Backward Wave Propagation Research Articles

Frequency-dependent breakdown of backward volume spin-wave soliton formation

This study investigates the propagation characteristics of spin waves in an yttrium iron garnet waveguide using a vector network analyzer and a real-time oscilloscope. We confirm the propagation of backward volume magnetostatic spin waves in the linear regime. Solitary spin-wave formation was observed, and the transition from linear to nonlinear response was verified by establishing a threshold power. In the nonlinear regime, collision experiments between two spin waves were conducted, revealing a dependence of attenuation on the input carrier frequency. A comparison with the transmission loss curve confirms the correlation between attenuation and the position of “frequency regions with strong dispersion.” Notably, only within a specific frequency range among these regions do the colliding spin waves maintain their shapes and momenta, passing through each other without dissipation. This remarkable phenomenon is crucial for dissipation-free information transfer. Our findings offer valuable insights into spin-wave behavior, particularly for developing spin-wave-based logic and long-distance magnonic soliton information transfer.

Spin Rotations in a Bose-Einstein Condensate Driven by Counterflow and Spin-Independent Interactions.

We observe spin rotations caused by atomic collisions in a nonequilibrium Bose-condensed gas of ^{87}Rb. Reflection from a pseudomagnetic barrier creates counterflow in which forward- and backward-propagating matter waves have partly transverse spin directions. Even though inter-atomic interaction strengths are state independent, the indistinguishability of parallel spins leads to spin dynamics. A local magnetodynamic model, which captures the salient features of the observed spin textures, highlights an essential connection between four-wave mixing and collisional spin rotation. The observed phenomenon is commonly thought not to occur in Bose condensates; our observations and model clarify the nature of these effective-magnetic spin rotations.

Second Harmonic Electromagnetic Wave Emissions from a Turbulent Plasma with Random Density Fluctuations

In the solar wind, electromagnetic waves at the harmonic plasma frequency 2ω p can be generated as a result of coalescence between forward- and backward-propagating Langmuir waves. A new approach to calculate their radiation efficiency in plasmas with external background density fluctuations is developed. The evolution of Langmuir wave turbulence is studied by solving numerically the Zakharov equations in a two-dimensional randomly inhomogeneous plasma. Then, the dynamics of the nonlinear electric currents modulated at frequencies close to 2ω p are calculated, as well as their radiation into harmonic electromagnetic waves. In the frame of this non-self-consistent approach where all transformations of Langmuir waves on density inhomogeneities are taken into account, the electromagnetic wave radiation rate (emissivity) is determined numerically as well as analytically, providing in both cases similar results. Moreover, scaling laws of the harmonic wave emissivity as a function of the ratio of the light velocity to the electron plasma thermal velocity are found. It is also shown how the emissivity depends on the average level of density fluctuations and on the isotropic/anisotropic character of the Langmuir waves’ and density fluctuations’ spectra.

High-harmonic Plasma Emission Induced by Electron Beams in Weakly Magnetized Plasmas

Electromagnetic radiation at higher harmonics of the plasma frequency (ω ∼ n ω pe, n > 2) has been occasionally observed in type II and type III solar radio bursts, yet the underlying mechanism remains undetermined. Here we present two-dimensional fully kinetic electromagnetic particle-in-cell simulations with high spectral resolution to investigate the beam-driven plasma emission process in weakly magnetized plasmas of typical coronal conditions. We focused on the generation mechanisms of high-harmonic emission. We found that a larger beam velocity (u d ) favors the generation of the higher-harmonic emission. The emissions grow later for higher harmonics and decrease in intensity by ∼2 orders of magnitude for each jump of the harmonic number. The second and third harmonic (H2 and H3) emissions get closer in intensity with larger u d . We also show that (1) the H3 emission is mainly generated via the coalescence of the H2 emission with the Langmuir waves, i.e., H2 + L → H3, wherein the coalescence with the forward-propagating beam-Langmuir wave leads to the forward-propagating H3, and coalescence with the backward-propagating Langmuir wave leads to the backward-propagating H3; and (2) the H4 emission mainly arises from the coalescence of the H3 emission with the forward- (backward-)propagating Langmuir wave, in terms of H3 + L → H4.

