Nonmonochromatic Waves Research Articles

Space–Time–Frequency Modulation Mechanisms of Monochromatic and Nonmonochromatic Electromagnetic Waves on a Digital Programmable Transmission Metasurface

AbstractBy dynamically configuring unit structures, a digital programmable metasurface (DPM) can perform space, time, and frequency modulations of electromagnetic (EM) waves directly on the aperture, and hence linking the metasurface physics to digital information worlds. However, the interactions between DPMs and EM waves have not yet been systematically and efficiently depicted. Based on the Huygens–Fresnel principle and Fourier analysis, here the authors demonstrate the foundations of space–time–frequency joint controls of monochromatic or nonmonochromatic EM waves by DPM. Due to linear superposition properties of Fourier transform in the analysis, the space– and time–frequency modulations are naturally decoupled, hence enabling simultaneous and independent space–time–frequency controls of the EM waves. A transmissive DPM is designed and fabricated to interpret the space–time–frequency joint modulations. This work will facilitate the researches on DPMs and promote the applications of DPMs in wireless communications, intelligent sensing, and radar systems.

Fourier Acoustical Tweezers: Synthesizing Arbitrary Radiation Force Using Nonmonochromatic Waves on Discrete-Frequency Basis

Existing acoustical tweezers (ATs) modulate source geometries to achieve monochromatic focusing, the wide frequency space allowed by sources is neglected. Here an analogous approach is proposed to synthesize AT fields in temporal frequency instead of wave vector. The base element is a standing wave, its counterpart in beam ATs is the field of a pitch. After field periodization, radiation-force theory is extended to nonmonochromatic waves having arbitrary in-period force based on discrete-frequency Fourier analysis. Fourier acoustical tweezers (FATs) achieve a minimal spacing of $\ensuremath{\lambda}/4$ for independent trapping. System complexity is reduced to two sources per dimension.

On possible applications of media described by fractional-order models in electromagnetic cloaking

The purpose of this paper is to open a scientific discussion on possible applications of media described by fractional-order (FO) models (FOMs) in electromagnetic cloaking. A 2-D cloak based on active sources and the surface equivalence theorem is simulated. It employs a medium described by FOM in communication with sources cancelling the scattered field. A perfect electromagnetic active cloak is thereby demonstrated with the use of a finite-difference time-domain method combined with a simulation algorithm of non-monochromatic wave propagation in the media described by FOM. The application of constitutive relations based on FOMs in Maxwell’s equations provides solutions which correspond to the results reported for the time-fractional diffusion-wave equation, which is non-relativistic, like the classical diffusion equation. This property is employed in the presented cloaking scheme for communication with active current sources around the cloak, which cancel the scattered field of an object inside the cloak. Although in the real world perfect invisibility is impossible to obtain due to the constraint of light speed, it is possible to obtain a perfect cloak in theoretical considerations by using FO formulation of electromagnetism. It is worth noticing that numerous literature sources experimentally confirm the existence of electromagnetic media described by FOMs; hence, the presented numerical results should hopefully stimulate further investigations related to applications of FOMs in electromagnetic cloaking.

Peculiarities of light pulse propagation in quasi-PT symmetric periodic structures

We study the peculiarities of light pulse propagation in the quasi-parity-time (quasi- P T ) symmetric periodic media in the Bragg geometry. Our focus is the investigation of the competition between the Bragg reflection and the P T symmetry contribution provided different pulse duration. The mechanisms of nonsymmetric interaction between the counterpropagating waves are revealed and the various regimes of the monochromatic and nonmonochromatic wave propagation are determined. It is demonstrated that regardless the gain and loss level, the propagation of so-called long pulses in a quasi- P T -symmetric medium is analogous to monochromatic waves propagation in a “pure” P T -symmetric medium. At the same time, the transmittance of the short pulses is accompanied by strong distortions determined by the gain and loss level.

Signal propagation in electromagnetic media described by fractional-order models

In this paper, signal propagation is analysed in electromagnetic media described by fractional-order (FO) models (FOMs). Maxwell’s equations with FO constitutive relations are introduced in the time domain. Then, their phasor representation is derived for one-dimensional case of the plane wave propagation. With the use of the Fourier transformation, the algorithm for simulation of the non-monochromatic wave propagation is introduced. Its implementation in Matlab allows for generation of time-domain waveforms of signals propagating in the media described by FOMs. It is demonstrated that despite high attenuation, a small perturbation of the time-derivative orders in Maxwell’s equations allows for tuning of the time of signal arrival to the observation point. In all the cases studied, the rate of pulse advancement increases, with simultaneous decrease of the value of the time-derivative orders in FO Maxwell’s equations.

