scholarly journals Электромагнитные волны в волноводе с периодически модулированным магнитодиэлектрическим заполнением

2021 ◽  
Vol 129 (7) ◽  
pp. 899
Author(s):  
Э.А. Геворкян
Keyword(s):  
Differential Equations ◽  
Electromagnetic Waves ◽  
Wave Equations ◽  
Transverse Electric ◽  
Transverse Magnetic ◽  
Signal Wave ◽  
Bragg Condition ◽  
Periodic Coefficients ◽  
Regular Waveguide ◽  
Three Space

The propagation of electromagnetic waves in an ideal regular waveguide, filling of which is periodically modulated in space and time, is considered. It is assumed that the modulation depths are small and the modulation of the waveguide filling does not lead to the interaction between different waveguide modes. Wave equations are obtained for transverse-electric (TE) and transverse-magnetic (TM) fields in the waveguide with respect to the longitudinal components of the magnetic and electric vectors, respectively, are obtained. They represent second order partial differential equations with periodic coefficients. By changing the variables these equations are reduced to ordinary differential equations with periodic coefficients of the Mathieu-Hill type. Solutions of these equations are found in the first approximation with respect to small modulation depths in the region of “weak” interaction between the signal wave and the modulation wave (the Wulff-Bragg condition is not satisfied). The obtained results show that TE and TM fields in the waveguide in the above approximation are represented as the sum of three space-time harmonics (zero and plus and minus first) with complicated amplitudes and frequencies.

Lateral and transverse shifts in reflected dipole radiation

2011 ◽  
Vol 467 (2133) ◽  
pp. 2500-2519 ◽  
Author(s):  
M. V. Berry
Keyword(s):  
Electromagnetic Waves ◽  
Poynting Vector ◽  
Transverse Electric ◽  
Transverse Magnetic ◽  
Magnetic Polarization ◽  
Dipole Radiation ◽  
Plane Transverse ◽  
Out Of Plane ◽  
Transverse Magnetic Polarization ◽  
Large Peak

In-plane (lateral) and out-of-plane (transverse) shifts in the direction of arbitrarily polarized electromagnetic waves in a denser medium, reflected totally or partially at an interface with a rarer medium, are calculated exactly, in terms of the deviation of the Poynting vector from radial. The shifts are analogous to the Goos–Hänchen and Fedorov–Imbert shifts for beams. There is a transverse shift even for unreflected dipole radiation if the polarization is not linear. With reflection, there is a transverse shift for linear polarization, provided this is not pure transverse electric or transverse magnetic. The contributions from the geometrical ray, the lateral ray that interferes strongly with it, and the large peak at the Brewster angle (for transverse magnetic polarization), are calculated asymptotically far from the geometrical image. At the critical angle, the lowest order asymptotics is inadequate and a more sophisticated treatment is devised, reproducing the exact shifts accurately.

Singularities in the transverse fields of electromagnetic waves. I. Theory

1987 ◽  
Vol 414 (1847) ◽  
pp. 433-446 ◽  
Keyword(s):  
Magnetic Fields ◽  
Electromagnetic Waves ◽  
Transverse Electric ◽  
Wave Theory ◽  
Structural Features ◽  
Transverse Magnetic ◽  
Left Hand ◽  
Polarized Waves ◽  
Pulsed Electromagnetic ◽  
Magnetic Vectors

Electromagnetic waves generally contain three kinds of singularities called C lines, S surfaces and disclinations. These singularities are features of the transverse electric and transverse magnetic fields of the waves and all three kinds usually occur in any given wavefield. We show that in the case of nominally uniformly polarized waves, the simple line zeros predicted for interference fringes by scalar wave theory in fact have an underlying polarization structure consisting of two C lines and an S surface. In consequence, virtually all monochromatic electromagnetic waves contain polarization states ranging from right-hand circular, through linear to left-hand circular polarization. Singularities of the electric and magnetic fields are not generally coincident in space; in fact they can be separated by arbitrarily large distances. The separation of the electric and magnetic S surfaces means that there are regions where the transverse electric and transverse magnetic vectors counterrotate. C lines are probably the most significant of the singularities, since they are not only structural features of polarization, but also organize the time structure of electromagnetic waves. They play a crucial role in determining the topology of disclinations in paraxial wavefields. In pulsed electromagnetic waves all three singularities move through space. Their behaviour, including interactions between pairs of C lines, S surfaces or disclinations, which are likely to be frequent events in pulsed waves, is discussed.

