Geometrical Optics Approximation Research Articles

Absorption properties by irregularly shaped particles with inclusions at visible and near-infrared wavelength regions

The absorption properties of snow and ice particles containing impurities such as black carbon (BC) and mineral dust (DS) were investigated using the geometrical optics approximation method (GOM). This study focuses on analyzing the single scattering co-albedo (SSCA) characteristics of non-spherical particles, aiming to enhance the interpretation of radiation observations in snow and ice regions. Particle sizes were varied (rva=50,200 and 500μm) and two types of inclusions (1 ppmw of BC and 100 ppmw DS) were considered. Significant differences in SSCA, ranging from one to two orders of magnitude were observed at λ=0.5μm between the “homogeneous model” with effective medium approximation method (EMA) and the “inhomogeneous model” with 50 BC inclusions. Similarly, differences of a factor of 2 to 4 were found for DS with 100 ppmw at λ=0.5μm and BC with 1 ppmw at λ=0.875μm. To bridge intermediate SSCA values between these models, we propose an “inhomogeneous model with EMA”, introducing two parameters to account for impurity concentration and inclusion aggregation. Our findings highlight the importance of selecting appropriate single scattering calculation methods in the analysis of observation data, particularly when dealing with BC impurity with significant absorption characteristics. This research contributes to a deeper understanding of solar radiation absorption in snow and ice regions, with potential implications for the optical remote sensing of snow and ice and climate modeling studies.

TDiff invariant field theories for cosmology

We study scalar field theories invariant under transverse diffeomorphismsin cosmological contexts. We show that in the geometric optics approximation, the corresponding particles move along geodesics and contribute with the same active mass (energy) to the gravitational field as in Diff invariant theories. However, for low-frequency (super-Hubble) modes, the contributions to the energy-momentum tensor differ from that of Diff invariant theories. This opens up a wide range of possibilities for cosmological model building. As an example, we show that the simplest TDiff invariant scalar field theory with only kinetic term could drive inflation and generate a nearly scale invariant (red-tilted) spectrum of density fluctuations. We also present a detailed analysis of cosmological perturbations and show that the breaking of full Diff invariance generically induces new non-adiabatic pressure perturbations. A simple scalar field dark matter model based on a purely kinetic term that exhibits the same clustering properties as standard cold dark matter is also presented.

Перенос аврорального километрового радиоизлучения посредством каналов с пониженной плотностью на границе плазмосферы

We present the results of Auroral Kilometric Radiation (AKR) measurements near the plasmapause on the ERG (Arase) satellite. The apogee of the satellite's orbit is located near the ecliptic plane, at latitudes ±30°. According to the generally accepted point of view, AKR observation is impossible in this region since it is shielded by the plasmasphere. Simultaneous measurements of AKR and local plasma density made it possible to determine that AKR in near-equatorial regions occur in plasma channels — density inhomogeneities elongated along magnetic field lines. AKR from sources located in the auroral magnetosphere is transferred by these channels to the equatorial region. This work analyzes the conditions for the capture and propagation of AKR in low plasma density channels. In the geometrical optics approximation, we have simulated the conditions for the radiation capture and propagation. The calculation results show that the proposed scheme for AKR capture into plasma channels can explain the measurement results — the radiation transfer from the auroral region to the near-equatorial region.

Transfer of auroral kilometric radiation through low-density channels at the boundary of plasmasphere

We present the results of Auroral Kilometric Radiation (AKR) measurements near the plasmapause on the ERG (Arase) satellite. The apogee of the satellite's orbit is located near the ecliptic plane, at latitudes ±30°. According to the generally accepted point of view, AKR observation is impossible in this region since it is shielded by the plasmasphere. Simultaneous measurements of AKR and local plasma density made it possible to determine that AKR in near-equatorial regions occur in plasma channels — density inhomogeneities elongated along magnetic field lines. AKR from sources located in the auroral magnetosphere is transferred by these channels to the equatorial region. This work analyzes the conditions for the capture and propagation of AKR in low plasma density channels. In the geometrical optics approximation, we have simulated the conditions for the radiation capture and propagation. The calculation results show that the proposed scheme for AKR capture into plasma channels can explain the measurement results — the radiation transfer from the auroral region to the near-equatorial region.

Проблема обнаружения аномальных волн на воде навигационными радиолокаторами. 2. Решение уравнения радиолокации

Simple options for the effective scattering area of anomalous waves are considered in the geometric optics approximation for two types of targets: a single wave and a white wall. The radar equation has been solved to find the maximum radar range for such targets, taking into account the influence of significant wave heights on the effective scattering area of anomalous waves and taking into account interference due to the scattering of electromagnetic waves on sea waves. Conditions are proposed for the lifetime and height of anomalous waves necessary for observing these waves with standard ship radars.

