Oleksandr Stadnyk

The problem of generalization of the classical results on the electric dipole radiation over the Earth's surface in the case of the left-handed metamaterial half-space is important for many practical applications related to the focusing of wave fields. It is desirable to do without undue simplifications: geometrical optics approximation, neglecting losses, restrictions on the wave packet associated with the introduction of the group velocity, and neglecting the type (only monopole) of source. In the paper, the model problem of radiation of the elementary electric dipole situated normally to the interface plane between dissipative left-handed and ordinry media has been rigorously solved. The numerical simulation revealed the expected radar pattern-like structure of the reflected field in the first medium and complex (on average cone-shaped) interference field structure with an apparent peak in the region of the left-handed metamaterial half-space. The spatial distribution of the ...

The flat lens conception was considered in the pioneering work of V.G. Veselago, who considered the possibility of electromagnetic waves propagation in media with simultaneously negative permittivity and permeability (according to modern terminology – in the left-handed metamaterials). Later, J.B. Pendry put forward the idea of the so-called " superlens " , the resolution of which would exceed the diffraction limit. In view of the prospects for the practical applications it has caused a discussion on the possibility of anti-parallelism of phase and group velocities and the actual super-resolution implementation for the source in the form of a monopole. However, using the ray theory approximation reduced the generality of the results, neglecting losses radically distorted them, and errors in the theoretical analysis led to the wrong physical interpretation. In this paper, we obtained a rigorous solution to the problem of focusing radiation from elementary electric dipole located perpendicularly to the plane layer of finite thickness made of the left-handed metamaterial with absorption. Spatial distribution of the electromagnetic field in the layer, as well as the incident and reflected fields at various heights of the dipole, layer thickness and losses in each medium are numerically simulated. The analysis of the calculated spatial structure of the electromagnetic field confirmed the focusing ability of the interfaces between ordinary and left-handed media, as well as a flat lens.

Концепция плоской линзы впервые была рассмотрена в работе В. Г. Веселаго, посвященной распространению электро-магнитных волн в средах с одновременно отрицательными диэлектрической и магнитной проницаемостями (согласно современной терминологии – в левосторонних метаматериалах). Позднее Дж. Б. Пендри выдвинул идею так называемой «суперлинзы», разре-шающая способность которой могла бы превышать дифракционный предел. Ввиду перспективности для практических приложений это вызвало дискуссию, посвященную возможности как антипараллельности фазовой и групповой скоростей, так и самой реализа-ции сверхразрешения для источника излучения в виде монополя. Однако использованные при этом приближения лучевой теории уменьшили общность полученных результатов, пренебрежение потерями радикально исказило их, а ошибки в теоретическом ана-лизе привели к неправильной физической трактовке. В данной работе получено строгое решение задачи о фокусировке излучения элементарного электрического диполя, ориентированного вертикально относительно плоского слоя конечной толщины из левосто-роннего метаматериала с поглощением. Численно промоделировано пространственное распределение электромагнитного поля в слое, а также прошедшее и отраженное от него поле при различных высотах диполя, толщинах слоя и потерях в каждой среде. Анализ рассчитанной пространственной структуры электромагнитного поля подтвердил фокусирующие способности границ разде-ла обычной и левосторонней сред, а также плоской линзы. Ил. 5. Библиогр.: 26 назв. Ключевые слова: электрический диполь, электромагнитное поле, левосторонний метаматериал, суперлинза.

