Monochromatic Plane Research Articles

Influence of acoustic type waves on the vortex wake behind a wing in the supersonic flow

In this paper an investigation of an acoustic type waves influence on a wingtip vortex wake parameters was performed in a supersonic flow. The supersonic flow around a straight wing with sharp leading and trailing edges was considered at an attack angle of 10 degrees at Mach number of incoming flow M = 2.Perturbations were introduced into a steady state stream in the form of monochromatic plane waves with small amplitude. Numerical simulations were carried out at the Keldysh Institute of Applied Mathematics RAS using the parallel algorithm for turbulent flow simulation. For the numerical studies an approach based on the URANS method with using the SA turbulence model was applied. Numerical simulations were carried out on the supercomputing system K-60.Numerical data were obtained in the area exceeding 30 wing chords downstreamfrom a wing axis. A numerical data on the pulsation of gasdynamic parameters in the vortex wake influenced by disturbance are obtained, in particular, frequencies and disturbance ranges on the wingtip vortex axis are investigated depending on a distance from the wing - vortex generator.

Frequency-dependent current density tensors as density functions of dynamic polarizabilities.

Relationships accounting for contributions to the first-order charge density ρ(1) and current density J(1), induced in the electrons of a molecule by a monochromatic plane wave, have been obtained via time-dependent quantum mechanical perturbation theory. Their gauge invariance and invariance in passive translations of the coordinate system have been demonstrated (i) within the (long wavelengths) electric dipole approximation, in which only the electric field contributions to these densities are required, and (ii) within the electric quadrupole approximation, in which nonseparable terms provided by the magnetic field and by the electric field gradient, assumed uniform over the molecular domain, are needed. It is shown that the physical meaning of current density tensors depending on the frequency ω of the monochromatic wave shone on the molecule, and corresponding to derivatives of the current density J(1)(r, ω) with respect to components of the perturbing fields, is that of property density. Therefore, frequency-dependent current density tensors can be interpreted as the integrand function in 3d-space integrals defining dynamic molecular response tensors, e.g., electric dipole, mixed electric dipole-magnetic dipole, and electric dipole-quadrupole polarizabilites. Plots of current density tensors are expected to provide important information on the molecular domains giving dominant contributions to these properties.

Full-wave analysis of the scattering of a pulsed light beam by dielectric cylinders embedded in a homogeneous medium

An approach to study the time-domain scattering by a set of dielectric cylinders with circular cross section, placed in a semi-infinite medium, is presented. The illuminating light comes from a pulsed beam impinging onto the cylinders from outside the medium. The solution is developed in a semi-analytical way, starting from results based on the cylindrical wave approach pertinent to the case of illumination by a monochromatic plane wave. The method is numerically implemented to simulate the scattering response of buried cylinders illuminated by a pulsed Gaussian beam. In the presented results, the different contributions to the total scattered field are recognizable, giving an account of all the interactions between incident field, target and interface. The model adopted is well suited to the study, at optical frequencies, of scattering problems involving biological samples, such as vessels and fibers, embedded in tissues or immersed in fluids, through fast and accurate electromagnetic simulation.

Interpretation of Departure from the Broad-line Region Scaling in Active Galactic Nuclei

Abstract Most results of the reverberation monitoring of active galaxies showed a universal scaling of the time delay of the Hβ emission region with the monochromatic flux at 5100 Å, with very small dispersion. Such a scaling favored the dust-based formation mechanism of the broad-line region (BLR). Recent reverberation measurements showed that actually a significant fraction of objects exhibit shorter lags than the previously found scaling. Here we demonstrate that these shorter lags can be explained by the old concept of scaling of the BLR size with the ionization parameter. Assuming a universal value of this parameter and a universal value of the cloud density reproduces the distribution of observational points in the time delay–monochromatic flux plane, provided that a range of black hole spins is allowed. However, a confirmation of the new measurements for low/moderate Eddington ratio sources is strongly needed before the dust-based origin of the BLR can be excluded.

