Unit Solid Angle Research Articles

The Influence of Different Phase Function Combinations on Communication Quality in NLOS Communication Model

Wireless ultraviolet communication is a new type of communication technology, which uses the atmosphere as the transmission medium, and uses the scattering effect of atmospheric molecules and aerosol particles to change the propagation direction of the optical signal carrying information, bypass the blocking obstacles and finally reach the receiving end. The study of the scattering characteristics of ultraviolet light requires the use of scattering phase function. The scattering phase function is the ratio of the scattering energy in the unit solid angle in a specific direction to the average scattering energy in all directions. The scattering of ultraviolet light by the atmosphere is usually divided into two cases : Rayleigh scattering and Mie scattering. Therefore, the scattering phase function is also divided into two cases : Rayleigh scattering phase function and Mie scattering phase function. The scattering phase function in this paper is obtained by the weighted average of the two. There are many empirical formulas for Rayleigh scattering phase function and Mie scattering phase function. In this paper, the ultraviolet light of 266 nm wavelength is taken as an example to simulate and analyze the variation trend of scattering coefficient with wavelength and visibility, and the influence of the combination of different scattering phase functions on the received light power per unit area in the process of ultraviolet atmospheric transmission.

Time evolution of temporal, spatial and spectral distribution of high-energy electron radiation in intense laser pulses

To study the time evolution of high-energy electron radiation in circularly polarized intense laser pulses in detail, a model of the interaction between the high-energy single electron and intense laser pulses is constructed based on the Lagrangian equation and the electron energy equation. Through simulation, this article vividly displays the evolution process of radiation in the spatial, frequency and time domain. By modulating the interaction time between the laser and electron and referring to the spatial distribution image of energy, the value and direction of the maximum radiation energy per unit solid angle are calculated. In addition, in specific directions, this paper discusses the effects of interaction duration on the energy frequency distribution and the power variation pattern. The results prove that the maximum radiation energy per unit solid angle will appear when the interaction time comes to about 450 fs, which is also the boundary moment when the frequency and time spectrum no longer change obviously. Therefore, by modifying the duration of the electron–laser interaction, it is possible to produce the electron radiation with desired characteristics more precisely.

The gravitational energy-momentum pseudo-tensor in higher-order theories of gravity

The problem of non-localizability and the non-uniqueness of gravitational energy in general relativity has been considered by many authors. Several gravitational pseudo-tensor prescriptions have been proposed by physicists, such as Einstein, Tolman, Landau, Lifshitz, Papapetrou, Moller, andWeinberg. We examine here the energy-momentum complex in higher-order theories of gravity applying the Noether theorem for the invariance of gravitational action under rigid translations. This, in general, is not a tensor quantity because it is not a covariant object but only an affine tensor, that is, a pseudo-tensor. Therefore we propose a possible prescription of gravitational energy and momentum density for ?k gravity governed by the gravitational Lagrangian L1 = (R + a0R2 + Pp k=1 akR?kR) ??g and generally for n-order gravity described by the gravitational Lagrangian L = L (g??, g??,i1, 1??,i1i2, g??,i1i2i3 ,..., g??,i1i2i3...in). The extended pseudo-tensor reduces to the one introduced by Einstein in the limit of general relativity where corrections vanish. Then, we explicitly show a useful calculation, i.e., the power per unit solid angle ? emitted by a massive system and carried by a gravitational wave in the direction ? x for a fixed wave number k. We fix a suitable gauge, by means of the average value of the pseudo-tensor over a spacetime domain and we verify that the local pseudo-tensor conservation holds. The gravitational energy-momentum pseudo-tensor may be a useful tool to search for possible further gravitational modes beyond the two standard ones of general relativity. Their finding could be a possible observable signatures for alternative theories of gravity.

Influence of Target-Substrate Distance on the Transport Process of Sputtered Atoms: MC-MD Multiscale Coupling Simulation.