The problem of generalization of the classical results on the electric dipole radiation over the Earth's surface in the case of the left-handed metamaterial half-space is important for many practical applications related to the focusing of wave fields. It is desirable to do without undue simplifications: geometrical optics approximation, neglecting losses, restrictions on the wave packet associated with the introduction of the group velocity, and neglecting the type (only monopole) of source. In the paper, the model problem of radiation of the elementary electric dipole situated normally to the interface plane between dissipative left-handed and ordinry media has been rigorously solved. The numerical simulation revealed the expected radar pattern-like structure of the reflected field in the first medium and complex (on average cone-shaped) interference field structure with an apparent peak in the region of the left-handed metamaterial half-space. The spatial distribution of the electromagnetic field in two media, depending on the height of the dipole and the magnitude of losses in the left-handed metamaterial is presented. The analysis of the Poynting vector streamlines confirmed the hypothesis, previously put forward by the authors, that the change in sign of the tangential component at the interface, that is common for electromagnetic surface waves, is the cause of the focusing ability of the interface between the ordinary and the left-handed media, rather than each of them individually.

An expression for the rotation-angle dispersion of the signal polarization plane during transionospheric propagation is obtained in the smooth-perturbation approximation. A stepwise model of the ionospheric irregularity spectrum is used to explain strong fluctuations of the rotation angles of geostationary-satellite signals at 136 MHz observed near humps of the equatorial anomaly.

ABSTRACT It is known that the fluctuations seen in the parameters of radio waves after passing through the ionosphere are caused by inhomogeneities in the ionosphere's electron concentration. These inhomogeneities occur mainly at the heights of the F region. Autocorrelation and cross-correlation functions of the phase and level of a spherical radio wave incident at an angle on a layer of a randomly inhomogeneous ionosphere are obtained here using the approximation method involving continuous perturbations. The expressions obtained are used to calculate numerically the corresponding correlation functions and the index of scintillation S4. The spectral density of the fluctuations in electron concentration is taken to be Gaussian.

ABSTRACT The method of smooth perturbations is used to obtain spatial and frequency correlation functions for the level and phase of a spherical wave incident at an arbitrary angle on a plane inhomogeneous layer of finite thickness. The derived expression for the complex phase of the wave can be used to determine the statistical characteristics of a radio signal transitted through a multiscale ionosphere. Numerical results are presented for the propagation of meter waves.

Only the complete diffraction picture in contrast to [1,2] provides access to the correct description of all relevant effects of loss in media, distance from the boarder etc. Though the theory has been developed for a simple model of a point electric dipole, due to its general character, it may also provide a qualitative insight into the peculiarities of other types of emitters over the boundary between ordinary medium and metamaterial [6]. We do not need to use the concept of negative refraction - the refractive index is pointless in such a problem because simple geometric optical models, based on Snell's law, are no longer appropriate.

The authors suggest a modified technique, based on using metamaterial substrates with known characteristics, which enables one to employ coaxial probes for determining the complex dielectric permittivity of liquids. As it is proven below, by a certain relations between the electric parameters and the thickness of the medium layer to be tested and that of the substrate, there is a resonance decrease of reflections from the probe end, loaded on such a double‐layered structure. Knowing this relation, one can determine the complex dielectric permittivity of the tested medium in a wide variation range, using only the measurements of the probe reflection factor amplitudes in a limited frequency range and matching the optimal layer thickness of the medium under investigation.

The problem of focusing of wave fields of different physical nature and frequency bands is relevant both for scientific experiments and practical applications in industry, health care and technology. However, the unique opportunities for the development of devices focusing electromagnetic fields, which are associated with the emergence of metamaterials (left-handed media), can not be fully realized in the framework of the ray-optical approach used in most studies, the main advantage of which is the visibility. Since this approach does not allow an evaluation of the influence of losses, location, orientation and type of the source on the structure of the radiated field, there is a need for a electrodynamic solution to model problems. The problem of radiation from elementary electric dipole located horizontally above the plane interface between passive normal and left media is rigorous solved from the first principles and numerically simulated in this paper. It is shown that the electromagnetic field of the dipole, penetrating into the metamaterial half-space, is focused into spatial distribution of the field with a pronounced maximum and complex interference structure. The dependence of the focusing on the dipole, position and orientation, as well as losses in metamaterials were studied. A hypothesis that the focusing ability is the property of the interface between ordinary and left-handed media, but not of each of them separately is set forth and qualitative arguments are given.