Case Of Plane Wave Research Articles

Dynamics, quantum states and Compton scattering in nonlinear gravitational waves

The classical dynamics and the construction of quantum states in a plane wave curved spacetime are examined, paying particular attention to the similarities with the case of an electromagnetic plane wave in flat spacetime. A natural map connecting the dynamics of a particle in the Rosen metric and the motion of a charged particle in an electromagnetic plane wave is unveiled. We then discuss how this map can be translated into the quantum description by exploiting the large number of underlying symmetries. We examine the complete analogy between Volkov solutions and fermion states in the Rosen chart and properly extend this to massive vector bosons. We finally report the squared S-matrix element of Compton scattering in a sandwich plane wave spacetime in the form of a two-dimensional integral.

Rotating speed estimation of spinning objects based on rotational Doppler effect

Rotational Doppler effect is an important phenomenon when the vortex electromagnetic wave carrying orbital angular momentum is used to detect a rotating target. Compared with the traditional plane wave case, rotational Doppler effect enables the vortex electromagnetic wave to detect the spin motion along the rotation axis of target. However, there are still some blind zones when the integer orbital angular momentum beams are used to detect specific spinning objects. To expand the application scope of detection scheme based on the rotational Doppler effect, according to the time-frequency analysis, in this paper we study the method of estimating the rotation speed of spinning objects under the normal incidence and oblique incidence of fractional orbital angular momentum beams. Firstly, based on the ideal scattering point model, the echo models are derived under the normal incidence and oblique incidence of integer orbital angular momentum beam and fractional orbital angular momentum beam, respectively, as well as theoretical time-frequency curves. Then taking the three-dimensional practical object for example, the echo under the incidence of fractional orbital angular momentum beams and its time-frequency graph are achieved by using the momentum method and short-time Fourier transform. The time-frequency ridge and its fluctuation period are extracted from the time-frequency graph, thereby estimating the spinning speed of target. The results show that the fractional orbital angular momentum beams can be used to estimate the rotation speed of spinning objects effectively, whether it is normal incidence or oblique incidence, thereby solving the problem about the detection blind zone of integer orbital angular momentum beams, and improving the applicability in detecting spin motion.

Cross-beam energy transfer between spatially smoothed laser beams

The crossing of two spatially smoothed laser beams amounts to the crossings of a large number of speckles. The energy transfer between two of these speckles is mediated by laser induced electron/ion density ripples that act as a Bragg grating. In a weakly Landau-damped plasma, this ion acoustic wave (IAW) may propagate from one crossing region to another, hence perturbing the local electron/ion grating [Oudin et al. Phys. Rev. Lett. 127, 265001 (2021)] even without phase shift between IAWs. In this paper, we investigate how the phase-shifted IAWs generated at the speckle scale interfere and affect the overall energy exchange. To this aim, we perform 2D particle-in-cell simulations with in-phase and out-of-phase Gaussian beams. In the latter situation, which better matches a smoothed laser beam, we find that the destructive interferences between the ion waves significantly reduce the energy exchange compared to the plane wave case. Additional 2D particle-in-cell simulations with random phase plate smoothed laser beams confirm the relevance of this effect in carbon plasma. A second effect is that cross-beam energy transfer (CBET) inhibition persists in strongly damped plasmas when the speckle radius is comparable with the IAW damping distance. There, the reduction in the IAW amplitude is attributed to the smallness of the speckle's envelop. These results are supported by a simple model that analytically estimates the CBET and clearly shows that neglecting the inhomogeneities in the laser intensity would usually lead to an overestimate of the energy exchange.

Quadratic cross-sections in the multiple scattering by a pair of liquid cylinders insonified by arbitrary-shaped acoustical sheets

Stemming from the law of energy conservation applied to scattering, generalized exact partial-wave series expressions are derived for the extrinsic and intrinsic acoustic scattering, extinction and absorption cross-sections for a pair of fluid/liquid-like (viscous) cylinders of arbitrary radii. The incident insonifying field is of arbitrary shape such that any structured wavefront in two-dimensions is accomodated by this formalism, in contrast with the case of plane waves. The modal expansion method in combination with the translational addition theorem for cylindrical wave functions are used to derive the exact analytical expressions for the quadratic (nonlinear) cross-sections, and numerical computations for a non-paraxial focused Gaussian acoustical sheet chosen as an example illustrate the analysis. The results clearly show the difference between the behavior of the extrinsic and intrinsic cross-sections. The formalism presented here is generalized for any acoustical sheet such that Airy, Hermite-Gaussian and other wavefronts (in 2D) can be considered provided the appropriate beam-shape coefficients are used. The analogy with the optical counterpart is also noted.