A Monte Carlo (MC) and molecular dynamics (MD) coupling simulation scheme for sputtered particle transport was first proposed in this work. In this scheme, the MC method was utilized to model the free-flight process of sputtered atoms, while the MD model was adopted to simulate the collision between the sputtered atom and background gas atom so as to self-consistently calculate the post-collision velocity of the sputtered atom. The reliability of the MD collision model has been verified by comparing the computation results of the MD model and of an analytical model. This MC-MD coupling simulation scheme was used to investigate the influence of target-substrate distance on the transport characteristic parameters of sputtered Cu atoms during magnetron sputtering discharge. As the target-substrate distance increased from 30 to 150 mm, the peak energy of the incident energy distribution of deposited Cu atoms decreased from 2 to 1 eV due to the gradual thermalization of sputtered atoms. The distribution of differential deposition rate in unit solid angle firstly became more forward-peaked and then reversely approached the cosine distribution, which was agreed with the existing experimental observations. This work is expected to provide a more realistic simulation scheme for sputtered particle transport, which can be further combined with the MD simulation of sputtered film growth to explore the influence mechanism of process parameters on the properties of sputtered film.

Scattering by a low-velocity charge with applied magnetic fields in a Laguerre–Gaussian beam

A method to analyze the scattering characteristics of a Laguerre–Gaussian (LG) vortex beam by a low-velocity charge in a steady applied magnetic field is investigated in this paper. Based on the plane wave angular spectrum representation and the electromagnetic radiation theory of a moving charge, the expressions of the scattered field and scattered power per unit solid angle are presented. Considering a low-velocity electron, the distribution of the scattered power per unit solid angle is numerically simulated. The effects of electron motion parameters, beam parameters, and applied magnetic field are discussed in detail. The results show that the longitudinal motion of the electron, which is parallel to the direction of the applied magnetic field, makes the distribution of the scattered power no longer maintain radial consistency but has a concave–convex distribution. Due to the periodicity of the circular motion of the electron in the applied magnetic field, the scattering power distribution pattern consists of many annular lobes. The spectral characteristics of the backscattered field are analyzed by fast Fourier transform. It is confirmed that the scattered field satisfies the rotational and the linear Doppler effects, and the accuracy of the formula provided in this paper is verified. This work lays a foundation for further study of the scattering characteristics of plasma on vortex electromagnetic waves and helps to promote the in-depth development of vortex beams in the field of plasma diagnosis.

Gravitational wave stochastic background in reduced Horndeski theories

We generalize to reduced Horndeski theories of gravity, where gravitational waves (GWs) travel at the speed of light, the expression of a statistically homogeneous and unpolarized stochastic gravitational wave background (SGWB) signal measured as the correlation between the individual signals detected by two interferometers in arbitrary configurations. We also discuss some results found in the literature regarding cosmological distances in modified theories, namely, the simultaneous validity of a duality distance relation for GW signals and of the coincidence between the gravitational wave luminosity distance, based on the energy flux, and the distance inferred from the wave amplitude. This discussion allows us to conclude that the spectral energy density per unit solid angle of an astrophysical SGWB signal has the same functional dependency with the luminosity of each emitting source as in General Relativity (GR). Using the generalized expression of the GW energy-momentum tensor and the modified propagation law for the tensor modes, we conclude that the energy density of a SGWB maintains the same functional relation with the scale factor as in GR, provided that the modified theory coincides with GR in a given hypersurface of constant time. However, the relation between the detected signal and the spectral energy density is changed by the global factor $G_4(\varphi(t_0))$, thus potentially serving as a probe for modified gravity theories.

Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity

An unambiguous definition of gravitational energy remains one of the unresolved issues of physics today. This problem is related to the non-localization of gravitational energy density. In General Relativity, there have been many proposals for defining the gravitational energy density, notably those proposed by Einstein, Tolman, Landau and Lifshitz, Papapetrou, Møller, and Weinberg. In this review, we firstly explored the energy–momentum complex in an nth order gravitational Lagrangian L=Lgμν,gμν,i1,gμν,i1i2,gμν,i1i2i3,⋯,gμν,i1i2i3⋯in and then in a gravitational Lagrangian as Lg=(R¯+a0R2+∑k=1pakR□kR)−g. Its gravitational part was obtained by invariance of gravitational action under infinitesimal rigid translations using Noether’s theorem. We also showed that this tensor, in general, is not a covariant object but only an affine object, that is, a pseudo-tensor. Therefore, the pseudo-tensor ταη becomes the one introduced by Einstein if we limit ourselves to General Relativity and its extended corrections have been explicitly indicated. The same method was used to derive the energy–momentum complex in fR gravity both in Palatini and metric approaches. Moreover, in the weak field approximation the pseudo-tensor ταη to lowest order in the metric perturbation h was calculated. As a practical application, the power per unit solid angle Ω emitted by a localized source carried by a gravitational wave in a direction x^ for a fixed wave number k under a suitable gauge was obtained, through the average value of the pseudo-tensor over a suitable spacetime domain and the local conservation of the pseudo-tensor. As a cosmological application, in a flat Friedmann–Lemaître–Robertson–Walker spacetime, the gravitational and matter energy density in f(R) gravity both in Palatini and metric formalism was proposed. The gravitational energy–momentum pseudo-tensor could be a useful tool to investigate further modes of gravitational radiation beyond two standard modes required by General Relativity and to deal with non-local theories of gravity involving □−k terms.

Power absorption by a dipole in a laser beam

An oscillating electric dipole in a laser beam absorbs energy from the external field and emits it then as dipole radiation. The absorption is a result of interference between the laser field and the emitted dipole radiation, a process referred to as extinction. It appears that the energy represented by this cross term follows an intricate flow pattern before it reached the particle. Field lines alternate between running inward and outward, and these counter-running flow lines are connected by loops. We show that most of the energy associated with the cross term swings around the dipole in the near field, and does not contribute to the absorption. We derive an expression for the absorbed power per unit solid angle, and we find that the angular distribution for absorption is not the same as for emission.

Cone photoreceptor density in the Copenhagen Child Cohort at age 16-17years.

To examine cone density in relation to gestational and morphological parameters in the Copenhagen Child Cohort (CCC2000). The macula was imaged using adaptive optics in 1,296 adolescents aged 16-17years. Axial length and distance visual acuity were determined. Absolute and angular cone photoreceptor density were analysed for an 80×80-pixel area, 2degrees temporal to the fovea. Association with axial length was analysed with linear regression. Correlation with visual acuity was described with a Pearson correlation coefficient. Associations of cone density with gestational parameters, maternal smoking, sex and age were analysed using multiple regression adjusted for axial length. Mean absolute cone density was 30,007cones/mm2 (SD±3,802) and mean angular cone density was 2,383cones/deg2 (SD±231). Peri- and postnatal parameters, sex and age had no statistically significant effect on cone density (p>0.05). Absolute cone density decreased with longer axial length (-2,855cones/mm2 per mm or -9.7% per mm, p<0.0001). For angular density, which included a correction for the geometrical enlargement of the eye with axial length, a decrease with axial length was detectable, but it was small (-20cones/deg2 per mm or -0.84% per mm, p=0.009). The decrease in cone density per unit solid angle with increasing axial length was small, less than 1 percent per mm, indicating that expansion of the posterior pole during the development of refraction takes place without a clinically significant loss of cones. Perinatal parameters, within the spectrum presented by the study population, had no detectable effect on cone density.

Thomson scattering of a vector Bessel vortex beam by a non-relativistic electron

Thomson scattering of a vector Bessel vortex beam (VBVB) by a non-relativistic electron is studied in this paper in order to explore the prospects of vortex beams in Thomson scattering diagnostic in ionospheric or laboratory plasmas. Combining with the plane wave angular spectrum representation of a VBVB, the expressions of scattered electric and magnetic fields are derived with the aid of Thomson scattering theory. The scattered power per unit solid angle and the frequency spectrum of the scattered field in the backscatter direction are simulated numerically, and the effects of polarization, topological charge, half-cone angle, and the electron's motion are analyzed in detail. The results show that the polarization affects the spatial distribution of scattered power. The distance between the electron and the observer's location, where maximum power is received, is affected by the topological charge, and the gaps between sub-maxima are related to the half-cone angle. These characteristics are the manifestation of the retarded effect in radiation. The amplitude spectrum of scattered field is analyzed in which a feature of double peaks is observed. The frequency shifts of peaks are the sum of the shifts brought by the electron's velocity components parallel and perpendicular to the beam's axis. The work provides a significant theoretical foundation for deeply investigating the Thomson scattering of vortex beams by plasmas and is meaningful for the development of plasma diagnostic.

