Several methods of investigation of propagation were developed for study of empty curved waveguide and bends [7–10]. The results of precise numerical computations and extensive analytical investigation of the angular propagation constants were presented for various electromagnetic modes which may exit in waveguide bends of rectangular crosssection . A new equivalent circuit for circular E-plane bends, suitable for any curvature radius and rectangular waveguide type was presented in Ref. . An accurate and efficient method of moments solution together with a mode-matching technique for the analysis of curved bends in a general parallel-plate waveguide was described in the case of a rectangular waveguides . A rigorous differential method describing the propagation of an electromagneticwave in a bent waveguide was presented in Ref. .
Abstract—This paper presents a rigorous approach for the propagation of electromagnetic (EM) fields along a helical waveguide with slab and rectangular dielectric profiles in the rectangular crosssection. The main objective is to develop a numerical method for the calculation of the output fields, for an arbitrary step’s angle and the radius of the cylinder of the helical waveguide. The other objectives are to present the technique to calculate the dielectric profiles and their transverse derivatives in the cross-section and to demonstrate the ability of the model to solve practical problems with slab and rectangular dielectric profiles in the rectangular crosssection of the helical waveguide. The method is based on Fourier coefficients of the transverse dielectric profile and those of the input wave profile. Laplace transform is necessary to obtain the comfortable and simple input- output connections of the fields. This model is useful for the analysis of helical waveguides with slab and rectangular dielectric profiles in the metallic helical waveguides in the microwave and the millimeter- wave regimes. The output power transmission and the output power density are improved by increasing the step’s angle or the radius of the cylinder of the helical waveguide, especially in the cases of space curved waveguides.
Since the pioneering work of high impedance surfaces (HIS) in 1999 by Daniel Sievenpiper , it found a lot of applications because of its artiﬁcial magnetic conductor (AMC) property at a particular frequency. It consists of frequency selective surfaces (FSS) over a metal backed dielectric substrate. At the resonant frequency, the input impedance of HIS is characterized by very high real part and the imaginary part showing a smooth transition through zero . Thus most of the incident electromagneticwave is reﬂected back without any phase reversal resulting in +1 reﬂection coeﬃcient. Because of this interesting metamaterial property, HIS has found many relevant application in microwaves areas such as radar crosssection reduction, low-proﬁle antennas, Fabry-Perot or Leaky wave antennas, EMI/EMC applications, etc.
Abstract—A spacecraft will experience the well-known “blackout” problem in the re-entry into the Earth’s atmosphere, which results in communication failures between the spacecraft and ground control center. It is important to study the blackout mitigation method. The effects of external magnetic field on electromagneticwavepropagation in plasma are studied by theoretical and experimental methods in this paper. The numerical results show that the attenuation of electromagneticwave in plasma is reduced by the presence of a magnetized field. The propagation properties of electromagneticwave in unmagnetized and magnetized plasma have been studied experimentally with plasma torch, and the experimental results are in good agreement with the theory. Both the theoretical and experimental results indicate that magnetic window is an alternative and promising way to improve the radio blackout issue.
We end this paper by some general remarks. The ultimate origin of nonlocality is the non-vanishing ﬁnite spatial extension of the wavefunctions of the particles constituting the medium under interest . This means that a self-consistent approach, at least in the semi- classical sense, should directly provide expressions for the response functions that include both temporal and spatial dispersion. While many such methods are available in literature, e.g., see  and , the computational complexity of a realistic problem comprising, say, periodic arrangements of unit cells engineered to achieve desired electromagnetic performance, makes the method very diﬃcult to apply in iterated design procedures. Instead, one may develop a suitable eﬀective-ﬁeld theory, taking into consideration some of the physical mechanisms that generate nonlocality in the electromagnetic response. Then, this theory, once tested and reﬁned, can be used in an iterative optimization algorithm to achieve the required goals. Moreover, it may be possible to achieve nonlocal eﬀects even within the regime of classical electrodynamics by carefully exploiting near-ﬁeld interactions at the nanoscale .
