Geometrical Optics Ray Research Articles

Some Features of Scattering of a Plane ElectromaElectromagnetic Wave on a Plane Magnetodielectric Plate

The two-dimensional problem of scattering of a plane electromagnetic wave on a flat homogeneous magnetodielectric plate of finite dimensions is considered. The problem is solved by the method of integral equations for auxiliary surface currents. Algebraization of integral equations was carried out using the collocation method and overlapping three-step basis functions. The results characterizing the efficiency of the proposed algorithm are presented. The influence of the geometric and material parameters of the plate on its effective scattering surface (ESS) in the direction of wave incidence, which characterizes the effects of “invisibility” of the plate, is studied. It is shown that the minimum of the specified ESS is achieved at a plate thickness close to the thickness that ensures the in-phase geometry of the geometric-optical rays that have passed through the plate and the rays that have passed by the plate. The ESS of a plate made of a material with positive and negative refractive indices is compared.

Optical characterisation of two novel myopia control spectacle lenses.

To quantify the amount of myopic defocus, contrast modulation and other optical characteristics of two novel spectacle lenses (MiYOSMART by Hoya and Stellest by Essilor) with the inclusion of lenslets in their designs were investigated computationally and experimentally. This paper examined the hypothesis that despite the non-coaxial nature of the optics, image degradation will exist due to the fragmented nature of the base optic when imaging through the lens regions populated by lenslets. Optical power was evaluated by computing wavefront vergence and curvature from wavefront slope measured with the Optocraft aberrometer within 1.0 and 6.0 mm apertures across MiYOSMART hexagons and Stellest rings. Point-spread functions (PSFs) were computed using physical (wave) optics and geometrical ray optics principles, and compared with experimental measurements using a 4f optical system. Simulated retinal images and modulation transfer functions (MTFs) were computed from PSF-derived optical transfer functions (OTFs). Mean lenslet power in MiYOSMART was +3.95 ± 0.10 D through the hexagons and +6.00 ± 0.15 D in Stellest in rings 1-5 and decreased by 0.42 D/ring reaching 3.50 D in the final one. Stellest lenslets included up to -0.015 microns of primary spherical aberration. PSFs and retinal images revealed simultaneous contributions of the base optic and lenslets. MTFs showed a decrease in contrast at low (1-10 c/deg) spatial frequencies (SFs) comparable to 0.25 D of defocus, and retention of diminished levels of contrast at higher SFs. Varying sagittal power and consistent curvature power across the lenslets is an identifying signature of the novel non-coaxial lens design included in both spectacle lenses. Lenslet array structure itself plays a significant role in determining image characteristics. For both lenses, the blur created by the fragmented base optic contributes to the image quality. The reduced MTFs over a wide range of spatial frequencies result in lowered image contrast.

Development of the EM Field in a Shielding Enclosure with Aperture after Interference Caused by a Subnanosecond High-Power Parallelly Polarized EM Plane Wave Pulse

Due to the increase in the threat of attacks with high-power electromagnetic (EM) pulses, there is great interest in metallic enclosures with high shielding effectiveness (SE). Necessary technological apertures in these enclosures reduce their effectiveness. Understanding the penetration and internal propagation of the high-power EM pulses into an apertured enclosure is fundamental to assessing the EM SE of the enclosure. In the present paper, results of the numerical simulations of development of the EM field in a shielding enclosure with aperture after the interference of a subnanosecond high-power EM plane wave pulse of the parallel polarization (having the duration of 0.3558 ns and the amplitudes of the electric and magnetic fields of 106 V/m and 2.6 × 103 A/m, respectively) are presented. The results obtained include 3D and 2D images , vector maps of the EM field developed inside the enclosure, and time-varying distributions of the electric charges formed on the inner walls of the enclosure. They revealed the mechanism of formation of the EM field inside the enclosure caused by the subnanosecond high-power parallelly polarized EM pulse. The EM field formed in the enclosure with aperture has the form of the electric and magnetic field interference structures. They are a superposition of the incident EM pulse field, which entered the enclosure through the aperture in the way described by the geometrical (ray) optics, the electric field generated by the electric charges formed on the aperture edges and inner sides of the walls of the enclosure, and the magnetic field generated by the surface current formed on the aperture edges and on the inner walls of the enclosure. The amplitudes of the electric and magnetic fields of the strongest EM interference structures decrease non-monotonically to about 0.7 × 105 V/m and 200 A/m at t = 5 ns. We found that the points in the enclosure are subjected to the disturbance of a long series of subnanosecond EM pulses, which we have called internal EM pulses. The amplitudes of these internal pulses are lower than those of the incident EM pulse. Nevertheless, they can pose a severe EM hazard inside the enclosure due to their large number (about 900 internal pulses in 30 ns). This means a fundamental change in the character of the EM disturbance caused by the subnanosecond pulse when the enclosure with aperture is used as a shield.

