Arbitrary Plane Wave Research Articles

Estimation of flexural wavenumbers in the presence of multiple wave components

The separation of closely spaced spectral components is a known problem in signal processing, be it response data either in the spatial or temporal domain. Herein an experimental method based on the maximization of the correlation between measured data and an arbitrary plane wave field is investigated for its capability in distinguishing closely spaced flexural wavenumbers. Limitations arising from data sampling and windowing are considered. These processes are used along with numerical simulations as a basis to establish the boundaries within which the method successfully detects the components present. An example from experimental data is also shown, where an alternative method, the empirical mode decomposition, is applied to verify the results and to determine the accuracy of the correlation method in comparison to another existing technique.

Proportionality of gravitational and electromagnetic radiation by an electron in an intense plane wave

Accelerated charges emit both electromagnetic and gravitational radiation. Classically, it was found that the electromagnetic energy spectrum radiated by an electron in a monochromatic plane wave is proportional to the corresponding gravitational one. Quantum mechanically, it was shown that the amplitudes of graviton photoproduction and Compton scattering are proportional to each other at tree level. Here, by combining strong-field QED and quantum gravity, we demonstrate that the amplitude of nonlinear graviton photoproduction in an arbitrary plane wave is proportional to the corresponding amplitude of nonlinear Compton scattering. Also, introducing classical amplitudes we prove that the proportionality relies on the semiclassical nature of the electron's motion in a plane wave and on energy-momentum conservation laws, leading to the same proportionality constant in the classical and quantum case. These results deepen the intertwine between gravity and electromagnetism into both a nonlinear and a quantum level.

Quasiclassical representation of the Volkov propagator and the tadpole diagram in a plane wave

The solution of the Dirac equation in the presence of an arbitrary plane wave, corresponding to the so-called Volkov states, has provided an enormous insight in strong-field QED. In [Phys. Rev. A \textbf{103}, 076011 (2021)] a new "fully quasiclassical" representation of the Volkov states has been found, which is equivalent to the one known in the literature but which more transparently shows the quasiclassical nature of the quantum dynamics of an electron in a plane-wave field. Here, we derive the corresponding expression of the propagator by constructing it using the fully quasiclassical form of the Volkov states. The found expression allows one, together with the fully quasiclassical expression of the Volkov states, to compute probabilities in strong-field QED in an intense plane wave by manipulating only 2-by-2 rather than 4-by-4 Dirac matrices as in the usual approach. Moreover, apart from the exponential functions featuring the classical action of an electron in a plane wave, the fully quasiclassical Volkov propagator depends only on the electron kinetic four-momentum in the plane wave, which is a gauge-invariant quantity. Finally, we also compute the one-loop tadpole diagram in a plane wave starting from the Volkov propagator and we find that after renormalization it identically vanishes.

Electron mass shift in an intense plane wave

Upcoming experiments on the interaction of electrons with intense laser fields are envisaged to become more and more accurate, which calls for theoretical computations of rates and probabilities with correspondingly higher precision. In strong-field QED this requires the knowledge of radiative corrections to be added to leading-order results. Here, we first derive the mass operator in momentum space of an off-shell electron in the presence of an arbitrary plane wave. By taking the average of the mass operator in momentum space over an on-shell electron state, we obtain a new representation, equivalent to but more compact than the known one computed in [Sov. Phys. JETP \textbf{42}, 400 (1975)]. Moreover, we use the obtained mass operator to determine the electron mass shift in an arbitrary plane wave, which generalizes the already known expression in a constant crossed field. The spin-dependent part of the electron mass shift can be related to the anomalous magnetic moment of the electron in the plane wave. We show that within the locally constant field approximation it is possible to conveniently define a local expression of the electron anomalous magnetic moment, which reduces to the known expression in a constant crossed field. Beyond the locally constant field approximation, however, the interaction between the electron and the plane wave is non-local such that it is not possible to conveniently introduce an electron anomalous magnetic moment.