Спиновые волны в одномерных магнонных кристаллах с двумя пространственными периодами

The propagation of surface and backward volume magnetostatic waves in a one-dimensional magnonic crystal in the form of a yttrium iron garnet film with two periodic lattices of grooves with different periods etched on its surface was experimentally studied. It is shown that the form of the frequency dependence of the transmission coefficient of magnetostatic waves in such crystal is not a simple superposition of similar dependences for two magnonic crystals with the same lattice periods.

Ion-acoustic waves in weakly ionized plasmas with charge-exchange collisions

Ion-neutral charge-exchange collisions in plasmas of laboratory, space, and astrophysical origins are fundamental to understanding wave dissipation and wave generation phenomena. This paper implements a charge-exchange collision operator in the Boltzmann–Poisson system equations for a weakly ionized plasma. When considering an electric field perturbation, the governing kinetic equations provide significant results concerning the plasma conductivity and the dielectric function, appearing in simple, sensible forms. The present analysis reveals a backward wave propagation phenomenon at maximum conductivity when the wavenumber of the plasma wave is smaller than the reciprocal of the ion-neutral collisions mean free path. In addition, it is shown that ion-neutral coupling resulting from charge-exchange collisions enhances ion-acoustic waves below and beyond the ion plasma frequency and leads to the onset of a fundamental instability that overcomes Landau damping under certain circumstances. The collisionless model is recovered as a limiting case, i.e., in the asymptotic limit of a long mean free path.

Bandgap merging and backward wave propagation in inertial amplification metamaterials

The aim of this study is to investigate the wave propagation characteristics of one-dimensional inertial amplification (IA) metamaterials with double resonators. The IA Angle is introduced by the IA mechanism as a critical parameter to modulate elastic waves. Double attenuation peaks in the bandgaps caused by coupling the IA mechanism and local resonance can be created in different ranges by adjusting the IA Angle. Moreover, a novel phenomenon of negative relative group velocity is observed in the region of double-negative effective properties, denoting negative energy flow. Numerical simulations using Gaussian pulse excitation are performed to validate the existence of a backward wave corresponding to the negative relative group velocity in the time domain. Furthermore, bandgap merging occurs in the region of double-zero effective properties, resulting in broadband wave attenuation. In particular, instead of using traditional metamaterials, two local resonator bandgaps can be merged to expand the bandgap range by at least 30% without changing the unit cell mass. The research results can be used to tune wave propagation in metamaterials, providing ideas for metamaterial design.

Multi-Depth Computer-Generated Hologram Based on Stochastic Gradient Descent Algorithm with Weighted Complex Loss Function and Masked Diffraction

In this paper, we propose a method to generate multi-depth phase-only holograms using stochastic gradient descent (SGD) algorithm with weighted complex loss function and masked multi-layer diffraction. The 3D scene can be represented by a combination of layers in different depths. In the wave propagation procedure of multiple layers in different depths, the complex amplitude of layers in different depths will gradually diffuse and produce occlusion at another layer. To solve this occlusion problem, a mask is used in the process of layers diffracting. Whether it is forward wave propagation or backward wave propagation of layers, the mask can reduce the occlusion problem between different layers. Otherwise, weighted complex loss function is implemented in the gradient descent optimization process, which analyzes the real part, the imaginary part, and the amplitude part of the focus region between the reconstructed images of the hologram and the target images. The weight parameter is used to adjust the ratio of the amplitude loss of the focus region in the whole loss function. The weight amplitude loss part in weighted complex loss function can decrease the interference of the focus region from the defocus region. The simulations and experiments have validated the effectiveness of the proposed method.

A self-biased non-reciprocal magnetic metasurface for bidirectional phase modulation

Non-reciprocal metasurfaces can encode optical functions on forward- and backward-propagating waves, and could be used to create non-reciprocal antennas and radomes for full-duplex wireless communication and radar systems. However, such metasurfaces typically require external electric- or magnetic-field biasing or rely on non-linear effects, which makes practical implementation challenging. Here we report a self-biased non-reciprocal metasurface based on magnetic meta-atoms made from lanthanum-doped barium hexaferrite. The metasurface offers a transmittance of up to 77% and an operation angle of ±64°. We show that they can be used for on-demand bidirectional phase modulation, which provides non-reciprocal functionalities including microwave isolation, non-reciprocal beam steering, non-reciprocal focusing and non-reciprocal holography. The approach could also be potentially extended to megahertz and optical frequencies by using different self-biased magnetic materials.