Abstract—Molecular communications (MC) has been studied as a bio-inspired information carrier for micro-scale and nano- scale environments. On the macro-scale, it can also be considered as an alternative to electromagnetic (EM) wave based systems, especially in environments where there is significant attenuation to EM wave power. This paper goes beyond the unbounded free space propagation to examine three macro-scale environments: the pipe, the knife edge, and the mesh channel. Approximate analytical expressions shown in this paper demonstrate that MC has an advantage over EM wave communications when: (i) the EM frequency is below the cut-off frequency for the pipe channel, (ii) the EM wavelength is considerably larger than the mesh period, and (iii) when the receiver is in the high diffraction loss region of an obstacle.
Abstract—Diﬀraction of a plane wave from a geometry which contains an inﬁnite slit in a perfect electric conducting (PEC) plane and a perfectly electromagnetic conductor (PEMC) cylinder is presented. The method is based on the extension of Clemmow, Karp and Russek solution for the diﬀraction by a wide slit. The results are compared with the published work and agreement is fairly good.
Abstract—The analytical expression of scattering ﬁeld from a conductor elliptic cylinder is presented, as the electromagneticwave propagating vertical to the axis of an elliptic cylinder with arbitrary incident angle and polarization. The obtained result is in agreement with that in the reference when we use this analytical expression to calculate the scattering ﬁeld from a cylinder. Simulations show that the vertical size of the elliptic cylinder greatly aﬀects the scattering ﬁeld when we observe it in the direction perpendicular to the direction of the incident wave. The scattering ﬁeld is strong as the polarization direction of incident wave parallel to the axis of the elliptic cylinder. The algorithm used in the article is valid to investigate the scattering characteristics of other elliptic cylinders. The obtained result oﬀers a theoretical foundation for the practical applications such as electromagnetic remote sensing of target’s size and shape.
The radiation from an electric dipole source has been studied in great details. Among many standout researchers, Weaver  derived the solutions for horizontal and vertical electric dipole (HED/VED) in a two-layer conductive medium, and the two-layer model was extended by [11–16]. Furthermore, the works in  and [17–19] gave the solutions on the radiation problem when the HED or VED was placed in a conducting medium or dielectric layer. Finally, Fares et al.  conducted experiments to verify Weaver’s work. They measured the magnetic ﬁelds generated by HED and VED antennas in shallow seawater at bandwidth of 20 to 500 Hz, and the results indicated that the magnetic ﬁelds picked up by tri-axial magnetometer were consistent with Weaver’s model.
A study of radio wavepropagation over the ice-covered sea areas is of great importance in the connection with the problem of the surfaceelectromagneticwave (SEW). Many of VLF-LF-MF-HF radio systems in the Arctic seas work in the range of 100 kHz to 5 MHz. The review of literature on the area of water of the Arctic and the Antarctic showed that the electromagnetic characteristics of the “ice-sea” stratified media with sharply contrasting electric properties and the processes of radio wavepropagation over them are not sufficiently studied [1,2]. The aim of this study is efficiency assessment of communication and navigation channels in the Arctic regions on the basis of analysis of numerical data of modeling of the LF-MF-HF radio wavepropagation over the “ice-sea” stratified medium within the range of 100-5000 kHz (attenuation function W, electromagnetic field level E).
With the rapid development of micro-nano-components, there is an increas- ing demand for understanding the mechanical behavior of small-sized materials and structures, which often differ distinctly from their macroscopic counterparts. As the volume of the object decreases, the ratio of surface area to volume in- creases, and the surface effect is significant, thus exhibiting mechanical behavior different from the macroscopic case. For example, geckos can walk freely on ver- tical walls and mosquitoes walk on the water. Based on Gurtin’s surface elasticity theory  , Sharma, et al.  studied the size dependence of the elastic field around the nano-cylindrical and nano-sphere inclusions in the whole space. Using the wave function expansion method, Wang, et al.   discussed the diffraction of plane compressional wave (P-wave) in nano-hole. Shen, et al.  discussed the influence of surface effects on the stress field around na- no-inclusions. Ou, et al.    discussed the mechanical behaviors of in- clusions and holes subjected to uniform loads at nano-scale.