Effect of in-material losses on terahertz absorption, transmission, and reflection in photonic crystals made of polar dielectrics

The effect of the material absorption factor on terahertz absorption (A), transmittance (T), and reflectance (R) for slabs of PhC that comprise rods made of GaAs, a polar dielectric, is studied. The main goal was to illustrate how critical a choice of the absorption factor for simulations is and to indicate the importance of the possible modification of the absorption ability by using either active or lossy impurities. The spectra of A, T, and R are strongly sensitive to the location of the polaritonic gap with respect to the photonic pass and stop bands connected with periodicity that enables the efficient combination of the effects of material and structural parameters. It will be shown that the spectra can strongly depend on the utilized value of the material absorption factor. In particular, both narrow and wide absorption bands may appear owing to a variation of the material parameters with a frequency in the vicinity of the polaritonic gap. The latter are often achieved at wideband suppression of transmission, so that an ultra-wide stop band can appear as a result of adjustment of the stop bands having different origin. The results obtained at simultaneous variation of the absorption factor and frequency, and angle of incidence and frequency, indicate the possibility of the existence of wide ranges of tolerance, in which the basic features do remain. This allows for mitigating the accuracy requirements for the absorption factor in simulations and promises the efficient absorption of nonmonochromatic waves and beams with a wide angular spectrum. Suppression of narrowband effects in transmission is demonstrated at rather large values of the absorption factor, when they appear due to either the defect modes related to structural defects or dispersion inspired variations of the material parameters in the vicinity of the polaritonic gap. Comparison with auxiliary structures helps one to detect the common features and differences of homogeneous slabs and slabs of a PhC, which are made of GaAs.

Coupling Theory of Emergent Spin Electromagnetic Field and Electromagnetic Field

In ferromagnetic metals, an effective electromagnetic field which couples to conduction electron spin is induced by the sd exchange interaction. We investigate how this effective field, spin electromagnetic field, interacts with the ordinary electromagnetic field by deriving an effective Hamiltonian based on the path-integral formalism. It turns out that the dominant coupling term is the product of the electric field and the spin gauge field. This term descrives the spin-transfer effect, as was pointed out before. The electric field couples also to the spin electric field, but this contribution is smaller than the spin-transfer contribution in the low frequency regime. The magnetic field couples to the spin magnetic field, and this interaction suggests an intriguing intrinsic mechanism of frustration in very weak metallic ferromagnets under a uniform magnetic field. We also propose a voltage generation mechanism due to a non-linear effect of non-monochromatic spin wave excitation.

Wakefield radiation from the open end of an internally coated metallic tube

In this paper the problem of radiation from the open end of a semi-infinite circular metallic waveguide with perfectly conducting walls and a thin internal low-conducting metal coating is considered. Electromagnetic fields are generated by the ultrarelativistic point charge moving along the axis of the waveguide. The far fields of radiation are obtained using the near-field to far-field recovery technique. The technique is extended for the nonmonochromatic waves. It is shown that the radiation has a narrow-band and narrow-directional character.

Parametric decay of radial Alfvén waves in the expanding accelerating solar wind

We study the onset and evolution of the Alfvén wave parametric decay instability within the Accelerating Expanding Box model in the framework of a one‐fluid description of the plasma. As we are interested in understanding wave propagation and dissipation in the inner heliosphere and solar wind, the expansion of the solar wind itself may not be neglected. In this sense, the Accelerating Expanding Box provides a useful and simple model to mimic the effects that the expansion of the underlying atmosphere has on wave propagation and plasma dynamics. In the simulations, we follow the evolution of Alfvén waves along a fast solar wind stream, from the sub‐Alfvénic region up to a maximum heliocentric distance of nearly 4 AU. We consider exact solutions of the compressible MHD system given by circularly polarized Alfvén waves which propagate in the radial direction, along the mean magnetic field. Both monochromatic waves and a nonmonochromatic wave are considered. Monochromatic waves have periods ranging from a few minutes to a few hours, the latter being stabilized by the expansion. The nonmonochromatic wave has a central period of the order of a few minutes, with a broad spectrum containing frequencies near the threshold of the instability. In this case the Alfvén wave partly decays into backward daughter Alfvén waves up to the instability saturation, then giving rise to a nonlinear cascade of incompressible and compressible modes.