Modulation instability solitons in oppositely double-doped directed couplers with two negative refractive index material channel and non-Kerr nonlinearity

In a three-core nonlinear contrarily directed coupler with two negative-index material channels, we theoretically explore the instability in the presence of a non-Kerr-like nonlinear refractive-index shift. Through the use of linear stability analysis, we determine an expression for the instability gain. It is discovered that the septic saturation, the ratio of the forward- to backward-propagating wave power, pump power, and nonlinearity all have a substantial impact on the MI in the nonlinear three-core contrarily directed coupler. The septic and saturation nonlinearity is found to improve the MI in the case of forward-to-backward ratio power (f) by boosting the width and gain of the instability profile in both normal and abnormal dispersion regimes. However, septic nonlinearity improves the MI in the case of pumps by boosting both its width gain and in the abnormal dispersion regime alone. Using 2D pictures, we could investigate the MI's dynamic behaviour during an anomalous dispersion regime. We discovered from the contour images that the gain of the instability profile grows as septic and saturation nonlinearity increases in both normal and abnormal dispersion regimes. So, with a focus on a negative refractive material channel in the existence of contamination and saturation nonlinearity, we report new techniques for producing and controlling MI and soliton in three-core contrarily directed couplers.

Nonreciprocal propagation of surface electromagnetic waves in structures comprising magneto-optical materials

This paper investigates theoretically the effect of nonreciprocity on surface electromagnetic waves (SEWs) propagating in magneto-optical structures in mutually opposite directions, i.e., on waves with tangential wave numbers $k$ of opposite sign. Namely, of our interest is a correlation between the numbers of forward ($k>0$) and backward ($k<0$) propagating SEWs, which manifests itself as a limit on the total number of SEWs. The peculiarity of this limit is that the maximum total number of forward- and backward-propagating SEWs is less than the sum of the maximum numbers of SEWs for each of the opposite directions taken individually. We derive a relation between the electromagnetic surface impedances relevant to forward- and backward-propagating waves. Afterward, by using general properties of these impedances valid regardless of the crystallographic symmetry, we analyze the roots of dispersion equations without solving them explicitly. Various types of magneto-optical structures are considered. In particular, it is shown that, in the bicrystal formed of two half-infinite magneto-optical media, the maximum total number of forward- and backward-propagating SEWs is two at a given value of $|k|$, whereas in each of the mutually opposite directions two SEWs can exist. For example, if two forward-propagating SEWs are known to exist, then no backward-propagating SEW exists. In the case where a metal film is inserted between two different half-infinite magneto-optical media, the maximum number of SEWs in one direction is four but the maximum of the total number of forward- and backward-propagating SEWs is six rather than eight.

A Poisson scaling approach to backward wave propagation in a tube.

A mathematical analysis of wave propagation along an elastic cylindrical tube is presented, with the aim of determining the range of Poisson's ratio for which backward wave propagation (i.e. at negative group velocity) can occur near the ring frequency. This range includes zero Poisson's ratio and a surrounding interval of positive and negative values, whose width depends on the thickness of the tube. The whole range of Poisson's ratio is considered, so that the work applies to modern materials, e.g. composites. All results are presented in simple analytic form by means of a dominant balance in parameter space. The identification of this balance, which is unique, is a main new result in the paper, which makes possible a new type of shell theory based on 'Poisson scaling'. The mathematical approach is deductive from the equations of motion, rather than being based on kinematic hypotheses. A key finding, accessible via the Poisson scaling, is that the regime of negative group velocities extends to high wavenumbers, while being confined to a narrow band of frequencies. Thus responses localized in space are possible for near-monochromatic forcing, an important fact for nonlinear theories of tube dynamics near the ring frequency. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

On the slow ionization waves forming the breakdown in a long capillary tube with helium at low pressure