We will present a crosssection where λ is plotted against k. This shows the band structure of the sample the clearest. The four different types of cross sections that we will make are shown in figure 24, they are the same as in chapter 5. The polarization of the light in the measurements is 0˚as defined in figure 24. The four different cross sections are shown in figure 31. At least three bands are clearly visible. The bands that have a higher wavelength (and therefore a lower energy) contain more light than the bands with a lower wavelength. The low bands are therefore hard to distinguish. A possible explanation for this is that the semiconductor layers, responsible for the gain, does not work that well. V.T. Tenner et al. 4 measured the fluorescence as a function of wavelength, and found that for the wavelengths in the
Using Equations (6)-(8), the matrix elements and the unknown coefficients are calculated assuming that the potential of the plate is equal to 1. Using Equations (8) and (9), the capacitance of an elliptical isolated disk with eccentricity e = 0.85 has been calculated. The conver- gence of the computed numerical values is illustrated in shown in Figure 5. The converged value of the capaci- tance is 49.873 pF. The computed capacitance as a func- tion of eccentricity is presented in Figure 6 and the nu- merical value of the capacitance is presented in Table 1. The numerical results can be compared with a closed form solution for a circular disk (eccentricity=0) in Ta- ble 1 .
It should also be noted that the numerical analysis of the dispersion Equation (33) does not allow to show the presence of strictly limit the speed of wavepropagation modes, since the computer cannot handle infinitely large quantities. We can only speak about the numerical stability result in a large frequency range, which is confirmed by research. For example, when tg ϕ = 2 0.2 value of the phase velocity of a measured without shear wave velocity at ω = 3 and ω = 40 It differs fifth sign that corresponds to the accuracy of calculations, resulting in test problem.
Abstract—A concept of an experimental simulator for studying longitudinal magnetic waves in dielectric samples and its electrodynamic justiﬁcation are presented. The simulator is intended to control impact power and frequencies of wave processes. The simulator is realized as a two-channel junction consisting of perpendicularly crossed inﬁnite rectangular waveguides with slot coupling. The simulation process is based on cyclic mechanical displacements of dielectric samples along the longitudinal axis of the waveguide in a quasi-stationary magnetic ﬁeld localized in the slot region.
Gaussian pulse propagates in a perfect conducting cavity . The cavity has 200 grid cells with Δ x = 0 . 0005 m, and the ﬁrst ﬁfty cells have dielectric material with relative permittivity r = 2 . 3. Other grid cells in the cavity are considered to be free space ( r = 1). The Gaussian pulse is initialized at the centre of the domain and is expressed as e −w 2 t 2 , where w = 4 . 14 × 10 10 1/s. As time advances the pulse propagates left . The representation of the electric ﬁelds after time t = 0 . 1418 , 0 . 2752, and 0.4186 ns are shown in Figure 7. As in the previous case of variable impedance media, when waves originating in a Riemann problem hit a material interface, part of the wave is transmitted, and part reﬂects back from the interface. These transmitted and reﬂected waves update appropriate range of downwind and upwind grid cell relative to the interface depending on locally deﬁned wave speed. The computational domain is also bounded with the perfect electric conducting (PEC) boundaries. As shown in Figures 7(b) and 7(c), the outgoing wave from the boundaries completely reﬂect back into the computational domain so as to have n× E = E y = 0 at PEC boundaries. This PEC boundary condition implementation was earlier described in detail by the authors in  for homogeneous medium. From the results the proﬁle of electric ﬁeld again agrees very well with the analytical solution for ν 1. The measured amplitude of transmitted and reﬂected waves, error L 2 , and CPU time for varying ν are again tabulated in Table 3 at t = 0 . 4186 ns. In this table E t is the amplitude of transmitted wave. The incident pulse initially hits the interface, and the amplitude of reﬂected wave is E r 1 in the table. As shown in Figure 7(b), the left moving transmitted wave after reﬂection from PEC boundary again hits the dielectric interface. A part of the wave is again reﬂected from the interface, and amplitude of this reﬂected wave is represented by E r 2 in the table. As in the homogeneous case , the discretization error decreases with increase in ν due to decrease in the number of operations with increasing Δ t . Table 3. Performance of LTS algorithm with varying ν , Z ( x ) = Z 0 , PEC boundaries.