Improved calculation of the Mie solution and the geometrical optics approximation for large droplets

This article considers energy distribution of light inside a uniformly illuminated transparent water droplet. Two methods are used: the geometrical optics approximation and the Mie solution derived from wave optics. The authors describe in detail calculation algorithms suitable for efficient computer implementation and ways to improve them. In the limit for large droplets, both similarities and differences between the methods are pointed out. Resonant states are discussed, when the usually dark regions of the droplet turn out to be illuminated.

The ‘thin lens’ in the light of idealisations

This paper argues that the simplifying idealisations assumed in making complex science tractable should be identified and discussed before model-building. It is suggested that alternative conceptions can persist, and learning difficulties arise for students when they do not adequately understand these idealisations. We argue that explicitly addressing idealisations for a particular physical phenomenon can ease students’ conceptual understanding. A theoretical framework for identifying and reflecting idealisations is introduced based on epistemological considerations from science philosophy. The thin lens approximation of geometric optics, a common topic taught in the introductory classroom, is used as an archetypal illustration.

Quasinormal modes from Penrose limits

We use Penrose limits to approximate quasinormal modes (QNMs) with large real frequencies. The Penrose limit associates a plane wave to a region of spacetime near a null geodesic. This plane wave can be argued to geometrically realize the geometrical optics approximation. Therefore, when applied to the bound null orbits around black holes, the Penrose limit can be used to study QNMs. For instance, this Penrose limit point of view makes manifest the symmetry that emerges in the geometrical optics approximation of QNMs in terms of isometries of the resulting plane wave spacetime. We apply the procedure to warped , Schwarzschild black holes and Kerr black holes. In the former we show explicitly how the symmetry algebra contracts to that of the limiting plane wave while in the latter we find the expected agreement with numerically computed QNMs for large (real) frequencies.

A novel test of gravity via black hole eikonal correspondence

When adopted in black hole spacetimes, geometric-optics approximations imply a mapping between the quasinormal mode (QNM) spectrum of black holes in the eikonal limit and black hole images. In particular, the real part and the imaginary part of eikonal QNM frequencies are associated with the apparent size and the detailed structure of the ring images, respectively. This correspondence could be violated when going beyond general relativity. We propose a novel method to test the eikonal correspondence via the comparison of two sets of observables from a nonrotating black hole, one extracted from QNM spectra and the other from the lensed photon rings on the image plane. Specifically, the photon ring observables robustly capture the information of the black hole spacetime itself regardless of the surrounding emission models. Therefore, the proposed test of eikonal correspondence can be validated in quite broad scenarios.

Nonstationary plane wave incidence on the perfectly conducting structures. Part 2. Diffraction of a nonstationary plane wave on the perfectly conducting sphere

The paper considers the incidence of a nonstationary plane wave on a perfectly conducting sphere. To find the current on the surface of the sphere, the well-known solution of the problem in the frequency domain has been used and the transition from the real frequency to the complex variable has been performed. Expressions for calculating the current on the sphere have been obtained using the residue formula. Graphs and vector images of the current have been plotted, which make it possible to observe its changes during the propagation of the incident wave. You can specify the following time intervals, differing in current distribution. At 0 < t < a/c, the current on the illuminated part of the sphere is close to the current determined in the geometrical optics approximation. In this case, there is naturally no current in the shadow region. For a/c < t < a/c + (π/2)a/c, a diffraction current appears in the shadow region, which turns out to be small compared to the current in the illuminated region. In the a/c + (π/2)a/c < t < a/c + πa/c, the current distribution on the sphere surface rapidly approaches the steady-state distribution. In the steady state, the streamlines represent circles obtained by sectioning the sphere with planes orthogonal to the magnetic field of the incident wave. At t > a/c + πa/c, the current practically does not change, and the steady-state distribution is preserved.

Geometric optics approximation for the Einstein vacuum equations

Geometric optics approximation for the Einstein vacuum equations

Nonstationary plane wave incidence on the perfectly conducting structures. Part 1. Diffraction of a nonstationary plane wave on the perfectly conducting cylinder

The paper considers the incidence of a nonstationary plane wave on a perfectly conducting cylinder. To find the current on the surface of the cylinder, the well-known solution of the problem in the frequency domain has been used and the transition from the real frequency to a complex variable has been performed. Expressions for calculating the current on the sphere have been obtained using the residue formula. Graphs of the current have been plotted, which make it possible to observe its changes during the propagation of the incident wave. You can specify the following time intervals, differing in current distribution. At 0 < t < a/c, the current on the illuminated part of the surface is close to the current determined in the geometrical optics approximation. In this case, there is naturally no current in the shadow region. For a/c < t < a/c + π/2a/c, a diffraction current appears in the shadow region, which turns out to be small compared to the current in the illuminated region. In the a/c + π/2a/c < t < a/c + πa/c, the current distribution on the cylinder surface rapidly approaches the steady-state distribution. In the steady state, the magnitude of the current is equal to the intensity of the magnetic field of the incident wave. At t > a/c + πa/c, the current practically does not change, and the steady-state distribution is preserved.