The results of studies of an electrical breakdown leading to the glow discharge ignition in a long capillary quartz tube are presented. Under such conditions, the breakdown completion is preceded by the development of direct, backward, and counter slow ionization waves (IWs) traveling in the tube. The initiation of the waves was created in helium at low pressure (P = 10 Torr) by the high-voltage pulses of positive and negative polarity with amplitude of several kilovolts. In the beginning, the regime without the breakdown completion in the tube was studied. In this regime, the propagation of only direct positive and direct negative IWs happens. The research on dynamics of the direct, backward, and counter positive and negative waves followed by a complete breakdown was done as well. The influence of the pre-existing plasma on the IWs propagation was also studied. The plasma was created in advance by low-current glow discharge being formed in the tube. The instant images of IWs were correlated with the electrical currents formed by the waves, that is, with the displacement current through the dielectric wall and the conductive current through the plasma column. In the experiments, the fine-sectioned electrode wrapped around the lateral tube surface was used. The usage of such electrode allowed one to study the dynamics of the surface charge deposition and deletion happening during the direct and backward wave propagation, respectively. Finally, a strong difference in the spatial structure and velocity of positive and negative direct waves traveling through non-ionized gas was revealed. Contrary, both the positive and negative backward waves traveling through the plasma formed by previous direct waves have the parameters close to each other.

Phase separation induces congestion waves in electric vehicle charging.

Electric vehicles may dominate motorized transport in the next decade, yet the impact of the collective dynamics of electric mobility on long-range traffic flow is still largely unknown. We demonstrate a type of congestion that arises if charging infrastructure is limited or electric vehicle density is high. This congestion emerges solely through indirect interactions at charging infrastructure by queue-avoidance behavior that-counterintuitively-induces clustering of occupied charging stations and phase separation of the flow into free and congested stations. The resulting congestion waves always propagate forward in the direction of travel, in contrast to typically backward-propagating congestion waves known from traditional traffic jams. These results may guide the planning and design of charging infrastructure and decision support applications in the near future.

An asymptotic Green's function method for the wave equation

We present an effective asymptotic Green's function method for propagating the waves through the linear scalar wave equation. The wave is first split into its forward-propagating and backward-propagating parts. Following that, the method, which combines the Huygens' principle and the geometrical optics approximations, is designed to propagate the forward-propagating and backward-propagating waves, where an integral with Green's functions that is based on the Huygens' principle is used to propagate the waves, and the Green's functions are approximated by the geometrical optics approximations. Upon obtaining analytic approximations for the phase and amplitude in the geometrical optics approximations through short-time Taylor series expansions, a short-time propagator for the waves is derived and the resulting integral can be evaluated efficiently by fast Fourier transform after appropriate lowrank approximations. The short-time propagator can be applied repeatedly to propagate the waves for a long time. In order to restrict the computation onto a bounded domain of interest, the perfectly matched layer technique with complex coordinate stretching transformation is incorporated. The method is first-order accurate, and has complexity O(tϵNlog⁡N) per time step with N the number of spatial points and tϵ the low rank for a prescribed accuracy requirement ϵ>0. Numerical experiments are presented to demonstrate the proposed method.

Directivity and Bandwidth Enhancement of Patch Antenna using Metamaterial

This manuscript is the outcome of detailed research. A novel metamaterial structure is proposed in this paper to improve the directivity of the antenna. In this research paper a method of implementing metamaterial over the patch is used to enhance the directivity of rectangular microstrip patch antenna. From the results proposed expectation has been achieved, it is noted that in the presence of the LHM, the antenna is more directive and has a higher gain. This proposed patch is designed at the frequency of 2.75 GHz. The proposed structure is a combination of circular rings by virtue of its backward wave propagation property and negative reflection it improve the parameters of antenna.

Double negative bend headed I-shaped metamaterial based Terahertz optical power splitter

Terahertz (THz) technology has piqued the interest of many researchers due to the fascinating characteristics of THz waves. Two new metamaterial array architectures are proposed in this paper to investigate power splitting via backward wave propagation. The first array pattern is a rectangular array arrangement, which is defined analytically and suggested as a power splitter in the TE (transverse electric) mode. From the proposed rectangular metamaterial array pattern, another cavity array structure was proposed which successfully increased DNG (double negative) response inside the metamaterial device and produced better splitting performance in the DNG condition. The unit cell and array patterns had almost identical effective parameter results, but some of them changed because the air-dielectric-metal combination was increased. The power splitter is demonstrated at the 0.91 THz frequency range where it shows the effective permittivity is −6, permeability is −6, and the refractive index is −6. At 0.94 THz, the DNG backward wave divider has negative effective parameters with an effective permittivity of −5.8, permeability of −5.8, and refractive index of −5.8.Both of the analytical structure patterns are proposed for optical power splitter and divider applications, which are used in various microwave circuits, such as mixers, balanced amplifiers, and antenna arrays.