First-order strong-field QED processes including the damping of particle states

Volkov states are exact solutions of the Dirac equation in the presence of an arbitrary plane wave. Volkov states, as well as free photon states, are not stable in the presence of the background plane-wave field but "decay" as electrons/positrons can emit photons and photons can transform into electron-positron pairs. By using the solutions of the corresponding Schwinger-Dyson equations within the locally-constant field approximation, we compute the probabilities of nonlinear single Compton scattering and nonlinear Breit-Wheeler pair production by including the effects of the decay of electron, positron, and photon states. As a result, we find that the probabilities of these processes can be expressed as the integral over the light-cone time of the known probabilities valid for stable states per unit of light-cone time times a light-cone time-dependent exponential damping function for each interacting particle. The exponential function for an incoming (outgoing) either electron/positron or photon at each light-cone time corresponds to the total probability that either the electron/positron emits a photon via nonlinear Compton scattering or the photon transforms into an electron-positron pair via nonlinear Breit-Wheeler pair production until that light-cone time (from that light-cone time on). It is interesting that the exponential damping terms depend not only on the particles momentum but also on their spin (for electrons/positrons) and polarization (for photons). This additional dependence on the discrete quantum numbers prevents the application of the electron/positron spin and photon polarization sum-rules, which significantly simplify the computations in the perturbative regime.

Analytical spectrum of nonlinear Thomson scattering including radiation reaction

Accelerated charges emit electromagnetic radiation and the consequent energy-momentum loss alters their trajectory. This phenomenon is known as radiation reaction and the Landau-Lifshitz (LL) equation is the classical equation of motion of the electron, which takes into account radiation-reaction effects in the electron trajectory. By using the analytical solution of the LL equation in an arbitrary plane wave, we compute the analytical expression of the classical emission spectrum via nonlinear Thomson scattering including radiation-reaction effects. Both the angularly resolved and the angularly integrated spectra are reported, which are valid in an arbitrary plane wave. Also, we have obtained a phase-dependent expression of the electron dressed mass, which includes radiation-reaction effects. Finally, the corresponding spectra within the locally constant field approximation have been derived.

Peripherally Excited Phased Array Architecture for Beam Steering with Reduced Number of Active Elements

An electronically scannable phased array antenna architecture is proposed with a drastically reduced number of active antenna elements. The proposed approach is based on the concept of Huygens’ metasurfaces, where the fields in a given region are controlled by active or passive electromagnetic sources on the boundary surface of this region. Using this approach, arbitrary plane waves are excited inside a metallic cavity by peripheral sources, and the cavity is engineered to radiate a single or multiple pencil beams through appropriately perforated slots on its top surface. The proposed peripherally excited (PEX) phased array architecture generates pencil beams that are electronically scanned by controlling the amplitudes and phases of the peripheral sources. The proposed concept has the potential to drastically reduce the required number of active elements in 2-D phased arrays without compromising directivity. However, the possible beam-pointing directions are constrained.

Scattering and Shielding Analyses of Carbon Fiber Composites-Based Cylindrical Shells Using a Multifilament Doublet Current Method

We present in this paper, a multifilament doublet current method (MFDCM) combined with the tensorial impedance boundary condition (TIBC) to simulate and analyze scattering and shielding performances of carbon fiber composite (CFC) material-based cylindrical shells. The TIBC of a shell made up with the multilayered CFC material with an arbitrary fiber orientation in each layer is introduced and derived. The MFDCM is subsequently formulated by employing the TIBC to handle numerical calculations with the anisotropic lossy material, such as a multilayered CFC material, for the first time. Monostatic and bistatic echo widths are investigated with reference to different layer numbers, fiber orientations, and incident wave polarizations. These different scenarios are also taken into consideration in the shielding effectiveness (SE) prediction. Both TE and TM modes are excited within the cylindrical shell under arbitrary incident plane waves over a high frequency range. Results are in excellent agreement with published ones. The proposed method has its merits on simplicity and conciseness. Also it can be applied to handle shells of arbitrary smooth cross sections.

Nonlinear trident pair production in an arbitrary plane wave: A focus on the properties of the transition amplitude

The process of nonlinear electron-positron pair production by an electron colliding with an arbitrary plane wave electromagnetic field (nonlinear trident pair production) is studied analytically and numerically. Special emphasis is put on the properties of the transition amplitude. In fact, its original expression as resulting from applying the Wick's theorem turns out to be divergent and not to manifestly fulfill gauge invariance. By restoring the latter, the amplitude is regularized and investigated in different regimes. In particular, the amplitude is divided into a two-step and a one-step contributions, depending on the scaling dependence on the laser pulse duration. The corresponding contributions to the positron angular distribution spectra and the resulting interference terms are studied numerically emphasizing the possibility of measuring experimentally the contribution of the one-step contribution.