Optimization Design of Heliostat Field Based on Biomathematical Models

The optimal design of heliostat field in solar power generation device is studied Heliostat field generates high temperature by focusing the sunlight reflected from the mirror surface, thus pushing the turbine to generate electricity. In order to improve the efficiency of power generation, this paper optimizes the parameters of heliostat field, establishes a single-objective optimization model, and uses mixed strategy whale optimization algorithm to solve it. Through geometric optical analysis and ray tracing model, the optical efficiency of heliostat field and the annual average output thermal power per mirror area are calculated. Finally, through the discussion and analysis of the model, the optimization design method is evaluated

Classical Limits of Light Quanta

It is argued that from a formal point of view, the classical limit of light quanta or photons is not that of a point-like particle but that of a geometric ray. According to this view, standard particle-wave dualism, which is often used in schools to describe the quantum behavior of massive objects, could be replaced by a ray-wave dualism (or even a particle-ray-wave trialism), which seems to be more appropriate for massless quantum objects such as photons. We compare the limits leading from quantum electrodynamics to a classical (Hamiltonian) theory of particles for electrons with those leading from photons via Maxwell’s equations to geometric ray optics. We also discuss the question to which extent Maxwell’s theory for electromagnetic waves should be considered as being on the same formal level as Schrödinger’s or Dirac’s theory.

Multiscale Optical Modeling of Perovskite-Si Tandem Solar Cells

With the success of silicon (Si) solar cell technology, research and development on higher efficiency multijunction solar cells is gaining much attention. Tandem cells with a perovskite top cell and a Si bottom cell show particular potential. However, the optical modeling of such devices is complicated by the broad range of length scales involved; the optically thin layers and nanoscale features of a perovskite solar cell require some version of wave optics or even full field electromagnetic (EM) calculations, while the micrometer scale structuring and large dimensions of Si cells are much more manageable using geometrical (ray) optics. In the present work, a method for combining EM and ray optical calculations is developed and described in detail, with examples provided in the software Comsol Multiphysics. For regions with thin films or nanoscale features, EM wave calculations are performed using the finite element method. These calculations provide the phase and amplitude of the waves diffracted into different orders, of which only the regular reflection and transmission are typically of relevance for nanoscale periodicity. In the ray optics simulation, the corresponding regions are implemented as diffracting interfaces, with deterministic transformations of the Stokes vector components according to the EM wave calculations. Meanwhile, the absorbed intensity of intersecting rays is recorded. The method is applied to separate perovskite and Si solar cells and to a few tandem solar cells of relevance for two- versus four-terminal configurations. Corrections for strongly absorbing media in the ray tracing algorithm, which use generalized versions of the Fresnel coefficients, Snell’s law and the Beer-Lambert law, are also evaluated. In a typical Si solar cell with a front surface structure of inverted pyramids, such corrections are found to reduce the absorption by up to 0.5 percentage units compared to a conventional ray tracing calculation. The difference is concluded to originate mainly from reduced absorption rates of inhomogeneous waves, rather than from enhanced escape probabilities for (quasi-) trapped rays at the Si front surface. The method is further applied to evaluate the effects of a plasmonic nanoparticle array, embedded in a perovskite solar cell stack that is located directly on the microstructured Si surface.

