure. On this ground, a phenomenological theory of the SPP-induced magnetization (predicted earlier based on the simplified microscopic approach) is outlined. Possible modifications and generalizations, including the transverse-electric (TE) SPP waves, are discussed. IntroductionDuring the past decades, a significant interest has been attracted to the study of localized optical fields associated with interfacial regions between nanostructured metals and dielectrics [1][2][3][4][5][6]. Especially, the running evanescent surface waves (surface plasmon-polaritons, SPP) are intensively investigated in connection with the optical nano-probing and precise optical manipulation. Additionally, the SPP fields pave new ways for the light wave-guiding, switching and controlling by sub-wavelength elements, which is crucial for further microminiaturizing of optical information devices and systems. Many applications are stimulated by the unique dynamical properties of the evanescent waves and SPPs, in particular, the transverse spin and momentum [7-9], the special spin-momentum locking [9,10], nonreciprocity and unidirectional propagation [9][10][11][12].Earlier, the wide application of SPP-based techniques was restricted by the rather special requirements to materials that support efficient SPP generation and propagation [2][3][4][5]. However, with advent of a novel class of engineered composite materials, including the metamaterials, lefthanded materials, sculptured films, etc. [4,[13][14][15][16], almost any combination of the electric and magnetic parameters in the optical frequency range is becoming available [4,10,[17][18][19], which offers additional and unexpected possibilities for the research and applications. As a rule, exclusive properties of new materials are accompanied by the strong dispersion (frequency dependence of the

Microscopic analysis of the energy, momentum, and spin distributions in a surface plasmon-polariton wave

“…This discontinuity owes completely to the dispersion [23]: when 2     , Eqs. ( 22), (23) describe the "naïve" (dispersion-free) Minkowski spin which is continuous due to the definition (21) and the boundary conditions (2).…”

“…Together with the strong spatial inhomogeneity of the SPP-supporting systems, this poses challenges in the theoretical description of the SPP field, especially its dynamical characteristics (DCs): energy, energy flow, momentum, angular momentum and their derivatives. The main problems relating the proper DC description in such "complex" media were recently resolved in a series of works [13][14][15][16][17][18][19][20][21][22][23]. This approach is, in fact, a generalization of the known Brillouin's method for the energy description in lossless dispersive media, which is based on the special dispersive corrections of their permittivities and permeabilities [24,25].…”

“…Being applied to the SPP field, this methodology offers a physically meaningful and consistent description of its momentum and angular momentum with their dependence on the media's properties and the radiation frequency [20][21][22][23]. Importantly, this phenomenological approach is justified by the microscopic analysis [20][21][22] based on the simplest lossless Drude model [2,5] for the electron gas in the metal.…”

Extraordinary transverse spin: hidden vorticity of the energy flow and momentum distributions in propagating light fields

“…Note also that the longitudinal momentum in the right-hand side of the spin-momentum rule (42) includes the orbital momentum and the helicity-dependent part of the SM rresponds to negligible energy dissipation). In such a system, a doubleevanescent TM wave may propagate along the interface with electric and magnetic field distributions [11,20,28,29] 41), (42) reduces to the simple rule of (31) in two cases: (i) for arbitrary waves if the dispersion is absent and (ii) for arbitrary dispersion if the waves' polarizations obey the condition…”

“…2 are calculated in Ref. [29]. The TM SPP represents a "classical" ES situation where the whole momentum is longitudinal and the whole spin is extraordinary.…”