Five-Wave Resonances in Deep Water Gravity Waves: Integrability, Numerical Simulations and Experiments

In this work we consider the problem of finding the simplest arrangement of resonant deep-water gravity waves in one-dimensional propagation, from three perspectives: Theoretical, numerical and experimental. Theoretically this requires using a normal-form Hamiltonian that focuses on 5-wave resonances. The simplest arrangement is based on a triad of wavevectors K1+K2=K3 (satisfying specific ratios) along with their negatives, corresponding to a scenario of encountering wavepackets, amenable to experiments and numerical simulations. The normal-form equations for these encountering waves in resonance are shown to be non-integrable, but they admit an integrable reduction in a symmetric configuration. Numerical simulations of the governing equations in natural variables using pseudospectral methods require the inclusion of up to 6-wave interactions, which imposes a strong dealiasing cut-off in order to properly resolve the evolving waves. We study the resonance numerically by looking at a target mode in the base triad and showing that the energy transfer to this mode is more efficient when the system is close to satisfying the resonant conditions. We first look at encountering plane waves with base frequencies in the range 1.32–2.35 Hz and steepnesses below 0.1, and show that the time evolution of the target mode’s energy is dramatically changed at the resonance. We then look at a scenario that is closer to experiments: Encountering wavepackets in a 400-m long numerical tank, where the interaction time is reduced with respect to the plane-wave case but the resonance is still observed; by mimicking a probe measurement of surface elevation we obtain efficiencies of up to 10% in frequency space after including near-resonant contributions. Finally, we perform preliminary experiments of encountering wavepackets in a 35-m long tank, which seem to show that the resonance exists physically. The measured efficiencies via probe measurements of surface elevation are relatively small, indicating that a finer search is needed along with longer wave flumes with much larger amplitudes and lower frequency waves. A further analysis of phases generated from probe data via the analytic signal approach (using the Hilbert transform) shows a strong triad phase synchronisation at the resonance, thus providing independent experimental evidence of the resonance.

Non uniqueness of non runaway solutions of Abraham—Lorentz—Dirac equation in an external laser pulse

In the paper (Carati et al 1995 Non Linearity 8 65-79) it was shown that, for motions on a line under the action of a potential barrier, the third-order Abraham–Lorentz–Dirac equation presents the phenomenon of non uniqueness of non runaway solutions. Namely, at least for a sufficiently steep barrier, the physical solutions of the equation are not determined by the ‘mechanical state’ of position and velocity, and knowledge of the initial acceleration too is required. Due to recent experiments, both in course and planned, on the interactions between strong laser pulses and ultra relativistic electrons, it becomes interesting to establish whether such a non uniqueness phenomenon extends to the latter case, and for which ranges of the parameters. In the present work we will consider just the simplest model, i.e., the case of an electromagnetic plane wave, and moreover the Abraham–Lorentz–Dirac equation will be dealt with in the non relativistic approximation. The result we found is that the non uniqueness phenomenon occurs if, at a given frequency of the incoming wave, the field intensity is sufficiently large. An analytic estimate of such a threshold is also given. At the moment it is unclear whether such a phenomenon applies also in the full relativistic case, which is the one of physical interest.

Diffraction of nonstationary waves on wedges and half‐planes under mixed boundary conditions: Exact solutions and weakening of blast waves by wedge‐shaped barriers

AbstractThe problem of diffraction of nonstationary plane waves on a wedge under mixed boundary conditions is considered when the Neumann condition is set on one side of the wedge and the Dirichlet condition is set on other side. For the case of an incident plane wave in the form of a step function, an exact solution of the problem (expressed through elementary functions) is obtained by the direct method based on self‐similarity of the problem, i.e., using the fact that its solution is a homogeneous function of space coordinates and time. This method reduces the dimension of the problem by unity and leads it to the initial‐boundary value problem for the equation of string oscillations in the hyperbolic region and to the mixed boundary problem for the two‐dimensional Laplace equation in the elliptic region. The exact solution is given by reducing the mixed problem for an elliptic domain to a problem with boundary conditions of one type on the whole boundary by means of analytic continuation of unknown function. The results for a half‐plane are significantly simplified in comparison with the solution for a wedge. The behaviour of the obtained solution at the tip of the wedge and near the diffraction front is investigated and qualitative differences from the results for diffraction problems with one‐type boundary conditions on the whole boundary are noted. The numerical comparison is given of the near‐front asymptotic solution of mixed diffraction problem and the similar asymptotic solution by Friedlander for a wedge with acoustically rigid walls. This comparison shows that in the case of a wedge with mixed boundary conditions there is a much greater weakening (attenuation) of the blast waves in the shadow region.