An Efficient Semianalytical Modal Analysis of Rectangular Waveguides Containing Metamaterials with Graded Inhomogeneity

Rectangular waveguides containing inhomogeneous metamaterials with graded refractive-index profiles have potential applications in bending waveguides and radiation-enhanced antennas, and accurate eigenvalue solutions are prerequisite. Commonly used commercial electromagnetic solvers such as HFSS, COMSOL, and CST could not efficiently calculate the eigenvalues of waveguides containing graded refractive-index dielectrics. In this paper, an accurate and efficient semianalytical method based on the modal expansion has been proposed to solve these waveguides. The proposed method has been employed to calculate the eigenvalues, including the cutoff wavenumbers and dispersion relations, for metamaterials with various graded refractive-index profiles. Calculated results are then validated by comparison, using commercial solver HFSS, which indicates the superiority of the proposed method in accuracy and efficiency. Below-cutoff backward wave propagation is observed in waveguides filled with graded refractive-index metamaterials, which provides a new approach for waveguide miniaturization.

Energy Plasmon Modes in Metamaterial-filled Double-layer Graphene-wrapped Cylindrical Waveguides

The characteristics of hybrid surface plasmon modes in a double-layer graphene cylindrical waveguide filled with metamaterials are theoretically investigated. The dispersion relation for different configurations of metamaterials (double positive (DPS)-graphene-double negative (DNG)-graphene-DPS and DNG-graphene-DPS-graphene-DNG) is derived by solving Maxwell’s equations for cylindrical symmetry and implementing impedance boundary conditions at the interface. The Kubo formalism is used for the modeling of the electromagnetic response of graphene. The influence of the interlayer distance of graphene, chemical potential of graphene, and permittivity of interlayer metamaterials on the dispersion curve, effective mode index, propagation length, and phase velocity are presented. It is observed that the existence of double layers of graphene along with metamaterials provides better control and tuning of the propagation of the surface waves. The coupled surface plasmon polariton (SPP) and surface phonon polariton (SPhP) in the optical regime are observed due to the coupling of electromagnetic waves between graphene layers. The forward- and backward-propagating surface waves for the fundamental mode are studied for different waveguide configurations. The active trapping of light and tunable fast and ultraslow plasmon modes for both forward and backward propagation modes for the proposed design may enable the realization of potential optoelectronic applications, such as modulators, fast forward-wave amplifiers, frequency selectors, back wave contra couplers, thermal sensors, circular polarizers, slow light devices, infrared (IR) and molecular spectroscopy, on-chip buffers, communication switches, and energy devices.

Wave propagation in a dual-periodic elastic metamaterial with multiple resonators

The behaviour of elastic metamaterials is dominated by the local structure of their representative cells and their periodicity. Previous works indicated that introducing multiple resonators in the representative cells can generate better performance, such as wider band gaps. Another interesting phenomenon observed in previous studies is that elastic metamaterials featuring dual periodicity can generate asymmetric wave transmission and negative effective mass and/or modulus. However, the general property of dual-periodic metamaterials coupled with multiple local resonators are rarely explored. In the current paper, the general mechanism of implementing multiple local resonators into dual-periodic metamaterial cells is systematically studied and a new elastic metamaterial model featuring negative effective mass and/or modulus based on translational resonances is presented. In this new model, the property of the multiple local resonators and the dual-periodicity can be conveniently adjusted to achieve single negativity (negative mass or negative modulus) or double negativity (negative mass and modulus) in different frequency ranges. Due to the great flexibility of generating negative effective parameters stemming from its unique structure, the proposed elastic metamaterial can generate a broad band gap in the low frequency range with exponential wave attenuation, and the positions of the frequency ranges featuring negative phase velocity can be modified according to the desired working frequencies. To elucidate the versatility of this model, numerical validation of typical examples has been provided to demonstrate the phenomena of wave attenuation and backward wave propagation.