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Cherenkov Radiation in Uniaxial and Biaxial Anisotropic Media

Marjan Jafari

Published Dec 1, 2019• 0 citations
Publisher

Abstract

Cherenkov radiation is one of the problems in light- matter interaction that can be opened new ideas in quantum electrodynamic. A quantum mechanic approach is presented for Cherenkov radiation of a moving atom in uniaxial and biaxial anisotropic medium. A moving particle in a medium emits Cherenkov radiation when its speed be larger than the phase velocity of light in the medium. The electromagnetic field is quantized in the anisotropic media, using maxwell and related constitute equations, phenomenologically. The Cherenkov radiation for an moving charged particle in the anisotropic medium with arbitrary real permittivity tensor is obtained. The dielectric structure can be changed the Cherenkov radiation. For uniaxial media, we give a close form of the Cherenkov radiation for arbitrary dipole alignment. In this manner, the Cherenkove radiation of the biaxial media is calculated.. It is shown the Cherenkov radiation in an isotropic medium can be obtained from the form of an anisotropic medium.

DOI
10.22128/ijaa.2019.376.1073

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Cherenkov radiation is one of the problems in light- matter interaction that can be opened new ideas in quantum electrodynamic. A quantum mechanic approach is presented for Cherenkov radiation of a moving atom in uniaxial and biaxial anisotropic medium. A moving particle in a medium emits Cherenkov radiation when its speed be larger than the phase velocity of light in the medium. The electromagnetic field is quantized in the anisotropic media, using maxwell and related constitute equations, phenomenologically. The Cherenkov radiation for an moving charged particle in the anisotropic medium with arbitrary real permittivity tensor is obtained. The dielectric structure can be changed the Cherenkov radiation. For uniaxial media, we give a close form of the Cherenkov radiation for arbitrary dipole alignment. In this manner, the Cherenkove radiation of the biaxial media is calculated.. It is shown the Cherenkov radiation in an isotropic medium can be obtained from the form of an anisotropic medium.
The emission properties of atoms lie at the foundations of both quantum theory and light-matter interactions. In the context of macroscopic media, exact knowledge thereof is important both in current quantum technologies and in fundamental studies. While for isotropic media, this is a very well-studied problem, there are still big gaps in the theory of anisotropic media. In particular, to the best of our knowledge, an explicit expression for the spontaneous emission rate in general anisotropic media has not been presented. In this work, we first derive the quantized electromagnetic field operators to calculate the emission rate in uniaxial media. For the more general case of biaxial media we propose an approximate expression based on interpolation between the limiting cases of uniaxial media. We support our model with numerical simulations which are in strong agreement for typical media configurations and, furthermore, show how local field effects can be taken into account in the model.
The macroscopic electromagnetic field is quantized in the presence of a uniformly moving permeable dielectric medium. We begin with the Maxwell-Minkowski equations, and the fields are quantized with the help of the Green function scheme. It is shown that for a homogeneous material, though the medium is assumed to be isotropic in its rest frame, it displays anisotropic character for the observer who detects the field observables in the laboratory frame. The field operators are expressed in terms of two independent infinite sets of bosonic field operators. Special attention is paid to the vacuum field fluctuation in moving media.
We discuss the quantum fluctuations of the fields associated with a broad class of optical scattering and transmission problems by developing the quantum electrodynamics of an idealized linear, but nonuniform, dielectric medium. We present and compare two quantization schemes for this purpose. The first is based on the expansion of the field in terms of a set of single-frequency solutions of the Maxwell equations. The second involves expanding the field in the set of plane-wave solutions of the Maxwell equations in the vacuum. The relation between the two quantization schemes is discussed in the framework of the scattering theory that connects them. The methods presented are used to show that various field components within a dielectric medium may be either superfluctuant or subfluctuant relative to their fundamental uncertainties in the vacuum. These alterations of the fluctuation properties of the fields are shown to lead to changes in the spontaneous emission rates for both electric and magnetic dipole transitions of excited atoms within or near dielectric media. We also analyze the quantum properties of the transition radiation emitted by a fast charged particle in passing from one dielectric medium to another.
Any charged particle moving faster than light through a medium emits Cherenkov radiation. We show that charged particles moving faster than light through the vacuum emit Cherenkov radiation. How can a particle move faster than light? The weak speed of a charged particle can exceed the speed of light. By definition, the weak velocity 〈v〉w〈\mathbf{v}{〉}_{w}〈v〉w​ is $〈{\ensuremath{\Psi}}_{\mathrm{fin}}|\mathbf{v}|{\ensuremath{\Psi}}_{\mathrm{in}}〉/〈{\ensuremath{\Psi}}_{\mathrm{fin}}|{\ensuremath{\Psi}}_{\mathrm{in}}〉,$ where v\mathbf{v}v is the velocity operator and $|{\ensuremath{\Psi}}_{\mathrm{in}}〉$ and $|{\ensuremath{\Psi}}_{\mathrm{fin}}〉$ are, respectively, the states of a particle before and after a velocity measurement. We discuss the consistency of weak values and show that superluminal weak speed is consistent with relativistic causality.
Quantization of the phenomenological Maxwell theory of the electromagnetic field in dispersive and absorbing dielectrics has been of increasing interest over the last years since it allows for a consistent formulation of quantum optics in the presence of dielectric bodies. We show, using a Dyson-type integral representation of the Green tensor, that the quantization scheme is consistent with QED for both isotropic and anisotropic media and therefore applies to arbitrary linear Kramers-Kronig media including amplifying media.