Arbitrary Tilt Research Articles

Quantum theory of orbital angular momentum in spatiotemporal optical vortices

Spatiotemporal Optical Vortices (STOVs) are structured electromagnetic fields propagating in free space with phase singularities in the space-time domain. Depending on the tilt of the helical phase front, STOVs can carry both longitudinal and transverse orbital angular momentum (OAM). Although STOVs have gained significant interest in the recent years, the current understanding is limited to the semi-classical picture. Here, we develop a quantum theory for STOVs with an arbitrary tilt, extending beyond the paraxial limit. We demonstrate that quantum STOV states, such as Fock and coherent twisted photon pulses, display non-vanishing longitudinal OAM fluctuations that are absent in conventional monochromatic twisted pulses. We show that these quantum fluctuations exhibit a unique texture, i.e. a spatial distribution which can be used to experimentally isolate these quantum effects. Our findings represent a step towards the exploitation of quantum effects of structured light for various applications such as OAM-based encoding protocols and platforms to explore novel light–matter interaction in 2D material systems.

A review: Performance of multibeam dual parabolic cylindrical reflector antennas in LEO satellites

The characteristics of multibeam dual parabolic cylindrical reflector antennas are summarized in this article. They can generate an arbitrary number of beams with arbitrary tilt angles for each beam. They can be remotely controlled to cover any arbitrary area, of any shape and size, even if the antenna was mounted on a quasi-stationary platform. Their performance in Low-Earth Orbit (LEO) satellites and ground stations (terminals) have been presented. A simple beam tracking technique was developed. For any specific satellite orbit, the orientation of the ground-station antenna could be adjusted such that its beams are parallel to the satellite's beams and directed toward them. The ground-station antenna can simultaneously communicate with multiple satellites in different orbits. A single antenna can cover the whole mm-band (17.8-30 GHz), which is one of the most widely used bands in LEO satellites. The overall size of a mm-wave antenna, generating 20-24 dB gain, is 14.8x10.4x3.7 cm3 and its weight is 0.37 kg.

Dynamic control of defocus, astigmatism, and tilt aberrations with a large area foveal liquid crystal lens

We have recently reported the dynamic adjustment of the focal length in an electrically tunable liquid crystal “foveal” lens, the center of which can be shifted over a large working area. In the present work, we show that this design allows also the independent generation of astigmatism with arbitrary axis and tilt of the light wavefront by simply changing the phase and the voltage differences between 4 control electrodes. Furthermore, we also demonstrate the capability of generating highly localized negative (defocusing) lenses with the same device by using a dual frequency liquid crystal.

Parameterization of anisotropic media by A-parameters

AbstractMost common parameterization of anisotropic media is by twenty one independent elements aijkl of the density-normalized stiffness tensor or by twenty one independent elements Aαβ of the density-normalized matrix of elastic parameters in the Voigt notation. These parameters are commonly of significantly different sizes, are dimensional, in (km/s)2, often appear in combinations. We are offering an alternative parameterization by twenty one A-parameters (anisotropic parameters), which removes the mentioned disadvantages and possesses some additional useful properties. For example, axes or planes of coordinate systems, in which A-parameters are defined, need not be related to symmetry axes or planes of the considered anisotropy symmetry as required in other similar parameterizations. In combination with the first-order weak-anisotropy approximation, in which anisotropy is considered as the first-order perturbation of reference isotropy, parameterization by A-parameters yields insight into the role of individual A-parameters in the wave propagation problems. For example, it turns out that in the first-order weak-anisotropy approximation, P- and S-wave velocities are each controlled by fifteen A-parameters. A set of six of them appears only in the expression for P-wave velocity, a set of other six A-parameters appears only in S-waves velocity expressions. Remaining set of nine A-parameters is common for both waves. We present transformation of A-parameters, analogue to Bond transformation, and useful formulae for the weak-anisotropy approximation for anisotropy of any symmetry and arbitrary tilt.