On the number of excursion sets of planar Gaussian fields

The Nazarov–Sodin constant describes the average number of nodal set components of smooth Gaussian fields on large scales. We generalise this to a functional describing the corresponding number of level set components for arbitrary levels. Using results from Morse theory, we express this functional as an integral over the level densities of different types of critical points, and as a result deduce the absolute continuity of the functional as the level varies. We further give upper and lower bounds showing that the functional is at least bimodal for certain isotropic fields, including the important special case of the random plane wave.

Scintillation index and BER performance for optical wave propagation in anisotropic underwater turbulence under the effect of eddy diffusivity ratio.

Underwater optical communication has been a promising technology but is severely affected by underwater turbulence due to the resulting fluctuations in the index of refraction. In this paper, a revised spatial power spectrum model is obtained that considers the refraction index to be a function of the eddy diffusivity ratio, assuming the underwater turbulence is anisotropic. The scintillation indices for both plane and spherical waves that propagate in underwater turbulence are derived based on this model. Thereafter, the performance of an optical communication system, i.e., the outage probability and bit error rate, with the associated aperture averaging effect is considered. The simulation results demonstrate that temperature-induced and salinity-induced turbulence have distinct influences on the scintillation index and consequently result in different system performances. In addition, the variation in the eddy diffusivity ratio in some intervals induces more complicated results for underwater optical communication. Moreover, the effect of the receiver aperture diameter on the aperture averaging factor is presented in anisotropic underwater turbulence. Such an effect is more obvious in the plane wave case than in the spherical wave case. These results can find potential application in the engineering design of optical communication systems in an underwater environment.

Nonlinear reflection of a two-dimensional finite-width internal gravity wave on a slope

The nonlinear reflection of a finite-width plane internal gravity wave incident onto a uniform slope is addressed, relying on the inviscid theory of Thorpe (J. Fluid Mech., vol. 178, 1987, pp. 279–302) for pure plane waves. The aim of this theory is to determine the conditions under which the incident and the reflected waves form a resonant triad with the second-harmonic wave resulting from their interaction. Thorpe’s theory leads to an indeterminacy of the second-harmonic wave amplitude at resonance. In waiving this indeterminacy, we show that the latter amplitude has a finite behaviour at resonance, increasing linearly from the slope. We investigate the influence of background rotation and find similar results with a weaker growth rate. We then adapt the theory to the case of an incident plane wave of finite width. In this case, nonlinear interactions are confined to the area where the incident and reflected finite-width waves superpose, implying that the amplitude of the second-harmonic wave is bounded at resonance. We find good agreement with the results of numerical simulations in a vertical plane as long as the dissipated power of the incident and reflected waves remain smaller than the power transferred to the second-harmonic wave. This is the case for small slope angles. As the slope angle increases, the focusing of the reflected wave enhances viscous effects and dissipation eventually dominates over nonlinear transfer. We finally discuss the relevance of laboratory experiments to assess the validity of the theoretical results.

Smoothness and monotonicity of the excursion set density of planar Gaussian fields

Nazarov and Sodin have shown that the number of connected components of the nodal set of a planar Gaussian field in a ball of radius $R$, normalised by area, converges to a constant as $R\to \infty $. This has been generalised to excursion/level sets at arbitrary levels, implying the existence of functionals $c_{ES}(\ell )$ and $c_{LS}(\ell )$ that encode the density of excursion/level set components at the level $\ell $. We prove that these functionals are continuously differentiable for a wide class of fields. This follows from a more general result, which derives differentiability of the functionals from the decay of the probability of `four-arm events' for the field conditioned to have a saddle point at the origin. For some fields, including the important special cases of the Random Plane Wave and the Bargmann-Fock field, we also derive stochastic monotonicity of the conditioned field, which allows us to deduce regions on which $c_{ES}(\ell )$ and $c_{LS}(\ell )$ are monotone.

Metasurface Matching Layers for Enhanced Electric Field Penetration Into the Human Body

The use of electromagnetic fields applied to human tissues has proven to be beneficial in several applications, such as monitoring physiological parameters and delivering medical treatments. Often applications rely on targeted energy deposition into the tissue, or rely on wireless powering of implanted devices. In such cases, the system energy efficiency, the stability of the field, and ultimately the process safety could all benefit from minimizing the mismatch at the air-skin interface. In this article, the maximization of the electric field transmitted into the muscle tissue is initially addressed by optimizing a dielectric-only matching layer in terms of thickness and relative dielectric permittivity, and under realistic constraints on low-cost available materials. The propagation of the electromagnetic field inside a multilayered medium that represents the body is evaluated by using the wave-transmission chain matrix approach. Furthermore, an innovative solution, based on the application of a metasurface matching layer (MML), is proposed to significantly improve the performance of the matching, thus enhancing the electromagnetic fields reaching the targeted muscle tissue. A thorough assessment of the performance is carried out considering both the presence of an air gap, and the case of plane waves impinging at oblique incidence.