Spherically bent mica analyzers as universal dispersing elements for X‐ray spectroscopy

Spherically‐bent crystal analyzers (SBCAs) see considerable use in very high‐resolution hard X‐ray wavelength dispersive X‐ray fluorescence spectroscopy, often called X‐ray emission spectroscopy (XES). While Si and Ge are the most frequently used diffractive components of SBCAs, we consider here the somewhat classical choice of muscovite mica as the dispersing element. We find that the various harmonics of a highest‐quality mica‐based SBCA show ~5–~40% of the integral reflectivity per unit solid angle of a typical Si or Ge SBCA in the hard X‐ray range, and that the mica SBCA have comparable energy resolution to the traditional SBCAs. Interestingly, the choice of mica comes with a practical benefit: the primary (0,0,2) reflection has sufficiently strong harmonics that are fairly tightly spaced in energy so that they span the complete energy range from ~4 to ~11 keV when used at convenient Bragg angles in a Rowland circle spectrometer. Hence, a single mica SBCA can be used for every K‐shell emission line of three dimensional transition metals and every L‐shell emission line of the lanthanide elements simply by selecting the correct mica (0,0,2) harmonic with a final energy‐dispersive solid state detector. The loss in efficiency is counteracted by an operational efficiency, i.e., the “universal” application of a single analyzer over a very large range of elements. This performance suggests future application of mica SBCAs in both laboratory‐based XES and synchrotron‐based photon‐in, photon‐out spectroscopies in the hard X‐ray range.

Afterglow light curves from misaligned structured jets

ABSTRACT GRB 170817A/GW 170817 is the first gamma-ray burst (GRB) clearly viewed far from the GRB jet’s symmetry axis. Its afterglow was densely monitored over a wide range of frequencies and times. It has been modelled extensively, primarily numerically, and although this endeavour was very fruitful, many of the underlying model parameters remain undetermined. We provide analytic modelling of GRB afterglows observed off-axis, considering jets with a narrow core (of half-opening angle θc) and power-law wings in energy per unit solid angle (ϵ = ϵcΘ−a where Θ = [1 + (θ/θc)2]1/2) and initial specific kinetic energy (Γ0 − 1 = [Γc, 0 − 1]Θ−b), as well as briefly discuss Gaussian jets. Our study reveals qualitatively different types of light curves that can be viewed in future off-axis GRBs, with either single or double peaks, depending on the jet structure and the viewing angle. Considering the light-curve shape rather than the absolute normalizations of times and/or fluxes, removes the dependence of the light curve on many of the highly degenerate burst parameters. This study can be easily used to determine the underlying jet structure, significantly reduce the effective parameter space for numerical fitting attempts and provide physical insights. As an illustration, we show that for GRB 170817A, there is a strong correlation between the allowed values of Γc, 0 and b, leading to a narrow strip of allowed solutions in the Γc, 0–b plane above some minimal values Γc, 0 ≳ 40, b ≳ 1.2. Furthermore, the Lorentz factor of the material dominating the early light curve can be constrained by three independent techniques to be Γ0(θmin, 0) ≈ 5–7.

Optical characteristics of oil spill based on polarization scattering rate.

As a new analytical method for identifying marine oil slicks, the primary function of the polarization scattering model is to determine the intensity of polarized scattered light from different oil spill zones. In the polarized light path, the energy reduction is mainly due to the scattering characteristics of the surface of the sample to be tested. To quantify equivalence, we define the polarized scattering rate (PSR). The PSR describes the probability that linearly polarized incident photons scatter into the unit solid angle in the direction of scattering from the target surface. In order to verify the applicability of the model, we applied it to detect an actual oil spill at sea in the case of simulated sunlight. The research indicates that the PSR only characterizes the amplitude conversion between the polarized scattering wave and the incident wave and is not affected by the polarization characteristics of the incident wave, thus reflecting the true polarization characteristics of the target itself. The PSR of crude oil and seawater depends not only on the physical properties of the target itself, but also on the observation conditions, such as relative attitude orientation, spatial geometric position relationship, and the working frequency of equipment and instruments.