Decay for the Kelvin–Voigt damped wave equation: Piecewise smooth damping

We study the energy decay rate of the Kelvin–Voigt damped wave equation with piecewise smooth damping on the multi-dimensional domain. Under suitable geometric assumptions on the support of the damping, we obtain the optimal polynomial decay rate which turns out to be different from the one-dimensional case studied in Liu and Rao [Z. Angew. Math. Phys. 56 (2005), no. 4, 630–644]. This optimal decay rate is saturated by high energy quasi-modes localized on geometric optics rays which hit the interface along non-orthogonal neither tangential directions. The proof uses semi-classical analysis of boundary value problems.

Application of Wigner Distribution Function for THz Propagation Analysis.

The construction of a transmission line (TL) for a wide tunable broad-spectrum THz radiation source is not a simple task. We present here a platform for the future use of designs of the TL through our homemade simulations. The TL is designed to be a component of the construction of an innovative accelerator at the Schlesinger Family Center for Compact Accelerators, Radiation Sources and Applications (FEL). We developed a three-dimensional space-frequency tool for the analysis of a radiation pulse. The total electromagnetic (EM) field on the edge of the source is represented in the frequency domain in terms of cavity eigenmodes. However, any pulse can be used regardless of its mathematical function, which is the key point of this work. The only requirement is the existence of the original pulse. This EM field is converted to geometric-optical ray representation through the Wigner transform at any desired resolution. Wigner’s representation allows us to describe the dynamics of field evolution in future propagation, which allows us to determine an initial design of the TL. Representation of the EM field by rays gives access to the ray tracing method and future processing, operating in the linear and non-linear regimes. This allows for fast work with graphics cards and parallel processing, providing great flexibility and serving as future preparation that enables us to apply advanced libraries such as machine learning. The platform is used to study the phase-amplitude and spectral characteristics of multimode radiation generation in a free-electron laser (FEL) operating in various operational parameters.

One-Sixteenth Spherical Homogeneous Dielectric Lens Antenna Using Partially Reflective Surface for Size Reduction and High-Gain Radiation

Size reduction of a 1/16 spherically sectoral homogeneous dielectric lens antenna is developed in this letter by integrating a planar partially reflective surface (PRS) to produce high-gain radiation. Such a PRS, optimized by a full-wave simulator and the geometrical optics (GO) ray tracing method, has replaced the external longitude portions of ground planes in the original sectoral lens antenna to make an aperture size of 11 × 15 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , which reduces the radius of the spherical dielectric lens by more than 33.3% (from 6 to 4 cm). The overall antenna length is reduced by 56% (from 15 to 6.59 cm). The PRS plate with a ground plane is designed by ray tracing to reach a relatively uniform field distribution on the PRS aperture for high-gain radiation. An antenna gain of 18.94 dBi has been achieved at 9 GHz from a sectoral lens fabricated by a 3-D printer using ABS (ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> = 2.429) material. The design was well validated by both numerical simulations and measurements with good agreement.

Identify the limits of geometric optics ray tracing by numerically solving the vector Kirchhoff integral.

The properties of a pencil of light as defined approximately in the geometric optics ray tracing method are investigated. The vector Kirchhoff integral is utilized to accurately compute the electromagnetic near field in and around the pencil of light with various beam base sizes, shapes, propagation directions and medium refractive indices. If a pencil of light has geometric mean cross section size of the order p times the wavelength, it can propagate independently to a distance p2 times the wavelength, where most of the beam energy diffuses out of the beam region. This is consistent with a statement that van de Hulst made in a classical text on light scattering. The electromagnetic near fields in the pencil of light are not uniform, have complicated patterns within short distances from the beam base, and the fields tend to converge to Fraunhofer diffraction fields far away from the base.

Nonstandard caustics for localized solutions of the 2d shallow water equations with applications to wave propagation and run-up on a shallow beach

The usual semiclassical approximation is not directly applicable to linearized two-dimensional shallow water equations with localized initial data describing long waves (for example, tsunami waves) in a bounded basin of variable depth, because the momentum variables on the geometric optics rays become infinite at the boundary of the region. To obtain asymptotic solutions, one needs to extend the phase space and introduce a modified Maslov canonical operator. The paper gives a brief survey of some results obtained in this direction by the authors and their colleagues.