Single-peak-regulation and wide-angle dual-band metamaterial absorber based on hollow-cross and solid-cross resonators

2020 ◽  
Vol 91 (3) ◽  
pp. 30901
Author(s):  
Yibo Tang ◽  
Longhui He ◽  
Jianming Xu ◽  
Hailang He ◽  
Yuhan Li ◽  
...  
Keyword(s):  
Transverse Electric ◽  
Surface Current ◽  
Dielectric Substrate ◽  
Transverse Magnetic ◽  
Metamaterial Absorber ◽  
Absorption Peak ◽  
Dual Band ◽  
Single Peak ◽  
Wide Angle ◽  
Surface Current Density

A dual-band microwave metamaterial absorber with single-peak regulation and wide-angle absorption has been proposed and illustrated. The designed metamaterial absorber is consisted of hollow-cross resonators, solid-cross resonators, dielectric substrate and metallic background plane. Strong absorption peak coefficients of 99.92% and 99.55% are achieved at 8.42 and 11.31 GHz, respectively, which is basically consistent with the experimental results. Surface current density and changing material properties are employed to illustrate the absorptive mechanism. More importantly, the proposed dual-band metamaterial absorber has the adjustable property of single absorption peak and could operate well at wide incidence angles for both transverse electric (TE) and transverse magnetic (TM) waves. Research results could provide and enrich instructive guidances for realizing a single-peak-regulation and wide-angle dual-band metamaterial absorber.

The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wei Tan ◽  
Zhao-Yang Yin
Keyword(s):  
Differential Equations ◽  
Wave Equations ◽  
Rogue Wave ◽  
Nonlinear Partial Differential Equations ◽  
Rogue Waves ◽  
Homoclinic Solutions ◽  
Nonlinear Wave Equations ◽  
Bilinear Method ◽  
Wave Solutions ◽  
Rogue Wave Solutions

Abstract The parameter limit method on the basis of Hirota’s bilinear method is proposed to construct the rogue wave solutions for nonlinear partial differential equations (NLPDEs). Some real and complex differential equations are used as concrete examples to illustrate the effectiveness and correctness of the described method. The rogue waves and homoclinic solutions of different structures are obtained and simulated by three-dimensional graphics, respectively. More importantly, we find that rogue wave solutions and homoclinic solutions appear in pairs. That is to say, for some NLPDEs, if there is a homoclinic solution, then there must be a rogue wave solution. The twin phenomenon of rogue wave solutions and homoclinic solutions of a class of NLPDEs is discussed.

Magnetic plasmons induced in a dielectric-metal heterostructure by optical magnetism

Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Shulei Li ◽  
Lidan Zhou ◽  
Mingcheng Panmai ◽  
Jin Xiang ◽  
Sheng Lan
Keyword(s):  
Transverse Electric ◽  
Incidence Angle ◽  
High Sensitivity ◽  
Critical Value ◽  
Transverse Magnetic ◽  
Quality Factors ◽  
Light Spectrum ◽  
Optical Resonances ◽  
Scattering Spectra ◽  
Plasmon Polaritons

Abstract We investigate numerically and experimentally the optical properties of the transverse electric (TE) waves supported by a dielectric-metal heterostructure. They are considered as the counterparts of the surface plasmon polaritons (i.e., the transverse magnetic (TM) waves) which have been extensively studied in the last several decades. We show that TE waves with resonant wavelengths in the visible light spectrum can be excited in a dielectric-metal heterostructure when the optical thickness of the dielectric layer exceeds a critical value. We reveal that the electric and magnetic field distributions for the TE waves are spatially separated, leading to higher quality factors or narrow linewidths as compared with the TM waves. We calculate the thickness, refractive index and incidence angle dispersion relations for the TE waves supported by a dielectric-metal heterostructure. In experiments, we observe optical resonances with linewidths as narrow as ∼10 nm in the reflection or scattering spectra of the TE waves excited in a Si3N4/Ag heterostructure. Finally, we demonstrate the applications of the lowest-order TE wave excited in a Si3N4/Ag heterostructure in optical display with good chromaticity and optical sensing with high sensitivity.

scholarly journals Oblique propagation of electromagnetic waves in a slowly-varying non-isotropic medium

1936 ◽  
Vol 155 (885) ◽  
pp. 235-257 ◽  
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Electron Density ◽  
Isotropic Medium ◽  
Electromagnetic Waves ◽  
Mathematical Theory ◽  
Stratified Medium ◽  
Oblique Propagation ◽  
Isotropic Media ◽  
Mathematical Justification