FDTD Simulation of Three-Wave Scattering Process in Time-Varying Cold Plasma Sheath

In this paper, a three-dimensional finite-difference time-domain (FDTD) method is developed to simulate the three-wave scattering process as a numerical experiment of the nonlinear interaction between two monochromatic plane waves in a plasma slab. This electromagnetic (EM)-plasma coupled system is governed by Maxwell's equations and the momentum equations of electron-only cold plasma. To model the system using the FDTD method, a simple and efficient periodic boundary condition is proposed and analyzed using the Floquet mode theory. The simulation result for the plasma slab with a linearly increasing electron density profile demonstrates that it is feasible to use the proposed formulations for the three-wave scattering process. Then, additional simulations are performed for the plasma slab with different electron density profiles and different incident angles of a signal wave as case studies to show the capability of the developed method for various environments.

From quantum optimal control theory to coherent destruction of tunneling

In this paper, we study coherent destruction of tunneling in driven spin-boson model. We formulate this physical process as a quantum optimal control problem. A running cost functional has been used to address the optimal control problem at hand. The dynamic is described by a Born–Markov master equation derived using the Bloch–Redfield formalism. We use the techniques of automatic differentiation to compute the gradient for the cost functional. We write the optimal control field as monochromatic plane wave. The robustness of the control profile against temperature and the system–bath coupling variations are also analyzed.

Perfect k-Colored Matchings and (k+2)-Gonal Tilings

We derive a simple bijection between geometric plane perfect matchings on 2n points in convex position and triangulations on n+2 points in convex position. We then extend this bijection to monochromatic plane perfect matchings on periodically k-colored vertices and (k+2)-gonal tilings of convex point sets. These structures are related to a generalization of Temperley–Lieb algebras and our bijections provide explicit one-to-one relations between matchings and tilings. Moreover, for a given element of one class, the corresponding element of the other class can be computed in linear time.

Gauge invariance and origin independence of electronic charge density and current density induced by optical fields.

Expressions for the first-order polarization charge density ρ (1) and current density J (1) induced in a molecule by a monochromatic plane wave, obtained by time-dependent quantum mechanical perturbation theory, have been investigated to assess their gauge invariance and independence of the coordinate system in passive and active translations. The conditions arrived at show that, within the (long wavelengths) dipole approximation, only the electric contributions to these densities are needed to rationalize the phenomenology. To the next higher quadrupole approximation, assuming that the magnetic field and the electric field gradient are uniform over the molecular dimensions, corresponding contributions to ρ (1) and J (1) are considered. It has been found that total densities are independent of the origin, whereas the contributions from electric and magnetic fields are not separately invariant. A magnetic contribution to J (1), which is by itself origin independent, can be defined by means of an approach based on continuous translation of the origin of the coordinate system.

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.

Manipulating graphene kinks through positive and negative radiation pressure effects

We introduce an idea of experimental verification of the counterintuitive negative radiation pressure effect in some classical field theories by means of buckled graphene. In this effect, a monochromatic plane wave interacting with topological solutions pulls these solutions towards the source of radiation. Using extensive molecular dynamics simulations, we investigate the traveling wave-induced motion of kinks in buckled graphene nanoribbons. It is shown that depending on the driving source frequency, amplitude and direction, the kink behavior varies from attraction to repulsion (the negative and positive radiation pressure effects, respectively). Some preliminary explanations are proposed based on the analogy to certain field theory models. Our findings open the way to a new approach to motion control on the nanoscale.

Ioffe-Regel criterion for Anderson localization in the model of resonant point scatterers

We establish a phase diagram of a model in which scalar waves are scattered by resonant point scatterers pinned at random positions in the free three-dimensional (3D) space. A transition to Anderson localization takes place in a narrow frequency band near the resonance frequency provided that the number density of scatterers $\rho$ exceeds a critical value $\rho_c \simeq 0.08 k_0^{3}$, where $k_0$ is the wave number in the free space. The localization condition $\rho > \rho_c$ can be rewritten as $k_0 \ell_0 < 1$, where $\ell_0$ is the on-resonance mean free path in the independent-scattering approximation. At mobility edges, the decay of the average amplitude of a monochromatic plane wave is not purely exponential and the growth of its phase is nonlinear with the propagation distance. This makes it impossible to define the mean free path $\ell$ and the effective wave number $k$ in a usual way. If the latter are defined as an effective decay length of the intensity and an effective growth rate of the phase of the average wave field, the Ioffe-Regel parameter $(k\ell)_c$ at the mobility edges can be calculated and takes values from 0.3 to 1.2 depending on $\rho$. Thus, the Ioffe-Regel criterion of localization $k\ell < (k\ell)_c = \mathrm{const} \sim 1$ is valid only qualitatively and cannot be used as a quantitative condition of Anderson localization in 3D.