ECRad: An electron cyclotron radiation transport solver for advanced data analysis in thermal and non-thermal fusion plasmas

We present a code for the large-scale data analysis of electron cyclotron emission (ECE) measurements from magnetized plasmas called ECRad – the Electron Cyclotron Radiation transport model for Advanced Data analysis. Its key features are low computational cost, high robustness and the capability to predict ECE spectra of plasmas with non-thermal electron populations. This is accomplished by combining the absorption coefficient given by Albajar et al. (2007) and a corresponding emissivity for the radiation transport with geometrical optics ray tracing for the computation of the diagnostic line of sight. Another important aspect of ECRad is that it has passed a large amount of verification tests against real measurements by conventional, oblique and ECE imaging diagnostics.This paper explains the physical model of ECRad and its implementation. Furthermore, it is discussed how the code can be used for the inference of the electron temperature from ECE measurements and how an oblique ECE diagnostic can be cross-calibrated with ECRad.

Scattering of light by dense particulate media in the geometric optics regime

We present a hybrid radiative transfer geometric optics approximation to model multiple light scattering in arbitrary finite discrete random media in the geometric optics regime. In the hybrid model, the medium is divided into a mantle composed of discrete particles and into a diffusely scattering core. In the mantle, multiple scattering is handled by using a ray-tracing algorithm with the generalized Snel’s law for inhomogeneous waves, whereas, in the core, ray tracing with diffuse scatterers is incorporated to approximate multiple scattering and absorption. The extinction distances required to compute the scattering in the core are derived numerically by tracing the distances of the scattering and absorption events instead of using the classical extinction mean free path length. We have written a new framework that can treat arbitrary meshes consisting of watertight surface meshes with multiple diffuse scatterers and refractive indices. Comparison between the “ground truth” obtained from pure geometric optics ray tracing, the solutions obtained by using radiative transfer, and the hybrid model show that the hybrid model can produce better results, particularly, if a densely-packed medium is studied. In the future, the new approximation could be used to solve light scattering from larger media, such as asteroid surfaces, that are out of reach for the pure geometric optics methods due to their computational complexity.

Geometrical-optics computer model of metal-knitted mesh for calculations of solar pressure on space deployable antenna reflectors.

A novel computer 3D model is presented for calculations of optical parameters (transmittance, reflectance, and absorbance) of a metal-knitted mesh textile as a structural element of deployable antenna reflectors for space satellites. The model is based on geometrical-optics ray tracing upon diffuse scattering of a broadband light source (Sun) at a complex knitted mesh structure with different inclinations to the radiative source. The proposed computer model is built for the special type of metal-wire textile (two-bar large void tricot) possessing extremely high transmittance and is verified by comparison with the experimental measurements of light scattering parameters of real antenna mesh samples of data-relaying satellites (Russian series "Loutch"). The model is used for calculations of solar radiation pressure exerted on a knitted mesh antenna reflector and gives the maximal pressure value of about 0.28 μN/m2.

Numerical description of mode coupled waves in inhomogeneous magnetized plasmas

Geometrical optics (GO) ray tracing has been widely used for a description of electron cyclotron resonance waves in inhomogeneous magnetized fusion plasmas. However, this reduced approach is not correct in sufficient low density plasmas with a sheared magnetic field, where mode coupling between two electromagnetic-like cold plasma modes can occur. Here, we extend a ray tracing method based on the first-order theory of extended geometrical optics (XGO), which captures mode coupled complex amplitude between O and X mode along the ray trajectory. In our approach, reference ray is calculated with ray equation to satisfy the lowest-order part of XGO theory and an evolution of complex amplitude profile along the reference ray is calculated with partial differential equation derived from first-order terms. Calculation results performed by extended ray tracing are in good agreement with 1D full wave analysis. By introducing second-order terms into our numerical approach, diffraction will be treated.