Plane Wave Diffraction by Arbitrary-Angled Lossless Wedges: High-Frequency and Time-Domain Solutions

This paper concerns the diffraction phenomenon originated by a uniform plane wave impacting an arbitrary-angled lossless dielectric wedge with planar surfaces. The high-frequency diffraction coefficients are obtained by performing uniform asymptotic evaluations of the radiation integrals resulting from the physical optics approximation of the electric and magnetic equivalent surface currents located on the inner and outer faces of the wedge. The final expressions are in closed form and contain the standard transition function of the uniform theory of diffraction and the Fresnel reflection and transmission coefficients related to the geometrical optics propagation mechanisms. Moreover, they allow a simple physical interpretation of each contribution and they are easy to use and to implement in a computer code. The knowledge of such diffraction coefficients in the frequency domain permits to apply the inverse Laplace transform to obtain the time-domain counterparts, which enable the evaluation of the transient diffracted field originated by an arbitrary function plane wave.

Padé approximation for time-domain plane wave reflected from a lossy earth

To deal with the behaviour of wire structures subjected to electromagnetic waves with the finite-difference time-domain (FDTD) method, it is necessary to establish the external electromagnetic excitation in time-domain. For a homogeneous lossy half-space problem, the Fresnel reflection coefficients for arbitrary polarization plane wave are usually multiplied by the pulse spectrum in the frequency domain and the result is transformed into the time-domain. In this paper, an accurate method based on the Padé approximation theory in conjunction with the partial fraction expansion is used, and leads to expressions of the field above a homogeneous lossy earth that can analytically be transformed into the time-domain. The influence of the common degree of the numerator and denominator of the Padé approximant on the accuracy of the proposed method is discussed.

Analytical infrared limit of nonlinear Thomson scattering including radiation reaction

If an electric charge is accelerated by a sufficiently intense electromagnetic field, the effects of the radiation emitted by the charge on the charge dynamics (radiation reaction) cannot be ignored. Here we show that classical radiation-reaction effects alter qualitatively and quantitatively the infrared behavior of the spectrum of the radiation emitted by an electron in the presence of an intense electromagnetic plane wave (nonlinear Thomson scattering). An analytical expression of the infrared limit of nonlinear Thomson scattering is provided, which includes radiation-reaction effects and is valid for an arbitrary plane wave. Apart from their own conceptual importance and as a signature of classical radiation reaction, these results provide the limiting expression of the corresponding and yet unknown exact infrared behavior of strong-field QED in an intense plane wave.

Diffraction by a Structure Composed of Metallic and Dielectric 90° Blocks

This letter deals with the plane wave diffraction by a composite structure consisting of metallic and lossless dielectric 90° blocks, which are adjacent and share the edge. Such a problem is first tackled in the frequency domain, and the related diffraction coefficients are determined by exploiting the uniform asymptotic physical optics approach. The inverse Laplace transform is applied to obtain the time-domain counterparts, which can be used to compute the transient diffracted field due to an arbitrary function plane wave.

Efficient Field Reconstruction Using Compressive Sensing

Compressive sensing is used to reconstruct the time-harmonic electric field created by multipath fading from a limited number of measurement points over a planar region. The multipath fading signal is shown to be the superposition of multiple plane wave components and thus has a sparse representation in the spatial-frequency domain. The discrete Fourier basis used as the dictionary for orthogonal matching pursuit is oversampled to ensure sufficient resolution in the spatial-frequency domain. Experimental results at 10 GHz using an arbitrary plane wave expansion show that the signal-to-error ratio of the compressive sensing reconstruction is approximately 16 dB when randomly selecting only 7.5% of the total points.

Embedding formulae for scattering in a waveguide containing polygonal obstacles

For certain wave scattering problems embedding formulae can be derived, which express the solution, or far-field behaviour of the solution, for arbitrary plane wave incident angle in terms of the corresponding quantities for a finite number of other related problems. Their scope has so far been limited to scattering in R^2, and to a lesser extent R^3; in this paper we derive embedding formulae for wave scattering in a class of two-dimensional waveguide. The waveguide is straight and of uniform width outside a finite length region within which the boundaries are piecewise-linear and the waveguide can contain polygonal obstacles, a restriction being that all boundaries of the waveguide and obstacles must be inclined at a rational angle to the axis of the waveguide. Once solutions are determined for a finite set of incident propagating modes, the embedding formulae provide expressions for reflection and transmission coefficients for all remaining incident propagating modes. The precise number of solutions required is a function of the number and nature of the corners of the boundaries and obstacles. The formulae are illustrated for a particular waveguide geometry for which the problem can be formulated as an integral equation and approximate numerical solutions determined using the Galerkin method.