Modification of multipole transitions by twisted light

A theoretical analysis is presented for the excitation of single many-electron atoms and ions by twisted (or vortex) light. Special emphasis is put on excitations that can proceed via several electric and magnetic multipole channels. We argue that the relative strength of these multipoles is very sensitive to the topological charge and kinematic parameters of the incident light and can be strongly modified with respect to the plane-wave case. Most remarkably, the modification of multipole transitions by twisted radiation can be described by means of a geometrical factor. This factor is independent of the shell structure of a particular target atom and just reflects the properties of the light beam as well as the position of an atom with respect to the vortex axis. An analytical expression for the geometrical factor is derived for Bessel photons and for a realistic experimental situation in which the position of an atom is not well determined. To illustrate the use of the geometrical factor for the analysis of (future) measurements, detailed calculations are presented for the $3s3p \, ^3P_1 \to 3s 3p \, ^1P_1$ excitation in neutral Mg.

Spacetime picture of baryon stopping in the color-glass condensate

We discuss baryon stopping in the Color Glass Condensate description of high energy scattering. We consider the scattering of a distribution of valence quarks on an ultra-relativistic sheet of colored charge. We compute the distribution of scattered quarks from a composite projectile, and calculate the baryon currents before and after the collisions and on an event by event basis. We obtain simple analytic estimates of the baryon number compression and rapidity shifts, which in the idealized case of plane wave scattering, produce results that agree with considerations of Anishetty-Koehler-McLerran.

Model of Steady-state Temperature Rise in Multilayer Tissues Due to Narrow-beam Millimeter-wave Radiofrequency Field Exposure.

The assessment of health effects due to localized exposures from radiofrequency fields is facilitated by characterizing the steady-state, surface temperature rise in tissue. A closed-form analytical model was developed that relates the steady-state, surface temperature rise in multilayer planar tissues as a function of the spatial-peak power density and beam dimensions of an incident millimeter wave. Model data was derived from finite-difference solutions of the Pennes bioheat transfer equation for both normal-incidence plane waves and for narrow, circularly symmetric beams with Gaussian intensity distribution on the surface. Monte Carlo techniques were employed by representing tissue layer thicknesses at different body sites as statistical distributions compiled from human data found in the literature. The finite-difference solutions were validated against analytical solutions of the bioheat equation for the plane wave case and against a narrow-beam solution performed using a commercial multiphysics simulation package. In both cases, agreement was within 1-2%. For a given frequency, the resulting analytical model has four input parameters, two of which are deterministic, describing the level of exposure (i.e., the spatial-peak power density and beam width). The remaining two are stochastic quantities, extracted from the Monte Carlo analyses. The analytical model is composed of relatively simple functions that can be programmed in a spreadsheet. Demonstration of the analytical model is provided in two examples: the calculation of spatial-peak power density vs. beam width that produces a predefined maximum steady-state surface temperature, and the performance evaluation of various proposed spatial-averaging areas for the incident power density.

An accurate theory of X-ray coplanar multiple SRMS diffractometry.

The article reports an accurate theory of X-ray coplanar multiple diffraction for an experimental setup that consists of a generic synchrotron radiation (SR) source, double-crystal monochromator (M) and slit (S). It is called for brevity the theory of X-ray coplanar multiple SRMS diffractometry. The theory takes into account the properties of synchrotron radiation as well as the features of diffraction of radiation in the monochromator crystals and the slit. It is shown that the angular and energy dependence (AED) of the sample reflectivity registered by a detector has the form of a convolution of the AED in the case of the monochromatic plane wave with the instrumental function which describes the angular and energy spectrum of radiation incident on the sample crystal. It is shown that such a scheme allows one to measure the rocking curves close to the case of the monochromatic incident plane wave, but only using the high-order reflections by monochromator crystals. The case of four-beam (220)(331)({\overline {11}}1) diffraction in Si is considered in detail.

Bohmian trajectories for the half-line barrier

Bohmian trajectories are considered for a particle that is free (i.e. the potential energy is zero), except for a half-line barrier. On the barrier, both Dirichlet and Neumann boundary conditions are considered. The half-line barrier yields one of the simplest cases of diffraction. Using the exact time-dependent propagator found by Schulman, the trajectories are computed numerically for different initial Gaussian wave packets. In particular, it is found that different boundary conditions may lead to qualitatively different sets of trajectories. In the Dirichlet case, the particles tend to be more strongly repelled. The case of an incoming plane wave is also considered. The corresponding Bohmian trajectories are compared with the trajectories of an oil drop hopping on the surface of a vibrating bath.