Broadband terahertz radiation from metal targets irradiated by a short pulse laser

The generation of low-frequency radiation from sub-picosecond laser pulses incident on metal targets is investigated. The laser field drives time-varying currents in a thin sub-surface layer of the metal, which emits broadband radiation that peaks at terahertz frequencies. We present a one-dimensional electrostatic model for copper appropriate for the interaction of laser pulses at normal incidence combined with a radiation model for an infinitely thin disk. The latter uses as input a single parameter, the temporal dependence of the integrated current density on axis, which is derived from the electrostatic model. The salient characteristics of the emitted radiation, such as power, energy, and spectra, are calculated for laser pulses with various intensities and pulse durations. The radiated energy per unit solid angle peaks at a small angle off the target normal and tapers off at larger angles. Analytical scaling of radiated energy with incident laser energy, in the low frequency limit, is obtained in the form εrad∼εlaser3/2. For accurate results, it is imperative to use the full expression for the heat capacity of electrons, in both the degenerate and ideal gas limits. Failure to do so may result in inaccuracies for the computed radiated energy, as large as one order of magnitude. A comparison of calculated and measured radiation energy in the 8–12 GHz frequency range indicates a similar trend with laser energy and comparable magnitude (∼1 fJ).

Signatures of the differential Klein‐Nishina electronic cross section in Compton's quantum theory of scattering of radiation

Here, we consider the problem of separating the relative contributions of kinematics and dynamics to the differential Klein‐Nishina electronic cross section using graphical and numerical analysis. We show that the values of the energy of scattered photons, and hence the kinetic energy of recoiled electrons calculated from Compton's quantum theory of scattering of radiation, show a degree of matching that increases with the increase in incident photon energy as quantified by chi-square goodness of fit test, with the calculated differential Klein‐Nishina electronic cross section per electron per unit solid angle for the scattering of an unpolarized photon by a stationary free electron, when appropriate normalization procedures are invoked. There is a high degree of matching in a regime where the total electronic Klein‐Nishina cross section for the Compton scattering on a free stationary electron scales as the inverse of the incident photon energy and the contribution of the electro-magnetic interaction to differential electronic cross section diminishes. Hence the third level explanation of Compton effect by quantum electrodynamics has a degree of matching with the first level of Compton's quantum theory. The degree of mismatch is an indicator of the relative contribution of dynamics to differential Klein‐Nishina electronic cross section compared to kinematics. For incident photon energies less than 1 MeV, we obtain the values of the scattering angles at which calculated differential cross section is nonzero but is kinematically limited which may lead to broadening of Compton profile. At the scattering angle where the differential cross section value is minimum for a given incident photon energy, we obtain the relative contribution of dynamics to the differential cross section compared to kinematics. Therefore, these predictions which need to be confirmed experimentally have significance to the understanding of the mechanisms of photon‐electron interactions in the Compton scattering.

Double-lattice photonic-crystal resonators enabling high-brightness semiconductor lasers with symmetric narrow-divergence beams.

Achieving high brightness (where brightness is defined as optical power per unit area per unit solid angle) in semiconductor lasers is important for various applications, including direct-laser processing and light detection and ranging for next-generation smart production and mobility. Although the brightness of semiconductor lasers has been increased by the use of edge-emitting-type resonators, their brightness is still one order of magnitude smaller than that of gas and solid-state/fibre lasers, and they often suffer from large beam divergence with strong asymmetry and astigmatism. Here, we develop a so-called 'double-lattice photonic crystal', where we superimpose two photonic lattice groups separated by one-quarter wavelength in the x and y directions. Using this resonator, an output power of 10 W with a very narrow-divergence-angle (<0.3°) symmetric surface-emitted beam is achieved from a circular emission area of 500 μm diameter under pulsed conditions, which corresponds to a brightness of over 300 MW cm-2 sr-1. In addition, an output power up to ~7 W is obtained under continuous-wave conditions. Detailed analyses on the double-lattice structure indicate that the resonators have the potential to realize a brightness of up to 10 GW cm-2 sr-1, suggesting that compact, affordable semiconductor lasers will be able to rival existing gas and fibre/disk lasers.