Computer simulations of optical turbulence in the weak- and strong-scattering regime: angle-of-arrival fluctuations obtained from ray optics and wave optics

It is known that certain geometrical-optics predictions often agree well with optical turbulence field observations even though theoretical constraints for ignoring diffraction may be violated. Geometrical optics assumptions can simplify analyses, and ray optics can significantly reduce simulation computation time. Here, an investigation into angle-of-arrival fluctuations is presented involving wave optics and geometrical (ray) optics computer simulations of a plane wave of visible light propagating through a turbulent refractive-index field. The simulation and Rytov-based theory results for the variances of aperture-filtered angle-of-arrival fluctuations generally agree well for weak scattering (Rytov variance, σR2≲0.2), but for increasing Rytov variance, the simulation results demonstrate a positive slope that can be significantly shallower than that predicted by the theory. For weak-to-moderate scattering regimes (σR2≲2.67), a comparison of the ray and wave results show they match for aperture diameters greater than about two Fresnel lengths. This result is consistent with a previous theoretical analysis by Cheon and Muschinski. For the strongest scattering case studied (σR2=26.7), the wave and ray simulations match for aperture diameters greater than about 10 Fresnel lengths. For smaller apertures, we attribute the disparity between the wave and ray simulation results to a Fresnel filtering effect.

Phase-Gradient Meta-Dome for Increasing Grating-Lobe-Free Scan Range in Phased Arrays

This paper presents a simple and effective way to increase the scan range of phased array antennas by using a metasurface (MTS) curved dome. The technique is based on a phase-gradient passive MTS that deflects the incident rays coming from the array aperture, and on a predistortion of amplitude and phase applied to the original phased array. We assume, therefore, to have at disposal an array capable of electronic beam scanning over a limited angular range with control of amplitude and phase. Geometrical optics ray tracing is used for the design of the metadome and physical optics for the analysis. For the sake of simplicity, the idea is illustrated here for a 2-D scan case; however, the extension to full 3-D scanning appears to be straightforward.

Geometrical optics-based ray field tracing method for complex source beam applications**Project supported by the National Natural Science Foundation of China (Grant Nos. 61301056 and 61231001), the Fundamental Research Funds for the Central Universities, China (Grant No. ZYGX2014J012), the Fok Ying Tung Education Foundation, China (Grant No. 141062), the Aero-Science Fund, China (Grant No. 20142580012), and the “111” Project (Grant No.

Due to the fact that traditional ray field tracking approaches require a large number of geometrical optical (GO) ray tubes, they are very inefficient in many practical applications. An improved ray model scheme for a complex source beam (CSB) tracking technique is proposed in this paper. The source field can be expressed by a superposition of CSBs, then every CSB basis function has a Gaussian-type amplitude distribution and is suitable for replacing a GO ray tube in the ray tracing approach. The complex phase matching technique is adopted to find the reflected beam in the reflection point where local approximation is used to represent the curved surface in its neighborhood. A new solution to multiple reflections using the conventional right-handed reflected system is used to track the field easily. Numerical results show the accuracy of the proposed method.

A tesselation-based model for intensity estimation and laser plasma interactions calculations in three dimensions

A three-dimensional laser propagation model for computation of laser-plasma interactions is presented. It is focused on indirect drive geometries in inertial confinement fusion and formulated for use at large temporal and spatial scales. A modified tesselation-based estimator and a relaxation scheme are used to estimate the intensity distribution in plasma from geometrical optics rays. Comparisons with reference solutions show that this approach is well-suited to reproduce realistic 3D intensity field distributions of beams smoothed by phase plates. It is shown that the method requires a reduced number of rays compared to traditional rigid-scale intensity estimation. Using this field estimator, we have implemented laser refraction, inverse-bremsstrahlung absorption, and steady-state crossed-beam energy transfer with a linear kinetic model in the numerical code Vampire. Probe beam amplification and laser spot shapes are compared with experimental results and pf3d paraxial simulations. These results are promising for the efficient and accurate computation of laser intensity distributions in holhraums, which is of importance for determining the capsule implosion shape and risks of laser-plasma instabilities such as hot electron generation and backscatter in multi-beam configurations.

Practical algorithm for custom-made caustic beams.

We present a practical algorithm for designing an aperture field (source) that propagates along a predefined generic beam trajectory that consists of both convex and concave sections. We employ here the mechanism that forms the well-known Airy beam in which the beam trajectory follows a smooth convex caustic of the geometric optics rays and generalize it for a class of beams that are referred to as "caustic beams" (CBs). The implementation is based on "back-tracing" rays from the predefined beam trajectory to the source's aperture to form its phase distribution. The amplitude is set in order to form a uniform smooth amplitude of the CBs along their trajectories. Several numerical examples are included.