Propagation of wave packets along large-scale background waves

We study propagation of high-frequency wave packets along a large-scale background wave, which evolves according to dispersionless hydrodynamic equations for two variables (fluid density and flow velocity). Influence of the wave packet on evolution of the background wave is neglected, so the large-scale evolution can be found independently of the wave packet's motion. At the same time, propagation of the packet depends in an essential way on the background wave, and it can be considered in a framework of the geometric optics approximation with the use of Hamilton equations for the carrier wave number and the mean co-ordinate of the packet. We derive equations for the carrier wave number as a function of the parameters, which describe the background wave. When they are solved, the path of the packet can be found by simple integration of the Hamilton equation. The theory is illustrated by its application to the problem of propagation of wave packets along expanding a large-scale wave, in which evolution is described by the shallow water equations. In particular, they correspond to the dispersionless limit of the defocusing nonlinear Schrödinger equation, and then the expanding wave can be considered as an expanding cloud of the Bose–Einstein condensate. Reflection of wave packets from upstream flows and their propagation along stationary flows are also discussed. The analytical solutions found for these particular cases agree very well with an exact numerical solution of the nonlinear Schrödinger equation.

Light-Scattering Properties for Aggregates of Atmospheric Ice Crystals within the Physical Optics Approximation

This paper presents the light-scattering matrices of atmospheric-aggregated hexagonal ice particles that appear in cirrus clouds. The aggregates consist of the same particles with different spatial orientations and numbers of these particles. Two types of particle shapes were studied: (1) hexagonal columns; (2) hexagonal plates. For both shapes, we studied compact and non-compact cases of particle arrangement in aggregates. As a result, four sets of aggregates were made: (1) compact columns; (2) non-compact columns; (3) compact plates; and (4) non-compact plates. Each set consists of eight aggregates with a different number of particles from two to nine. For practical reasons, the bullet-rosette and the aggregate of hexagonal columns with different sizes were also calculated. The light scattering matrices were calculated for the case of arbitrary spatial orientation within the geometrical optics approximation for sets of compact and non-compact aggregates and within the physical optics approximation for two additional aggregates. It was found that the light-scattering matrix elements for aggregates depend on the arrangement of particles they consist of.

Detectability of strongly lensed gravitational waves using model-independent image parameters

Strong gravitational lensing of gravitational waves (GWs) occurs when the GWs from a compact binary system travel near a massive object. The lensed waveform is given by the product of the lensing amplification factor $F$ and the unlensed waveform. For many axisymmetric lens models such as the point mass and singular isothermal sphere that we consider, $F$ can be calculated in terms of two lens parameters, the lens mass ${M}_{L}$ and source position $y$. In the geometrical-optics approximation, lensing in these models produces at most two discrete images which can be parametrized by two image parameters, the flux ratio $I$ and time delay $\mathrm{\ensuremath{\Delta}}{t}_{d}$ between images. In the macrolensing regime for which $\mathrm{\ensuremath{\Delta}}{t}_{d}$ is large compared to the time $T$ they spend within the sensitivity band of GW detectors, it is natural to parametrize lensing searches in terms of these image parameters. The functional dependence of the lensed signal on these image parameters is far simpler, facilitating data analysis for events with modest signal-to-noise ratios, and constraints on $I$ and $\mathrm{\ensuremath{\Delta}}{t}_{d}$ can be inverted to constrain ${M}_{L}$ and $y$ for any lens model. We propose that this use of image parameters can be extended to the microlensing regime ($\mathrm{\ensuremath{\Delta}}{t}_{d}<T$) in which the two interfering images are observed as a single GW event. We use image parameters to determine the detectability of gravitational lensing in GW the microlensing regime and find that for GW events with signal-to-noise ratios $\ensuremath{\rho}$ and total mass $M$, lensing should in principle be identifiable for flux ratios $I\ensuremath{\gtrsim}2{\ensuremath{\rho}}^{\ensuremath{-}2}$ and time delays $\mathrm{\ensuremath{\Delta}}{t}_{d}\ensuremath{\gtrsim}{M}^{\ensuremath{-}1}$.

