Nonlocal dispersion anomalies of Dyakonov-like surface waves at hyperbolic media interfaces

Diversiform hybrid-polarization surface plasmon polaritons in a dielectric–metal metamaterial

“…For simplicity and explicitness, the damping term in the metal permittivity is ignored in the process of analyzing and calculating their dispersion properties, as is usually done. 9,17,18,[20][21][22][23][24] Under the EMT, this MM is equivalent to a uniaxial effective medium with the optical axis along the structure-period direction. Its effective permittivity tensor is written as…”

“…The electric or magnetic field in or above the MM is equal to the product of its complex amplitude vector and the relevant phase term. The wave equations in the MM can yield two independent solutions, 13,20,21 one of which is the ordinary wave and the other is the extraordinary wave. For later discussion, we present a simple analytical process of solving the two solutions.…”

“…[18][19][20][21] In contrast to the above interface system, a layered metal-dielectric MM and an isotropic dielectric form another interface system, where HSPPs should result from the interface coupling of the ordinary evanescent wave in the dielectric and the ordinary and extraordinary evanescent waves in the MM, [20][21][22][23][24] and were called the Dyakonov-like surface wave. 20,25,26 These works 20-24 took a negative constant or an experimental value at a fixed frequency to replace the real part of metal permittivity and directly used the dispersion equations in Ref. 13, so they provided only the iso-frequency dispersion curves of the HSPP.…”

“…In fact, metals are a kind of dispersive media in the optical frequency range, so their permittivity is a function of frequency. In addition, we know that lower metal filling ratios were usually applied 20,21,26 to discuss HSPPs at the interface between the MM and an isotropic dielectric, so the works mentioned above could not give all possible HSPPs of the MM. In such a case, here, we focus on dispersion properties of the HSPPs at the interface between the layered MM and air (or the plot of their frequency versus wave vector), where the metal permittivity is described with an improved Drude model, i.e.…”

“…This permittivity is qualitatively equivalent to that used in other references. 17,18,20,21 We use ε d to denote the dielectric constant of dielectric layers. ε m and ε d are relative to the dielectric constant of vacuum (ε 0 ).…”