Surface-plasmon-polariton wave propagation supported by anisotropic materials: Multiple modes and mixed exponential and linear localization characteristics

Abstract

The canonical boundary-value problem for surface-plasmon-polariton (SPP) waves guided by the planar interface of a dielectric material and a plasmonic material was solved for cases wherein either partnering material could be a uniaxial material with optic axis lying in the interface plane. Numerical studies revealed that two different SPP waves, with different phase speeds, propagation lengths, and penetration depths, can propagate in a given direction in the interface plane; in contrast, the planar interface of isotropic partnering materials supports only one SPP wave for each propagation direction. Also, for a unique propagation direction in each quadrant of the interface plane, it was demonstrated that a new type of SPP wave -called a surface-plasmon-polariton-Voigt (SPP-V) wave -can exist. The fields of these SPP-V waves decay as the product of a linear and an exponential function of the distance from the interface in the anisotropic partnering material; in contrast, the fields of conventional SPP waves decay only exponentially with distance from the interface. Explicit analytic solutions of the dispersion relation for SPP-V waves exist and help establish constraints on the constitutive-parameter regimes for the partnering materials that support SPP-V-wave propagation. * E-mail: T.Mackay@ed.ac.uk. arXiv:1907.07211v2 [physics.optics] 4 Sep 2019 readily achieved indirectly via coupling with a prism [2][3][4] or surface-relief grating [5], for examples. SPP waves are of major technological importance: they have been widely exploited for optical sensing [5-7] and microscopy [8,9], and applications for optical communications [10][11][12][13][14] and harvesting solar energy [15][16][17] are on the horizon.The theory underpinning SPP-wave propagation is firmly established in the case where the two partnering materials are isotropic [1]. The case where an isotropic plasmonic material is partnered with an anisotropic dielectric material has also been considered previously [18][19][20]. However, SPP-wave propagation in the case where an anisotropic plasmonic material is partnered with an isotropic dielectric material has received scant attention from theorists, even though several experimental studies on this case have been reported recently [21][22][23][24][25][26].As we demonstrate in this paper, when anisotropic partnering materials are involved, some previously unreported SPP-wave characteristics emerge. Most notably, two different SPP waves, with different phase speeds, propagation lengths, and propagation depths, can propagate in a given direction in the interface plane. Analogously, this multiplicity of surface waves can also arise in the case of Dyakonov-wave propagation supported by dissipative anisotropic materials [27], and has also been reported in the case of SPP-wave propagation supported by periodically nonhomogeneous dielectric materials [28,29].Additionally, we demonstrate that when anisotropic partnering materials are involved, for a unique propagation direction in each quadrant of the interface plane...

Theory of Dyakonov–Tamm surface waves featuring Dyakonov–Tamm–Voigt surface waves

“…The unusual localization characteristics of DTV surface waves mirror those of Dyakonov-Voigt surface waves [35,40] and surface-plasmon-polariton-Voigt waves [41]. While the existence of DTV surface waves is established theoretically herein for an idealized scenario, i.e., the canonical boundary-value problem, further studies are required to elucidate the excitation of such waves and their propagation for partnering materials of finite thicknesses.…”

New Electromagnetic Surface Waves [Around the Globe]

“…In a related study, another new type of surface wave, namely a su r face -plasmonpolariton-Voigt (SPPV) wave [3], recently emerged as the solution to a canonical boundary-value problem involving the interface of an anisotropic insulator and a metal. The relationship between SPPV waves and SPP waves is analogous to the relationship between DV surface waves and Dyakonov surface waves.…”

Electromagnetic surface waves at exceptional points

“…can be numerically solved for q for a fixed value of ψ, by the Newton-Raphson method [17] Plots of q/k 0 versus ψ for Dyakonov surface waves guided by the planar interface of a non-dissipative uniaxial dielectric medium and a non-dissipative isotropic dielectric medium described by Eqs. (20). (a) ε s A = 1.5, ε t A = 6, and ε B = 1.8 (blue broken-dashed curve), 2 (red dashed curve), 2.2 (green solid curve); (b) ε s A = 1.5, ε B = 2, and ε t B = 5.5 (blue broken-dashed curve), 6 (red dashed curve), 6.5 (green solid curve); and (c) ε t A = 6, ε B = 2, and ε s A = 1.2 (blue broken-dashed curve), 1.5 (red dashed curve), 1.8 (green solid curve).…”

“…Examples of electromagnetic surface waves corresponding to the exceptional points of [P A ] have recently become available [18][19][20], though the exceptional nature of those surface waves has not been demonstrated yet. In order to highlight the exceptional nature of the occurrence of a Voigt surface wave, we now present three examples.…”

“…1(a), the same is not true of ε s A and ε t A as we note from Figs. (20). ε s A = 1.5 + δi and ε t A = 6 + 4δi with δ = 0.1, ε B = 2.0398 + 0.1360i (green solid curves); δ = 0.01, ε B = 2.1320 + 0.0142i (red dashed curves); and δ = 0.001, ε B = 2.2354 + 0.0015i (blue broken-dashed curves).…”