Evaluation of direct beam energy received by convex solar collectors and their optimal orientations

We use analytical and numerical methods to evaluate the daily beam energy received by some convex surfaces. Spherical, hemispherical, cylindrical, and semi-cylindrical convex surfaces with arbitrary tilt angles have been investigated and compared with a flat surface of unit area. Diffusive irradiations (sky and ground) were not considered. For hemispherical and semi-cylindrical surfaces, the optimal orientations at which the received beam energy is maximal were obtained for each day of the year. The dependence of the optimal tilt angle on the day of the year is qualitatively the same as for the flat surface. Clear sky condition has been assumed to hold in this work. It is shown that a flat surface per unit of its area receives highest beam energy among other convex surfaces whereas a sphere receives the least amount. Furthermore, the received daily beam energy per unit of the ground-occupied area has been calculated. In this case, a cylindrical surface with a range of values of radius to height ratio receives the highest amount of energy whereas a flat surface receives the least. This aspect becomes noticeable in places where there are some limits, e.g., land price or any other limitation on the available surface area.

Mathematical Modeling: Cisplatin Binding to Deoxyribonucleic Acid

The discovery of the cisplatin drug attracted considerable research attention as scientists strove to understand the drug’s mechanism in the human body that is responsible for destroying cancer cells, particularly the coordination between the cisplatin drug and deoxyribonucleic acid. Here, the binding energies of a cisplatin molecule relative to double-stranded deoxyribonucleic acid are obtained. The interactions of the system are determined by performing double integrals, and the analytical expressions are derived from the Lennard–Jones function and the continuum approximation; here, it is assumed that a discrete atomic structure might be replaced by surfaces with a constant average atomic density. The results observed that the cisplatin molecule is binding to the double-stranded deoxyribonucleic acid at either the minor or major grooves. By minimizing the interaction energies between the cisplatin molecule and the minor and major grooves, for arbitrary distances λ and arbitrary tilt angles φ from the axis of the helix of the double-stranded deoxyribonucleic acid, the binding energies are determined, and their values are ≈−6 and ≈−12.5 (kcal/mol), respectively. Thus, we may deduce that the major groove in double-stranded deoxyribonucleic acid is the most preferred groove for linking with the cisplatin molecule. The current analysis might help in the equivalent continuum modeling of deoxyribonucleic acids and nanocomposites.

Razvoj metodologije za utvrđivanje optimalne snage fotonaponske elektrane postavljene na nagnutom terenu

Models for the calculation of the production of large photovoltaic (PV) power plants with different types of modules (monofacial or bifacial) have been developed in detail in the literature. In addition, detailed models have been developed for PV power plants that have fixed modules as well as PV power plants with tracking the azimuth angle of the Sun and/or the tilt angle of the PV module. On the other hand, due to the increasing installation of PV power plant, their construction is often imposed on the field with complex geometry, so it is interesting to develop models that can optimize the spatial layout and geometric elements of panels on sloping surface in relation on horizontal. Namely, during various analyses in the literature, production models for PV power plants that are planned on sloping terrains have not been developed. Accordingly, in this paper, a procedure was developed for the calculation of the production of PV power plants that are placed on terrain that is not flat, but oriented towards the arbitrary side of the World and with an arbitrary tilt angle.

Weak-anisotropy approximation of P-wave reflection coefficient in anisotropic media of arbitrary symmetry and tilt

Applicability of the approximate expression for the P-wave reflection coefficient at a weak-contrast reflector separating two weakly anisotropic half-spaces of arbitrary symmetry is extended to media of arbitrary symmetry and tilt. The reflection coefficient consists of the approximate P-wave reflection coefficient at a weak-contrast interface separating two reference isotropic half-spaces and a correction term due to anisotropy. Along an arbitrarily chosen profile, the “isotropic” term depends on the density and P- and S-wave contrasts, and the correction term depends linearly on the contrasts of four profile weak-anisotropy (WA) parameters specifying anisotropy along the profile. In addition, both terms depend on the polar angle of incidence. In each half-space, the four profile WA parameters can be expressed as a linear combination of 12 of 21 global WA parameters specifying anisotropy of the half-space. Coefficients of this linear combination are functions of the azimuth of the profile. WA parameters are a generalization of Thomsen parameters to arbitrary anisotropy and represent an alternative to 21 independent elements of the stiffness tensor. WA parameters can be used for the approximation of other related concepts such as the reflection moveout or the geometric spreading. Presented tests illustrate high accuracy and flexibility of the proposed formula for the P-wave reflection coefficient. They also show that very accurate results can be obtained for contrasts and anisotropy, which cannot be considered weak.