On entropy-maximized velocity distributions in circularly polarized finite amplitude Alfvén waves

A special solution of the Vlasov-Maxwell system, which represents a circularly polarized Alfvén wave, is derived as an entropy-maximized state. It is shown that Alfvénic correlation between transverse bulk motion and magnetic field given by the entropy-maximized distribution is consistent with the equilibrium point of the single particle system. We demonstrate that as far as the monochromatic, circularly polarized magnetic field is concerned, the resultant distribution may be a relaxed state corresponding to one in the Hall-magnetohydrodynamic system. Stability of the distribution function is numerically discussed by using an ion-hybrid simulation code. Numerical results suggest that the relaxed states in nonmonochromatic waves are different from those in monochromatic waves.

Non-monochromatic whistler waves detected by Kaguya on the dayside surface of the moon

Non-monochromatic fluctuations of the magnetic field over the frequency range of 0.03–10 Hz were detected by Kaguya at an altitude of 100 km above the lunar surface. The fluctuations were almost always observed on the solar side of the moon, irrespective of the local lunar crustal field. They were also detected just nightside of the terminator (SZA < 123°), but were absent around the center of the wake. The level of the fluctuation enhanced over the wide range from 0.03 to 10 Hz, with no clear peak frequency. The fluctuations had the compressional component, and the polarization was not clear. The fluctuations were supposed to be whistler waves generated by the protons reflected by the lunar surface. The reflected protons are scattered in various directions, resulting a wide range of distribution of the velocity component parallel to the magnetic field. It may account for the wide range of frequency as observed, through cyclotron resonance of the wave with the reflected ions, in which the resonant frequency depends on the velocity component parallel to the magnetic field. However, there is also the possibility that the waves were generated by some nonresonant process.

A Sparse Aperture MIMO-SAR-Based UWB Imaging System for Concealed Weapon Detection

A high-resolution imaging system based on the combination of ultrawideband (UWB) transmission, multiple-input-multiple-output (MIMO) array, and synthetic aperture radar (SAR) is suggested and studied. Starting from the resolution requirements, spatial sampling criteria for nonmonochromatic waves are investigated. Exploring the decisive influence of the system's fractional bandwidth (instead of previously claimed aperture sparsity) on the imaging capabilities of sparse aperture arrays, a MIMO linear array is designed based on the principle of effective aperture. For the antenna array, an optimized UWB antenna is designed allowing for distortionless impulse radiation with more than 150% fractional bandwidth. By combining the digital beamforming in the MIMO array with the SAR in the orthogonal direction, a high-resolution 3-D volumetric imaging system with a significantly reduced number of antenna elements is proposed. The proposed imaging system is experimentally verified against the conventional 2-D SAR under different conditions, including a typical concealed-weapon-detection scenario. The imaging results confirm the correctness of the proposed system design and show a strong potential of the MIMO-SAR-based UWB system for security applications.

Dispersive cylindrical cloaks under nonmonochromatic illumination

Transformation-based cylindrical cloaks and concentrators are illuminated with nonmonochromatic waves and unusual effects are observed with interesting potential applications. The transient responses of the devices are studied numerically with the finite-difference time-domain method and the results are verified with analytical formulas. We compute the effective bandwidth of several cloaking schemes as well as the effect of losses on the performance of the structures. We also find that narrowband behavior, frequency shift effects, time delays, and spatial disturbances of the incoming waves are dominant due to the inherently dispersive nature of the devices. These effects are important and should be taken into account when designing metamaterial-based devices.

Response of dispersive cylindrical cloaks to a nonmonochromatic plane wave

The transmission line modeling method is used to get the time domain response of a dispersive cylindrical cloak to an electromagnetic (EM) plane wave that is slightly nonmonochromatic. Our objective is to numerically study two important phenomena derived from the dispersive nature of the invisibility shell: frequency shifts and time delays. On one hand, the frequency domain representation of the cloak's response shows that the frequency center is shifted once the EM wave has crossed the cloak; the shift intensity representation spans the entire rainbow spectrum depending on the observation angle. On the other hand, such a full-wave simulation constitutes tangible evidence of the existence of time delays when the EM wave passes through the device. We show that this phenomenon depends on the employed coordinate transformation.

Non-dispersive traveling waves in inclined shallow water channels

Existence of traveling waves propagating without internal reflection in inclined water channels of arbitrary slope is demonstrated. It is shown that traveling non-monochromatic waves exist in both linear and nonlinear shallow water theories in the case of a uniformly inclined channel with a parabolic cross-section. The properties of these waves are studied. It is shown that linear traveling waves should have a sign-variable shape. The amplitude of linear traveling waves in a channel satisfies the same Green's law, which is usually derived from the energy flux conservation for smoothly inhomogeneous media. Amplitudes of nonlinear traveling waves deviate from the linear Green's law, and the behavior of positive and negative amplitudes are different. Negative amplitude grows faster than positive amplitude in shallow water. The phase of nonlinear waves (travel time) is described well by the linear WKB approach. It is shown that nonlinear traveling waves of any amplitude always break near the shoreline if the boundary condition of the full absorption is applied.