Absorption of electromagnetic plane waves by rotating black holes

We study the absorption of monochromatic electromagnetic plane waves impinging upon a Kerr black hole, in the general case that the direction of incidence is not aligned with the black hole spin axis. We present numerical results that are in accord with low- and high-frequency approximations. We find that circularly-polarized waves are distinguished by the black hole spin, with counter-rotating polarizations being more absorbed than co-rotating polarizations. At low frequencies and moderate incidence angles, there exists a narrow parameter window in which superradiant emission in the dipole mode can exceed absorption in the non-superradiant modes, allowing a planar electromagnetic wave to stimulate net emission from a black hole.

Finite-element analysis of non-collinear mixing of two lowest-order antisymmetric Rayleigh-Lamb waves.

Recently, a perturbation approach was adopted for the non-collinear mixing of plate waves in an isotropic elastic plate with quadratic nonlinearity by Ishii, Biwa, and Adachi [J. Sound Vib. 419, 390-404 (2018)] and a resonance condition was derived theoretically, namely, that a significant scattered plate wave is generated when its frequency and wavevector coincide with the sum/difference of those of its primary waves. However, that analysis assumed monochromatic plane waves that interacted everywhere in the plate. To apply the non-collinear mixing of plate waves to nondestructive evaluation of plate-like structures, the influence of the spatial and temporal finiteness of the primary waves on the generation of the scattered wave must be elucidated. To that end, the present study conducts three-dimensional dynamic finite-element analyses on the mixing of lowest-order antisymmetric Rayleigh-Lamb waves that have finite beam widths and time durations. The generation of scattered lowest-order symmetric Rayleigh-Lamb and shear horizontal waves with sum frequencies is discussed for various beam widths, intersection angles, and primary frequencies. The resonance condition derived originally for monochromatic plane waves in the aforementioned study is found to be valid even when the wave interaction is allowed only within limited space and time.

Control of the electromagnetic drag using fluctuating light fields

An expression for the electromagnetic drag force experienced by an electric dipole in a light field consisting of a monochromatic plane wave with polarization and phase randomly fluctuating is obtained. The expression explicitly considers the transformations of the field and frequency due to the Doppler shift and the change of the polarizability response of the electric dipole. The conditions to be fulfilled by the polarizability of the dipole in order to obtain a positive, a null, and a negative drag coefficient are analytically determined and checked against numerical simulations for the dynamics of a silver nanoparticle. The theoretically predicted diffusive, superdiffusive, and exponentially accelerated dynamical regimes are numerically confirmed.

How fast is a twisted photon?

Recent measurements have highlighted that even in vacuum spatially shaped photons travel slower than c, the speed of monochromatic plane waves. Here we investigate the intrinsic delay introduced by “twisting” a photon, i.e., by introducing orbital angular momentum (OAM), and measure the photon time of flight with a Hong–Ou–Mandel interferometer. When all other parameters are held constant, the addition of OAM reduces the delay (accelerates) with respect to the same beam with no OAM. We support our results using a theoretical method to calculate the group velocity and gain an intuitive understanding of the measured OAM acceleration by considering a geometrical ray-tracing approach.

Dynamical characteristics of an electromagnetic field under conditions of total reflection

The dynamical characteristics of electromagnetic fields include energy, momentum, angular momentum (spin) and helicity. We analyze their spatial distributions near the planar interface between two transparent and non-dispersive media, when the incident monochromatic plane wave with arbitrary polarization is totally reflected, and an evanescent wave is formed in the medium with lower optical density. Based on the recent arguments in favor of the Minkowski definition of the electromagnetic momentum in a material medium (Philbin 2011 Phys. Rev. A 83 013823; Philbin and Allanson 2012 86 055802; Bliokh et al 2017 Phys. Rev. Lett. 119 073901), we derive the explicit expressions for the dynamical characteristics in both media, with special attention to their behavior at the interface. In particular, the ‘extraordinary’ spin and momentum components orthogonal to the plane of incidence are described, and a canonical (spin–orbital) momentum decomposition is performed that contains no singular terms. The field energy, helicity, the spin momentum and orbital momentum components are everywhere regular but experience discontinuities at the interface; the spin components parallel to the interface appear to be continuous, which testifies to the consistency of the adopted Minkowski picture. The results supply a meaningful example of the electromagnetic momentum decomposition, with separation of spatial and polarization degrees of freedom, in inhomogeneous media, and can be used in engineering the structured fields designed for optical sorting, dispatching and micromanipulation.