Influence of Misalignment on the Behavior of Electron Beam of an 800 GHz Gyrotron

The operation of gyrotrons highly depends on the alignment between the magnet and the tube, which will cause instability problems or degrade the output efficiency, especially for high-frequency gyrotrons with a small cavity size. In this letter, the influence of misalignment, including parallel shift, arbitrary tilt, and their co-existence, on the behavior of the electron beam was studied. A prototype of an 800 GHz gyrotron with a sapphire window was developed to study the correlation between the misalignment and the beam trajectory. A method to determine the tilt angle and shift distance was proposed. The feasibility of the misalignment correction method was verified in the experiment.

Finite-temperature instabilities of a two-dimensional dipolar Bose gas at arbitrary tilt angle

Advances in creating stable dipolar Bose systems, and ingenious box traps have generated tremendous interest. Theory study of dipolar bosons at finite temperature (T) has been limited. Motivated by these, we study 2D dipolar bosons at arbitrary tilt angle, $\theta$, using finite-T random phase approximation. We show that a comprehensive understanding of phases and instabilities at non-zero T can be obtained on concurrently considering dipole strength, density, temperature and $\theta$. We find the system to be in a homogeneous non-condensed phase that undergoes a collapse transition at large $\theta$, and a finite momentum instability, signaling a striped phase, at large dipolar strength; there are important differences with the T=0 case. At T = 0, BEC appears at critical dipolar strength, and at critical density. Our predictions for polar molecule system, $^{41}K^{87}Rb$, and $^{166}Er$ may provide tests of our results. Our approach may apply broadly to systems with long-range, anisotropic interactions.

Arrangement of polyhedral units for [0001]-symmetrical tilt grain boundaries in zinc oxide

Polycrystalline ZnO is used in a wide variety of electrical applications, and its properties are largely influenced by crystalline defects, such as grain boundaries (GBs). Therefore, in this study, the atomic structures of [0001]-symmetrical tilt GBs in ZnO have been characterized by scanning transmission electron microscopy, and the misorientation dependence of the atomic structures around GBs is thoroughly discussed based on the polyhedral-unit model. In addition to theoretical calculations, the polyhedral-unit arrangements for arbitrary tilt angles are described and predicted by a number-theory-based approach. The predicted structural-unit arrangements agreed well with those experimentally observed, indicating that geometrical restrictions determine the ZnO GB structures. Owing to the crystallographic relationship between the structural-unit Burgers vector and the GB-plane normal, the structural-unit arrangement was transformed at approximately 30∘, which is associated with a rigid-body translation from one grain to another.

Magneto-optical conductivity in generic Weyl semimetals

Magneto-optical studies of Weyl semimetals have been proposed as a versatile tool for observing low-energy Weyl fermions in candidate materials including the chiral Landau level. However, previous theoretical results have been restricted to the linearized regime around the Weyl node and are at odds with experimental findings. Here, we derive a closed form expression for the magneto-optical conductivity of generic Weyl semimetals in the presence of an external magnetic field aligned with the tilt of the spectrum. The systems are taken to have linear dispersion in two directions, while the tilting direction can consist of any arbitrary continuously differentiable function. This general calculation is then used to analytically evaluate the magneto-optical conductivity of Weyl semimetals expanded to cubic order in momentum. In particular, systems with arbitrary tilt, as well as systems hosting trivial Fermi pockets are investigated. The higher-order terms in momentum close the Fermi pockets in the type-II regime, removing the need for unphysical cutoffs when evaluating the magneto-optical conductivity. Crucially, the ability to take into account closed over-tilted and additional trivial Fermi pockets allows us to treat model systems closer to actual materials and we propose a simple explanation why the presence of parasitic trivial Fermi pockets can mask the characteristic signature of Weyl fermions in magneto-optical conductivity measurements.

Surface plasmon-polariton waves guided by an interface of a metal and an obliquely mounted uniaxially chiral, bianisotropic material

ABSTRACT The excitation of surface plasmon-polariton (SPP) waves was delineated for an interface of a metal and an obliquely mounted uniaxially chiral, bianisotropic material with optic axis making an arbitrary angle with the interface plane. Such a material can be fabricated as a parallel assembly of hellixes with the axis of the hellixes making an arbitrary tilt angle with the metallic substrate. The canonical boundary-value problem as well as the two prism-coupled configurations were investigated. The direction of propagation of SPP waves was restricted to be in the morphologically significant plane of the bianisotropic material that contains titled hellixes. It was found that the chirality parameter of the bianisotropic material has to have a magnitude smaller than a threshold in order for SPP waves to exist for all tilt angles. Also, the SPP wave can be excited in both prism-coupled configurations only by p-polarized plane waves.