The mutual interface scattering cross section

Scattering by the ocean surface or seafloor is often characterized by the interface scattering strength, the decibel equivalent of the scattering cross section per unit solid angle per unit area (referred to subsequently as the interface scattering cross section for brevity). The scattering cross section is a statistical second moment that allows modeling of the mean-square scattered pressure. Use of the interface scattering cross section requires that the incident field can be approximated by a single plane wave, a condition that is not satisfied when the interface is ensonified in the near field of a large array, as in synthetic-aperture sonar (SAS), or when multipath propagation is important as in modeling reverberation. The mutual cross section introduced in this presentation is a generalization of the interface scattering cross section to include ensonification by multiple plane waves. Examples of application to SAS and the ocean waveguide will be shown. In the latter case, it is seen that the mutual cross section can model peaks in the reverberation time series that occur as a result of multipath convergence on the interface. (Work supported by ONR.)

Non-perturbative results for the luminosity and area distances

The notion of luminosity distance is most often defined in purely FLRW (Friedmann-Lemaitre-Robertson-Walker) cosmological spacetimes, or small perturbations thereof. However, the abstract notion of luminosity distance is actually much more robust than this, and can be defined non-perturbatively in almost arbitrary spacetimes. Some quite general results are already known, in terms of dAobserver/dΩsource, the cross-sectional area per unit solid angle of a null geodesic spray emitted from some source and subsequently detected by some observer. We shall reformulate these results in terms of a suitably normalized null geodesic affine parameter and the van Vleck determinant, ΔvV. The contribution due to the null geodesic affine parameter is effectively the inverse square law for luminosity, and the van Vleck determinant can be viewed as providing a measure of deviations from the inverse square law. This formulation is closely related to the so-called Jacobi determinant, but the van Vleck determinant has somewhat nicer analytic properties and wider and deeper theoretical base in the general relativity, quantum physics, and quantum field theory communities. In the current article we shall concentrate on non-perturbative results, leaving near-FLRW perturbative investigation for future work.

Spin memory effect for compact binaries in the post-Newtonian approximation

The spin memory effect is a recently predicted relativistic phenomenon in asymptotically flat spacetimes that become nonradiative infinitely far in the past and future. Between these early and late times, the magnetic-parity part of the time integral of the gravitational-wave strain can undergo a nonzero change; this difference is the spin memory effect. Families of freely falling observers around an isolated source can measure this effect, in principle, and fluxes of angular momentum per unit solid angle (or changes in superspin charges) generate the effect. The spin memory effect had not been computed explicitly for astrophysical sources of gravitational waves, such as compact binaries. In this paper, we compute the spin memory in terms of a set of radiative multipole moments of the gravitational-wave strain. The result of this calculation allows us to establish the following results about the spin memory: (i) We find that the accumulation of the spin memory behaves in a qualitatively different way from that of the displacement memory effect for nonspinning, quasicircular compact binaries in the post-Newtonian approximation: the spin memory undergoes a large secular growth over the duration of the inspiral, whereas for the displacement effect this increase is small. (ii) The rate at which the spin memory grows is equivalent to a nonlinear, but nonoscillatory and nonhereditary effect in the gravitational waveform that had been previously calculated for nonspinning, quasicircular compact binaries. (iii) This rate of build-up of the spin memory could potentially be detected by future gravitational-wave detectors by carefully combining the measured waveforms from hundreds of gravitational-wave detections of compact binaries.

The gravitational energy‐momentum pseudo‐tensor of higher‐order theories of gravity

We derive the gravitational energy momentum tensor for a general Lagrangian of any order and in particular for a Lagrangian such as . We prove that this tensor, in general, is not covariant but only affine, then it is a pseudo‐tensor. Furthermore, the pseudo‐tensor is calculated in the weak field limit up to a first non‐vanishing term of order h2 where h is the metric perturbation. The average value of the pseudo‐tensor over a suitable spacetime domain is obtained. Finally we calculate the power per unit solid angle Ω carried by a gravitational wave in a direction for a fixed wave number under a suitable gauge. These results are useful in view of searching for further modes of gravitational radiation beyond the standard two modes of General Relativity and to deal with nonlocal theories of gravity where terms involving are present. The general aim of the approach is to deal with theories of any order under the same standard of Landau pseudo‐tensor.