Deformaciones de segundo orden en la transmisión de haces y pulsos gaussianos a través de una capa isótropa

Las ondas planas monocromáticas permiten describir adecuadamente muchas de las propiedades de la radiación propagada, reflejada y transmitida a través de medios de distintas propiedades ópticas. Sin embargo, algunas características solo aparecen considerando haces y/o pulsos limitados. En este trabajo determinamos y analizamos algunas características de transmisión de haces (limitados en el espacio) o pulsos (limitados en el tiempo) con distribución gaussiana. Consideraremos que la transmisión se realiza a través de una placa plano-paralela de material isótropo lineal y haciendo una aproximación a segundo orden. En el caso de un haz limitado en el espacio, consideramos que la dirección de onda media es perpendicular a la placa. Si está limitado en el tiempo, consideramos que la incidencia de todas las ondas es normal a la placa. Comparamos los efectos no geométricos para ambos tipos de limitación para los casos en que la placa es absorbente, transparente o con ganancia en condiciones de linealidad.

Ultra-narrow photonic nanojets through a glass cuboid embedded in a dielectric cylinder.

A glass cuboid, embedded inside a dielectric cylinder is studied when illuminated with a monochromatic plane wave. A photonic nanojet (PNJ) with a full-width at half-maximum (FWHM) waist of around 0.25λ0 is obtained outside the external surface of the cuboid. The influence of the parameters of a square section cuboid is studied. Three particular phenomena can be obtained and are discussed: an ultra-narrow PNJ on the external surface of the cuboid, a long photonic jet and the excitation of whispering gallery modes (WGMs). A parametric study, over the width and the height of a rectangular section cuboid, shows that these parameters can be used to control the photonic jet properties. We also study several other geometries of the insert, which shows that the key parameter is the refractive index of the inserted material. Finally, we show that by changing the incident angle we can obtain a curved photonic jet.

Quantum reflection in the linearly downward potential

In this work, the motion of a particle in one dimension under the influence of the linearly downward potential well is studied within the context of the non-relativistic quantum mechanics. The attention is paid on the paradoxical phenomenon of the reflection of a particle that is in contrast between classical and quantum physics. Classically, the reflection effect occurs only at a potential barrier. To demonstrate such counter-intuitive phenomenon, the Schrödinger equation is solved to obtain the reflection coefficient in the scattering state by considering an incident particle that is represented by a monochromatic plane wave having an energy E > 0, propagates freely from left to right, pass through the potential well. The continuity conditions at boundaries give the desired result that is expressed in terms of the Airy functions which depends on the incident energy E, the strength jV0j and the range L of the well. The value of the reflection coefficient R lies in the interval 0 < R < 1, and its behavior is the decreasing function with respect to the range L.

Analytical qualitative modeling of passive and active metamaterials [Invited

Metamaterials (MMs) are artificial media tailoring the propagation of light by a design of a unit cell (meta-atom, MA). There is the evident inclination in favor of numerical methods in the description of the optical properties of MMs at the expense of physical intuition. It is shown that complementary to the numerical ones, qualitative models can provide a deeper understanding of the basic physical processes. The phenomenological approach to the homogenization resulted in three possible representations of Maxwell equations: Casimir, Landau–Lifshitz, and new toroidal ones. The multipole approach has been formulated and extended to the case of coupling between MAs, including random MA positioning. It has been shown that the quadrupole moment inherently introduces nonlinear (second-order) material response. The multipole approach has been applied for the case of the quantum MM to the coupled carbon nanotubes, and for the case of MAs to regular and stochastic properties of the nanolaser (spaser), and monochromatic plane wave propagation in the MM consisting of nanolasers.