and Scalia  studied the spatial and temporal behavior in linear thermoelasticity of materials with voids. A theo- ry of thermoelastic materials with voids and without en- ergy dissipation is developed by Cicco and Diaco . Ciarletta et al.  presented a model for acoustic wavepropagation in a porous material which also allows for propagation of a thermal displacement wave. Singh  studied the wavepropagation in a homogeneous, iso- tropic generalized thermoelastic half space with voids in context of Lord and Shulman theory. Ciarletta et al.  studied the linear theory of micropolar thermoelasticity for materials with voids. Recently, Aoudai  derived the equations of the linear theory of thermoelastic diffu- sion in porous media based on the concept of volume fraction.
kumyan (BGM) wave can propagate in such piezoelec- tromagnetics. It is worth noticing that the surface BGM- wave in piezoelectromagnetics is analogous to the well- known surface Bleustein-Gulyaev (BG) wave [18,19] pro- pagating in the transversely isotropic piezoelectrics. More- over, recent book  has analytically found that the BGM-wave can also propagate in the cubic piezoelec- tromagnetics. This book published in 2011 has also dis- covered seven new SH-SAWs propagating on the surface of the cubic piezoelectromagnetics and discussed the main differences between the wave propagations in the cubic piezoelectromagnetics and the transversely isotro- pic piezoelectric composite materials. Note that the wave propagations in cubic piezomagnetics  and cubic pie- zoelectrics  are also different from those in the trans- versely isotropic materials. Also, Ref.  has stated that SH-SAWs can easily be produced by electromagnetic acoustic transducers (EMATs). According to books [24, 25], the EMATs offer a series of advantages over tradi- tional piezoelectric transducers. So, the EMATs can be used for measurements of SH-SAW characteristics when the wave propagations in the piezoelectrics, piezomag- netics, or piezoelectromagnetics are studied.
Dynamics of long sea waves in the channels of variable depth and variable rectangular cross-section is discussed within various approximations – from the shallow water equations to those of nonlinear dispersion theory. General approach permitting to find traveling (non-reflective) waves in inhomoge- neous channels is demonstrated within the framework of the shallow water linear theory. The appro- priate conditions are determined by solving a system of ordinary differential equations. The so-called self-consistent channel in which the width is connected with its depth in a specific way is studied in detail. Within the linear theory of shallow water, a wave does not reflect from the bottom irregulari- ties. The wave shape remains unchanged on the records of the wave gauges (mareographs) fixed along the channel axis, but it varies in space. Nonlinearity and dispersion lead to the wave transfor- mation in such a channel. Within the framework of the shallow water weakly nonlinear theory, the wave shape is described by the Riemann solution, and the wave breaks (gradient catastrophe) quicker in the zones of decreasing depth. The modified Korteweg – de Vries equation describing evolution of a solitary wave of weak but finite amplitude in a self-consistent channel, the depth of which can vary arbitrary, is derived. Some examples of a solitary wave transformation in such a channel are analyzed (particularly, a soliton adiabatic transformation in the channel with the slowly varying parameters, and a solitary wave fission into the group of solitons after it has passed the zone where the depth changes abruptly. The obtained solutions extend the class of those represented earlier by S.F. Dotsen- ko and his colleagues.