THz photonic bands of periodic stacks composed of resonant dielectric and nonlocal metal

We provide a functional framework and a numerical algorithm to compute the Bloch variety for Maxwell's equations when the electric permittivity is frequency dependent. We incorporate the idea of a mixed formulation for Maxwell's equations to obtain a quadratic eigenvalue for the wave-vector in terms of the frequency. We reformulate this problem as a larger linear eigenvalue problem and prove that this results in the need to compute eigenvalues of a compact operator. Using finite elements, we provide preliminary numerical examples of the scheme for both frequency independent and frequency dependent permittivity.

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“…Now let us introduce a stable mixed formulation using ( 6) - (7). Let H(C) denote the space consisting of constant functions on Ω.…”

Section: The Mixed Formulationmentioning

confidence: 99%

“…Proof. First suppose u is a solution to (2)-(3), then from equation ( 6)- (7), one can see that (u, 0, 0) ∈ H p (curl ; Ω) × H 1 p (Ω) × H(C) and η satisfy the quadratic eigenvalue problem ( 9)- (10).…”

Section: The Mixed Formulationmentioning

confidence: 99%

Determination of electromagnetic Bloch variety in a medium with frequency-dependent coefficients

Lackner¹,

Meng

Monk

2019

Journal of Computational and Applied Mathematics

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Quantum discretization of Landau damping

Castillo-López

Pérez-Rodrı́guez

Makarov

2018

Low Temperature Physics

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We derive and analyze analytical expressions for the quantum electron current density and electromagnetic field distribution inside a metallic nanoslab. Besides, we obtain general explicit expressions for the surface impedances of both metal slab boundaries. We found that the phenomenon of Landau damping manifests itself in the frequency dependence of the surface impedances as resonances associated with the discretization of the electromagnetic and electron wave numbers inside the metal nanoslab. In particular, the quantum nonlocal resonances of the surface impedances are clearly discernible at slab thicknesses smaller than the electromagnetic skin depth. The predictions for the surface impedances in the quantum regime turn out to be radically different from those of the quantum local approach, the semiclassical Boltzmann kinetic equation formalism and the classical Drude-Lorentz local model. The analytical study completely agrees with the respective numerical calculations.

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