The influence of the earth’s magnetic field on the propagation of wireless waves in the ionosphere has stimulated interest in the problem of the propagation of electromagnetic waves through a non-isotropic medium which is stratified in planes. Although the differential equations of such a medium have been elegantly deduced by Hartree,f it appears that no solution of them has yet been published for a medium which is both non-isotropic and non-homogeneous. Thus the work of Gans and Hartree dealt only with a stratified isotropic medium, while in the mathematical theory of crystal-optics the non-isotropic medium is always assumed to be homogeneous. In the same way Appleton’s magneto-ionic theory of propagation in an ionized medium under the influence of a magnetic field is confined to consideration of the “ characteristic ”waves which can be propagated through a homogeneous medium without change of form. In applying to stratified non-isotropic media these investigations concerning homogeneous non-isotropic media difficulty arises from the fact that the polarizations of the characteristic waves in general vary with the constitution of the medium, and it is not at all obvious that there exist waves which are propagated independently through the stratified medium and which are approximately characteristic at each stratum. The existence of such waves has usually been taken for granted, although for the ionosphere doubt has been cast upon this assumption by Appleton and Naismith, who suggest that we might “ expect the components ( i. e ., characteristic waves) to be continually splitting and resplitting”, even if the increase of electron density “ takes place slowly with increase of height”. It is clear that, until the existence of independently propagated approximately characteristic waves has been established, at any rate for a slowly-varying non-isotropic medium, no mathematical justification exists for applying Appleton's magnetoionic theory to the ionosphere. It is with the provision of this justification that we are primarily concerned in the present paper. This problem has been previously considered by Försterling and Lassen,f but we feel that their work does not carry conviction because they did not base their calculations on the differential equations for a non-homo-geneous medium, and were apparently unable to deal with the general case in which the characteristic polarizations vary with the constitution of the medium.

Electromagnetic field generated by an off‐axis source in a cylindrically layered medium with an arbitrary number of horizontal discontinuities

Geophysics ◽  
1993 ◽  
Vol 58 (5) ◽  
pp. 616-625 ◽  
Author(s):  
Qing‐Huo Liu
Keyword(s):  
Arbitrary Number ◽  
Electromagnetic Waves ◽  
Layered Medium ◽  
Azimuthal Angle ◽  
Well Logging ◽  
Transverse Magnetic ◽  
Numerical Results ◽  
Optical Fiber Communications ◽  
Eccentricity Effect ◽  
Large Eccentricity

We investigate the propagation of electromagnetic waves in a cylindrically layered medium with an arbitrary number of horizontal discontinuities. The dielectric constant, conductivity, and magnetic permeability of the medium are functions of ρ and z only (i.e., independent of the azimuthal angle ϕ), but the field generated by an off‐axis source in this medium is in general a function of ρ, ϕ, and z. This two and a half‐dimensional (2.5-D) problem is often encountered in electromagnetic well logging, as well as in other areas such as optical fiber communications and integrated optics. We show that a coupling exists between the transverse electric (TE) and transverse magnetic (TM) components of the field even in the absence of the horizontal discontinuities, which makes it difficult to solve for the field. We apply an efficient numerical mode‐matching (NMM) algorithm to tackle this 2.5-D problem. This algorithm uses the local reflection and transmission operators developed in the recent work on the diffraction of nonaxisymmetric waves in a cylindrically layered medium with a single horizontal discontinuity. For several special geometries, we compare the numerical results from this NMM algorithm with analytical solutions as well as the earlier numerical results for axisymmetric cases, and found excellent agreement between them. As an application to the geophysical subsurface sensing, we solve several practical problems, and find that a large eccentricity effect can occur in realistic electromagnetic well logging. Moreover, this large eccentricity effect is strongly coupled with thin‐bed effect. Conventional log interpretation methods cannot adequately account for these effects. With the NMM algorithm developed here, all these different effects can be accounted for simultaneously and accurately.

Sensitivity characterization of polarization operating by embedded reflective grating

2021 ◽  
Author(s):  
Jiaman Hong ◽  
Bo Wang ◽  
Xiaoqing Zhu ◽  
Zhichao Xiong ◽  
Yusen Huang ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Electric Field Intensity ◽  
High Efficiency ◽  
Transverse Electric ◽  
Tolerance Analysis ◽  
Transverse Magnetic ◽  
Infrared Band ◽  
Element Analysis ◽  
Field Intensity Distribution

In this paper, a novel embedded reflective grating (ERG) is presented to realize bi-function polarization operating at infrared band by finite element analysis (FEM). For transverse electric (TE) polarization, a two-port output (0th and −2nd orders) with an efficiency of more than 47% and excellent uniformity can be obtained. For transverse magnetic (TM) polarization, a high efficiency output of 94.72% can be achieved at the −2th order. The results of the analysis of the electric field intensity distribution, angular and wavelength bandwidths further demonstrate the advantages of the proposed grating. In addition, the tolerance analysis of period and duty cycle prove the feasibility of the grating in practical production.

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