Nonlocal effect on optic spectrum of a periodic dielectric-metal stack

Abstract

On the basis of the formalism of the Boltzmann kinetic equation for the distribution function of the conduction electrons, the photonic band structure of binary dielectric-metal superlattice is theoretically studied. Using the constitutive nonlocal relation between the electrical current density and the electric field inside the metallic layer, the dispersion equation for photonic eigenmodes in the periodic stack is analytically expressed in terms of the surface impedances at the interfaces of the metal and dielectric layers. In the case of very thin metallic layers, the optic spectrum for the superlattice exhibits narrow pass bands as a result of the strong contrast between the impedances of the dielectric and the metal. The narrow pass bands are attributed to Fabry-Perot resonances in the relatively-thick dielectric layer. The metal nonlocality is well pronounced in the infrared and, therefore, the nonlocal effect upon the photonic band structure of the superlattice can be strong when the Fabry-Perot resonance bands are in that frequency range. Our results for the photonic spectrum have been compared with those obtained within the local Drude-Lorentz model. Noticeably differences not only in the the magnitude, but also in the sign of the real part of the Bloch wave number in the Fabry-Perot resonance bands, have been found.

Nonlocal effect on transverse-magnetic photonic properties of periodic dielectric-metal stacks

“…Solution of equation (20) with boundary conditions equations ( 21) is easily found. Substituting it into equation (17) and performing integration over the Fermi sphere, we obtain the desired equations relating the components of the electrical current density with the corresponding components of the electric field…”

“…It is not difficult to check that in the case of normal propagation, θ=0, equation (46) becomes a dispersion relation obtained in [20].…”

Quantum discretization of Landau damping

“…This phenomenon is well manifested under conditions of strong spatial dispersion, or nonlocality, of the metal. Particularly, it has been studied in bulk samples (see, for example, [1] and references therein), thin films [3] and metal-dielectric periodic heterostructures [4][5][6] within the framework of the semiclassical formalism of the Boltzmann kinetic equation for the distribution function of the conduction electrons. As was shown there, Landau damping always exists and considerably alters the absorption, reflection and transmission spectra of all those metal systems within the THz and near-infrared frequency range.…”

“…In Sec. 4, we obtain explicit expressions for the surface impedances of both boundaries of the nanoslab in order to study its external response. Here, from the general expressions for the surface impedances we derive asymptotic formulas for three limits of the electromagnetic response of the metal nanoslab: i) the quantum local regime, ii) the semiclassical nonlocal limit, which can also be described by the Boltzmann kinetic equation formalism, and iii) the regime corresponding to the classical Drude-Lorentz local approach.…”

Landau damping of electromagnetic transport via dielectric–metal superlattices

“…The dispersion relation for the Bloch wave number κ of the superlattice is defined by the trace of the unit-cell transfer matrix (see, Ref. [5] for details).…”