Multiple scattering of a zero-order Bessel beam with arbitrary incidence by an aggregate of uniaxial anisotropic spheres

Based on the generalized multiparticle Mie theory, multiple scattering of an aggregate of uniaxial anisotropic spheres illuminated by a zero-order Bessel beam (ZOBB) with arbitrary propagation direction is investigated. The particle size and configuration are arbitrary. The arbitrary incident Bessel beam is expanded in terms of spherical vector wave functions (SVWFs). Utilizing the vector addition theorem of SVWFs, interactive and total scattering coefficients are derived through the continuous boundary conditions on which the interaction of the particles is considered. The accuracy of the theory and codes are verified by comparing results with those obtained for arbitrary plane wave incidence by CST simulation, and for ZOBB incidence by a numerical method. The effects of angle of incidence, pseudo-polarization angle, half-conical angle, beam center position, and permittivity tensor elements on the radar cross sections (RCSs) of several types of collective uniaxial anisotropic spheres, such as a linear chain, a 4×4×4 cube-shaped array, and other periodical structures consisting of massive spheres, are numerically analyzed. Selected results on the properties of typical particles such as TiO2, SiO2, or other particle lattices are calculated. This investigation could provide an effective test for further research on the scattering characteristics of an aggregate of anisotropic spheres by a high-order Bessel vortex beam. The results have important application in optical tweezers and particle manipulation.

TD-UAPO diffracted field evaluation for penetrable wedges with acute apex angle.

This study deals with the time domain (TD) diffraction phenomenon related to a penetrable acute-angled dielectric wedge. The transient diffracted field originated by an arbitrary function plane wave is evaluated via a convolution integral involving the TD diffraction coefficients, which are determined here in closed form, starting from the knowledge of the frequency domain counterparts. In particular, the inverse Laplace transform is applied to the uniform Asymptotic physical optics diffraction coefficients valid for the internal region of the wedge and the surrounding space. Diffraction by penetrable wedges in the TD framework is a challenging problem from the analytical point of view, and no other expressions are available in closed form for the diffraction coefficients associated with the considered problem.

Boundary Value Problem of an Infinite Array of Loaded Apertures

A mathematical model of the scattering by a periodically arranged apertures in conducting plates is presented. The boundary value problem of an infinite array of loaded apertures is formulated for an arbitrary incident plane wave. The reflection coefficient for some array geometries is obtained and the calculated values are in good agreement with the measurements in a previously published researches. All the rectangular apertures in the array are assumed to be identical and infinitesimally thin. The mathematical model is based on Floquet’s theorem that specifies the requirement of periodicity by the electromagnetic fields.

Vacuum refractive indices and helicity flip in strong-field QED

Vacuum birefringence is governed by the amplitude for a photon to flip helicity or polarisation state in an external field. Here we calculate the flip and non-flip amplitudes in arbitrary plane wave backgrounds, along with the induced spacetime-dependent refractive indices of the vacuum. We compare the behaviour of the amplitudes in the low energy and high energy regimes, and analyse the impact of pulse shape and energy. We also provide the first lightfront-QED derivation of the coefficients in the Heisenberg-Euler effective action.

Quasiclassical propagator of a relativistic particle via the path-dependent gauge potential

The proper time formalism for a particle propagator in an external electromagnetic field is combined with the path-dependent formulation of gauge theory to simplify the quasiclassical propagator of a relativistic particle. The latter is achieved due to a specific choice of gauge corresponding to the use of the classical path in the path-dependent formulation of gauge theory, which leads to cancellation of the interaction part of the classical action in the Feynman path integral. A simple expression for the quasiclassical propagator is obtained in all cases of the external field when the classical equations of motion in this field are integrable. As an example, simple expressions for the propagators are derived for a spinless charged particle interacting with the following fields: an arbitrary constant and uniform electromagnetic field, an arbitrary plane wave, and finally an arbitrary plane wave combined with an arbitrary constant and uniform electromagnetic field. In all these cases the quasiclassical propagator coincides with the exact result.