Photon rings around warped black holes

The black hole photon ring is a prime target for upcoming space-based VLBI missions seeking to image the fine structure of astrophysical black holes. The classical Lyapunov exponents of the corresponding nearly bound null geodesics control the quasinormal ringing of a perturbed black hole as it settles back down to equilibrium, and they admit a holographic interpretation in terms of quantum Ruelle resonances of the microstate dual to the Kerr black hole. Recent work has identified a number of emergent symmetries related to the intricate self-similar structure of the photon ring. Here, we explore this web of interrelated phenomena in an exactly soluble example that arises as an approximation to the near-extremal Kerr black hole. The self-dual warped AdS3 geometry has a photon ring as well as isometries and an exactly calculable quasinormal mode (QNM) spectrum. We show explicitly that the geometric optics approximation reproduces the eikonal limit of the exact scalar QNM spectrum, as well as the approximate ‘near-ring’ wavefunctions. The isometries are directly related to the emergent conformal symmetry of the photon ring in black hole images but are distinct from a recently discussed conformal symmetry of the eikonal QNM spectrum. The equivalence of the classical QNM spectrum—and thus the photon ring—to the quantum Ruelle resonances in the context of a spacetime with a putative holographic dual suggests that the photon ring of a warped black hole is indeed part of the black hole hologram.

Light propagation in Kerr spacetime

We explicitly solve the equations for the propagation of an electromagnetic wave up to the subleading order geometric optics expansion in the Kerr spacetime. This is done in two nontrivial steps. We first construct a set of parallel propagated null tetrad in Kerr spacetime. Two of the components of such tetrad give the propagation and polarization of an electromagnetic wave in geometric optics approximation. Then we use the parallel propagated tetrad to solve the modified trajectory equation in Kerr spacetime. We obtain the wavelength-dependent deviation of the trajectory of electromagnetic waves, which gives the mathematical description of the gravitational spin Hall effect in Kerr spacetime.

Propagation of scalar and tensor gravitational waves in Horndeski theory

Gravitational waves travel through the distributions of matter and dark energy during propagation. For this reason, gravitational waves emitted from binary compact objects serve as a useful tool especially to probe the nature of dark energy. The geometrical optics approximation is a conventional way of investigating wave propagation. However, the approximation becomes less accurate as the wavelength approaches the curvature radius of the background, which can occur in generic situations. In this paper, we suggest a formulation for higher-order corrections of the geometrical optics expansion, applied to Horndeski theory which accommodates many dark energy models. At the level of the background, assuming that the derivative of the scalar field is non-vanishing and timelike, we choose the time slices to coincide with the contours of the scalar field. This choice of the background time slices is advantageous as the sound cones of both scalar and tensor gravitational waves are upright with respect to the background time slices whenever the scalar field behaves as a perfect fluid. We then analyze the equations of motion for scalar and tensor components of gravitational waves at the leading and next-to-leading order in the geometrical optics expansion, deriving the evolution equations for their amplitudes under certain conditions. In particular, for Generalized Brans-Dicke theories, we find a simple description of equations for gravitational waves in terms of an effective metric.

The Causes and Effects of Preannealed Radiative Property Variations Across Full‐Hard Advanced High‐Strength Steel Coils

This study investigates the connection between surface topography and radiative property variations across full‐hard (unannealed and cold‐rolled) advanced high‐strength steel (AHSS) coils. Directional–hemispherical reflectivities of samples extracted from various locations on a full‐hard DP‐780 coil are measured using a Fourier transform infrared spectroscopy spectrometer at wavelengths between 0.5 and 20 μm. Surface topography analysis is performed using optical profilometry, optical microscopy, and scanning electron microscopy. Surface height profiles are generated using 3D depth mapping of optical images. The surface profiles are then used in a geometric optical approximation model, which correlates the radiative properties to surface topography variations. Significant differences in radiative properties and surface topography are observed along the length and width of the coil. These variations in radiative properties may explain the temperature excursions that cause nonuniformities in mechanical properties observed across AHSS coils produced on continuous galvanizing lines in the industry.

Теория аксиальной томографии на основе обратного преобразования Радона для высокоапертурной мягкой рентгеновской микроскопии

For soft X-ray microscopy in the approximation of geometrical optics, a theoretical model for the formation of the received image is constructed - a relationship is found between the image recorded on the detector and the 3D distribution of the sample absorption index using a high-aperture mirror objective (NA>0.3) with a focus depth close to the diffraction limit. The solution of the inverse problem of tomography for determining this 3D distribution from the data of measurements in a high-aperture mirror SXR-microscope is obtained.