Compton scattering of Bessel light with large recoil parameter

Compton scattering of light from a Bessel beam is investigated for which the energy of a photon in the beam is comparable to the mass energy of an electron. Using a fully relativistic treatment, we present numerical results on how the angular distribution and polarization of the scattered photons depend on the opening angle, projection of orbital angular momentum, and the energy of the twisted Bessel photons of the incident beam and compare these results to the standard case of incident plane waves. Compton scattering of a superposition of two Bessel beams is also investigated. The energy of the incident twisted Bessel photon is found to significantly affect the angular distribution and polarization of the scattered radiation and their sensitivity to the other parameters of the incident photon.

Simulation of cold magnetized plasmas with the 3D electromagnetic software CST Microwave Studio®

Detailed designs of ICRF antennas were made possible by the development of sophisticated commercial 3D codes like CST Microwave Studio® (MWS). This program allows for very detailed geometries of the radiating structures, but was only considering simple materials like equivalent isotropic dielectrics to simulate the reflection and the refraction of RF waves at the vacuum/plasma interface. The code was nevertheless used intensively, notably for computing the coupling properties of the ITER ICRF antenna. Until recently it was not possible to simulate gyrotropic medias like magnetized plasmas, but recent improvements have allowed programming any material described by a general dielectric or/and diamagnetic tensor. A Visual Basic macro was developed to exploit this feature and was tested for the specific case of a monochromatic plane wave propagating longitudinally with respect to the magnetic field direction. For specific cases the exact solution can be expressed in 1D as the sum of two circularly polarized waves connected by a reflection coefficient that can be analytically computed. Solutions for stratified media can also be derived. This allows for a direct comparison with MWS results. The agreement is excellent but accurate simulations for realistic geometries require large memory resources that could significantly restrict the possibility of simulating cold plasmas to small-scale machines.

Extinction efficiency of “elastic–sheet” beams by a cylindrical (viscous) fluid inclusion embedded in an elastic medium and mode conversion—Examples of nonparaxial Gaussian and Airy beams

Stemming from the law of the conservation of energy in an elastic medium, this work extends the scope of the previous analysis for a scatterer immersed in a nonviscous liquid [F. G. Mitri, Ultrasonics 62, 20–26 (2015)] to the case of a (viscous) fluid circular cylinder cross-section encased in a homogeneous, isotropic, elastic matrix. Analytical expressions for the absorption, scattering, and extinction efficiencies (or cross-sections) are derived for “elastic-sheets” (i.e., finite beams in 2D propagating in elastic media) of arbitrary wavefront, in contrast to the ideal case of plane waves of infinite extent. The mathematical expressions are formulated in generalized partial-wave series expansions in cylindrical coordinates involving the beam-shape coefficients of finite elastic-sheet beams with arbitrary wavefront, and the scattering coefficients of the fluid cylinder encased in the elastic matrix. The analysis shows that in elastodynamic scattering, both the scattered L-wave as well as the scattered T-wave contribute to the time-averaged scattered efficiency (or power). However, the extinction efficiency only depends on the scattering coefficients characterizing the same type (L or T) as the incident wave. Numerical computations for the (non-dimensional energy) efficiency factors such as the absorption, scattering, and extinction efficiencies of a circular cylindrical viscous fluid cavity embedded in an elastic aluminum matrix are performed for nonparaxial focused Gaussian and Airy elastic-sheet beams with arbitrary longitudinal and transverse normally-polarized (shear) wave incidences in the Rayleigh and resonance regimes. A series of elastic resonances are manifested in the plots of the efficiencies as the non-dimensional size parameters for the L- and T-waves are varied. As the beam waist for the nonparaxial Gaussian beam increases, the plane wave result is recovered, while for a tightly focused wavefront, some of the elastic resonances can be suppressed. Moreover, the efficiencies for the embedded circular viscous fluid cylinder in the field of an Airy elastic-sheet display a spatial parabolic (nonlinear) type of absorption, scattering, and extinction, representative of the intrinsic property of the curved accelerating beam in the elastic matrix. The present analysis provides an improved method for the computations of energy efficiency factors in elastodynamics for finite beams in 2D, which can be used as a priori information in the direct or inverse characterization of the mechanical properties of cylindrical fiber-reinforced materials, pipes, vessels, etc., embedded in an elastic medium.