Rainbow and Blueshift Effect of a Dispersive Spherical Invisibility Cloak Impinged On by a Nonmonochromatic Plane Wave

We demonstrate some interesting phenomena associated with a nonmonochromatic plane wave passing through a spherical invisibility cloak whose radial permittivity and permeability are of Drude and Lorentz types. We observe that the frequency center of a quasimonochromatic incident wave will suffer a blueshift in the forward scattering direction. Different frequency components have different depths of penetration, causing a rainbowlike effect within the cloak. The concept of group velocity at the inner boundary of the cloak needs to be revisited. Extremely low scattering can still be achieved within a narrow band.

Full-wave solution of short impulses in inhomogeneous plasma

In this paper the problem of real impulse propagation in arbitrarily inhomogeneous media will be presented on a fundamentally new, general, theoretical way. The general problem of wave propagation of monochromatic signals in inhomogeneous media was enlightened in [1]. The earlier theoretical models for spatial inhomogeneities have some errors regarding the structure of the resultant signal originated from backward and forward propagating parts. The application of the method of inhomogeneous basic modes (MIBM) and the complete full-wave solution of arbitrarily shaped non-monochromatic plane waves in plasmas made it possible to obtain a better description of the problem, on a fully analytical way, directly from Maxwell’s equations. The model investigated in this paper is inhomogeneous of arbitrary order (while the wave pattern can exist), anisotropic (magnetized), linear, cold plasma, in which the gradient of the one-dimensional spatial inhomogeneity is parallel to the direction of propagation.

Parametric wave phase conjugation of nonlinear ultrasound waves

Real time acoustic wave phase conjugation (WPC), based on parametric self-consistent physical mechanisms, was realized up to the present time only for the monochromatic waves [A. P. Brysev et al., Phys.-Usp. 41, 793 (1998)]. Here the possibility of WPC of nonmonochromatic ultrasound waves is considered. For simultaneous WPC of the entire series of spectral components generated by nonlinear propagation of the incident wave we propose the use of phonon-plasmon interaction in piezosemiconductors. WPC of nonlinear acoustic waves can be accomplished by modulation of the electron density provided by a sequence of short laser pulses pumping the sample. If the periodicity of the optical pulses is half the period of the fundamental component of the acoustic wave, such wide-band, excitation leads to self-synchronized parametric conjugation of each spectral component in the incident wave. The conjugation efficiency depends sharply on relations between acoustical frequency content, laser pulse duration, and interband relaxation time. It is shown that under certain conditions the time profile of the conjugate wave may be efficiently controlled by varying the duration of the laser pulses. The time profile of the conjugate wave is investigated for some physical conditions of practical interest.

Nonlinear evolution of parametric instability of a large-amplitude nonmonochromatic Alfvén wave

The nonlinear evolution of the parametric instability of a finite amplitude Alfvén wave is studied in a one-dimensional geometry. The linear stage of this instability had been examined in a previous paper [Malara and Velli, Phys. Plasmas 3, 4427 (1996)], in which it has been shown that even a nonmonochromatic broad-band wave is unstable. In the present paper, the time evolution is followed up to saturation, by numerically integrating the full set of magnetohydrodynamic (MHD) equations. Several configurations of the Alfvénic pump wave, as well as different values of the plasma β are examined. The saturation level of the instability does not depend on the spectral width of the pump wave, but it depends on the value of β. For β≲0.5 the final state is characterized by a cross-helicity ∼0 and a moderate level of density fluctuations: The Alfvénic correlation of the initial wave is completely destroyed, even for a broad-band initial spectrum. For β=1 the final cross-helicity is closer to that of the initial wave, indicating a lower saturation level. The parametric process appears to be nonlocal in the wave-vector space also in the nonmonochromatic case, this feature becoming more relevant with increasing β.

Diffractive changes in the frequency spectrum of propagating radiation (the Wolf effect)

The propagation of a nonmonochromatic wave beam through a lossless dispersive medium is treated in the paraxial approximation. The frequency spectrum of the beam changes in the process because of the finite dimensions and the imperfect spatial coherence of the source. These changes are analyzed. A physical model is offered to explain the basic features of this effect. Methods for compensating for it are discussed. Possibilities for utilizing it are also discussed. The physical meaning of the "scaling law" is discussed.