August 31, 2005
The geometric representation at a fixed frequency of the wavevector (or dispersion) surface $\omega(\vec k)$ for lossless, homogeneous dielectric--magnetic uniaxial materials is explored, when the elements of the relative permittivity and permeability tensors of the material can have any sign. Electromagnetic plane waves propagating inside the material can exhibit dispersion surfaces in the form of ellipsoids of revolution, hyperboloids of one sheet, or hyperboloids of two sheets. Furthermore, depending on the relative orientation of the optic axis, the intersections of these surfaces with fixed planes of propagation can be circles, ellipses, hyperbolas, or straight lines. The obtained understanding is used to study the reflection and refraction of electromagnetic plane waves due to a planar interface with an isotropic medium.
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February 28, 2017
In this overview paper, we investigate the dispersion of electromagnetic waves for dissipative and non-dissipative dielectric-magnetic uniaxial mediums. Changing the sign of one component of dielectric permittivity ({\epsilon}) or magnetic permeability ({\mu}) from positive to negative will lead to sixteen different cases (real or imaginary) for a non-dissipative medium and eight different cases for dissipative one. In a non-dissipative medium, dispersion relations follow the...
June 7, 2005
The dispersion relations for conventional uniaxial dielectric mediums may be characterized as elliptical or elliptical-like, according to whether the medium is nondissipative or dissipative, respectively. However, under certain constitutive parameter regimes, the dispersion relations may be hyperbolic or hyperbolic-like. We investigate planewave propagation in a hyperbolic/hyperbolic-like uniaxial dielectric medium. For both evanescent and nonevanescent propagation, the phase...
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Surface polaritons in an anisotropic media posses a strong dependence of the wavevector on the propagation direction, which is called the isofrequency contour. This can lead to the fact that polariton propagation will be possible in a limited range of angles in the boundary plane. Notable examples are Dyakonov surface waves at the boundary of two dielectrics and hyperbolic plasmons in a hyperbolic metamaterial. Exact closed-form solutions of the polariton dispersion equation ...
August 3, 2015
We analyze surface electromagnetic waves with hyperbolic dispersion supported at the interface between a semi-infinite isotropic medium and an effective uniaxial material. Apart from known types plasmons with hyperbolic dispersion curve, sometimes referred to as Dyakonov plasmons [Z. Jacob and E. E. Narimanov, APL 93, 221109 (2008)], we classify two new types of surface waves with hyperbolic dispersion. One type of such waves, in contrary to Dyakonov plasmons, does not requir...
August 21, 2023
Despite the apparent simplicity, the problem of refraction of electromagnetic waves at the planar interface between two media has an incredibly rich spectrum of unusual phenomena. An example is the paradox that occurs when an electromagnetic wave is incident on the interface between a hyperbolic medium and an isotropic dielectric. At certain orientations of the optical axis of the hyperbolic medium relative to the interface, the reflected and transmitted waves are completely ...
May 10, 2006
We investigate the reflection and refraction behaviors of electromagnetic waves at the interface between an isotropic material and the anisotropic medium with a unique dispersion relation. We show that the refraction angle of whether phase or energy flow for $E$-polarized waves is opposite to that for $H$-polarized waves, though the dispersion relations for $E$- and $H$-polarized waves are the same in such anisotropic media. For a certain polarized wave the refraction behavio...
May 22, 2006
We investigate the wave propagation in the anisotropic metamaterial with single-sheeted hyperboloid dispersion relation. Based on boundary conditions and dispersion relations, we find that the opposite amphoteric refraction, such that E- (or H-) polarized waves are positively refracted whereas H- (or E-) polarized waves are negatively refracted, can occur at the interface associated with the anisotropic metamaterial. Under a certain condition, both E- and H-polarized waves ca...
November 23, 2014
We present a general method for retrieving the effective tensorial permittivity of any uniaxially anisotropic metamaterial. By relaxing the usually imposed condition of non-magnetic metal/dielectric metamaterials, we also retrieve the permeability tensor and show that hyperbolic metamaterials exhibit a strong diamagnetic response in the visible regime. We obtain global material parameters, directly measurable with spectroscopic ellipsometry and distinguishable from mere wave ...
May 28, 2013
We theoretically study negative refraction of inhomogeneous waves at the interface of lossy isotropic media. We obtain explicit (up to the sign) expressions for the parameters of a wave transmitted through the interface between two lossy media characterized by complex permittivity and permeability. We show that the criterion of negative refraction that requires negative permittivity and permeability can be used only in the case of a homogeneous incident wave at the interface ...
April 15, 2016
The extreme magnetoelectric medium (EME medium) is defined in terms of two medium dyadics, $\alpha$, producing electric polarization by the magnetic field and $\beta$, producing magnetic polarization by the electric field. Plane-wave propagation of time-harmonic fields of fixed finite frequency in the EME medium is studied. It is shown that (if $\omega\neq 0$) the dispersion equation has a cubic and homogeneous form, whence the wave vector $k$ is either zero or has arbitrary ...