Graphene-based hyperbolic metamaterial
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Abstract:
We introduce a graphene-based composite multilayer structure that exhibits hyperbolic-like wavevector dispersion at terahertz and mid-infrared frequencies. The multilayer structure comprises graphene sheets separated by dielectric layers. We formulate the effective permittivity tensor of the multilayer using a simple homogenization scheme. In addition, we employ Bloch theory for evaluating the wavevector dispersion for a propagation mode inside the HM, and show that the homogenization scheme is in good agreement with Bloch theory in a very wide spatial spectrum. We report the tunability of transition from elliptic to hyperbolic iso-frequency wavevector dispersion by varying the chemical potential of graphene sheets.Keywords:
Wave vector
Homogenization
Bloch wave
Spatial dispersion
Dispersion relation
We study Bloch wave homogenization of periodically heterogeneous media with fourth order singular perturbations. We recover different homogenization regimes depending on the relative strength of the singular perturbation and length scale of the periodic heterogeneity. The homogenized tensor is obtained in terms of the first Bloch eigenvalue. The higher Bloch modes do not contribute to the homogenization limit.
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Bloch wave
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The periodic structure of a photonic crystal causes the propagating waves to be governed by Bloch's theorem: they are composed of multiple wave vectors or harmonics. We found, by measuring the field with phase-sensitive near-field microscopy, that the evanescent field of the composite Bloch wave decays nonexponentially as a function of height. Even the individual Bloch harmonics, having only a single wave vector along the propagation direction, do not necessarily decay single exponentially, which has its origin in the spread of wave vectors required to confine the light to the waveguide. The complex decay leads to an evolution of the mode pattern as a function of the height above the structure.
Bloch wave
Wave vector
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Homogenization
Spatial dispersion
Dispersion relation
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We study the properties of nonlinear Bloch waves in a diamond chain waveguide lattice in the presence of a synthetic magnetic flux. In the linear limit, the lattice exhibits a completely flat (wavevector k-independent) band structure, resulting in perfect wave localization, known as Aharonov–Bohm caging. We find that in the presence of nonlinearity, the Bloch waves become sensitive to k, exhibiting bifurcations and instabilities. Performing numerical beam propagation simulations using the tight-binding model, we show how the instabilities can result in either the spontaneous or controlled formation of localized modes, which are immobile and remain pinned in place due to the synthetic magnetic flux.
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Wave vector
Lattice (music)
Bloch oscillations
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<p style='text-indent:20px;'>In this work, we study Bloch wave homogenization of periodically heterogeneous media with fourth order singular perturbations. We recover different homogenization regimes depending on the relative strength of the singular perturbation and length scale of the periodic heterogeneity. The homogenized tensor is obtained in terms of the first Bloch eigenvalue. The higher Bloch modes do not contribute to the homogenization limit. The main difficulty is the presence of two parameters which requires us to obtain uniform bounds on the Bloch spectral data in various regimes of the parameter.</p>
Homogenization
Bloch wave
Spectral gap
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We study Bloch wave homogenization of periodically heterogeneous media with fourth order singular perturbations. We recover different homogenization regimes depending on the relative strength of the singular perturbation and length scale of the periodic heterogeneity. The homogenized tensor is obtained in terms of the first Bloch eigenvalue. The higher Bloch modes do not contribute to the homogenization limit.
Homogenization
Bloch wave
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The warm-fluid equation derived from the drift kinetic equation is solved numerically to investigate the electrostatic low-frequency stability of an electron ribbon beam drifting in the crossed-fields of a planar magnetron. The temperature effect is manifested only for oblique propagation with respect to the drifting beam direction. The dispersion relation takes the form ω = ω( k⊥/ks∥) = ω(ks∥/k⊥ ), where k⊥ and k⊥ are respectively the components of the surface wave vector k parallel and perpendicular to the magnetic field. The obliqueness of the propagation direction and the non-zero temperature give rise to a resonant instability, in addition to the diocotron instability, and the wavenumber corresponding to the maximum diocotron growth rate shifts as the temperature changes.
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Wavenumber
Wave vector
Vlasov Equation
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The surface plasmons of a semi-infinite superlattice are studied. Analytical expressions for the dispersion relation and critical wave vector are derived in a hydrodynamic model. The analytical results agree with the numerical results within the random-phase approximation.
Dispersion relation
Wave vector
Semi-infinite
Random phase approximation
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Periodic homogenization result for selfadjoint operators via Bloch wave method was obtained by Conca and Vanninathan in [12]. Even though the spectral tools used in [12] are not available in non‐selfadjoint case, it is possible to recover the complete homogenization result of Murat and Tartar in the periodic case through the Bloch wave method. A dominant Bloch mode is introduced and plays the key role in the homogenization process. It is also established that the remainder does not contribute in the homogenization process. This requires separation of scales between the dominant Bloch mode and the rest. This separation is proved via a Poincaré‐type inequality. Further, the proof of homogenization theorem of [12] is simplified.
Homogenization
Elliptic operator
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An addition theorem is derived which describes how the Bloch wave vectors, for a given energy, of two pure one-dimensional lattices are to be combined to obtain the Bloch wave vector for a composite lattice formed of the two pure lattices. Applications are discussed. The theorem is valid for an ordered or a disordered lattice, but the detailed nature of the energy bands of a disordered lattice is determined by the details of the structure of the disordered array.
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Lattice (music)
Wave vector
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