Calculating the Energy Yield of Si-Based Solar Cells for Belgium and Vietnam Regions at Arbitrary Tilt and Orientation under Actual Weather Conditions

Predicting actual energy harvesting of a photovoltaic (PV) installation as per site-specific conditions is essential, from the customer’s point of view, to choose suitable PV technologies as well as orientations, since most PVs usually have been designed and evaluated under standard illumination. Hence, the tendency lives in the PV community to evaluate the performance on the energy yield and not purely on the efficiency. The major drawback is that weather conditions play an important role, and recording solar spectra in different orientations is an expensive and time-consuming business. We, therefore, present a model to calculate the daily, monthly and annual energy yield of Si-based PV installations included in commercial panels as well as tandem solar cells. This methodology will be used to evaluate the benefit of potential new technologies for domestic and building integrated applications. The first advantage of such a numerical model is that the orientation of solar panels and their properties can be easily varied without extra experiments. The second advantage is that this method can be transferred to other locations since it is based on a minimum of input parameters. In this paper, the energy yield of PV installations for different regions in Belgium and Vietnam will be calculated.

Microwave and submillimeter wave scattering of oriented ice particles

Abstract. Microwave (1–300 GHz) dual-polarization measurements above 100 GHz are so far sparse, but they consistently show polarized scattering signals of ice clouds. Existing scattering databases of realistically shaped ice crystals for microwaves and submillimeter waves (>300 GHz) typically assume total random orientation, which cannot explain the polarized signals. Conceptual models show that the polarization signals are caused by oriented ice particles. Only a few works that consider oriented ice crystals exist, but they are limited to microwaves only. Assuming azimuthally randomly oriented ice particles with a fixed but arbitrary tilt angle, we produced scattering data for two particle habits (51 hexagonal plates and 18 plate aggregates), 35 frequencies between 1 and 864 GHz, and 3 temperatures (190, 230 and 270 K). In general, the scattering data of azimuthally randomly oriented particles depend on the incidence angle and two scattering angles, in contrast to total random orientation, which depends on a single angle. The additional tilt angle further increases the complexity. The simulations are based on the discrete dipole approximation in combination with a self-developed orientation averaging approach. The scattering data are publicly available from Zenodo (https://doi.org/10.5281/zenodo.3463003). This effort is also an essential part of preparing for the upcoming Ice Cloud Imager (ICI) that will perform polarized observations at 243 and 664 GHz. Using our scattering data radiative transfer simulations with two liquid hydrometeor species and four frozen hydrometeor species of polarized Global Precipitation Measurement (GPM) Microwave Imager (GMI) observations at 166 GHz were conducted. The simulations recreate the observed polarization patterns. For slightly fluttering snow and ice particles, the simulations show polarization differences up to 11 K using plate aggregates for snow, hexagonal plates for cloud ice and totally randomly oriented particles for the remaining species. Simulations using strongly fluttering hexagonal plates for snow and ice show similar polarization signals. Orientation, shape and the hydrometeor composition affect the polarization. Ignoring orientation can cause a negative bias for vertically polarized observations and a positive bias for horizontally polarized observations.

Solar energy and daylight on tilt planes under CIE standard skies

The CIE (International Commission on Illuminance) Standard Skies depicts the typical diffuse luminance and radiance distributions over the skydome. However, it can be challenging to interpret the luminance and radiance distribution into the irradiance and illuminance contributions on tilt planes by numerical integrations. This paper proposes a surrogate model that determines the ratio of the diffuse irradiance on an arbitrary tilt plane to that on the unobstructed horizontal plane without the complicated and time-consuming numerical integrations. The model is determined using solar altitude, sky conditions, and the angular distance of the plane (surface normal) and the sun. The proposed model is validated by measurement of the vertical illuminance and irradiance that are taken in 2004 and 2005, and the irradiance on planes of different tilt angles and azimuth directions from February to May in 2015. All measurements were in the 10-minute interval. For vertical planes, the proposed approach gives the ratio of the root mean square errors to the measurement average 1.38% to 2.04% lower than a classical model for irradiance and 3.6% to 4.6% for illuminance, when the Skies can be accurately identified. The model thus accurately interprets the luminance and radiance distributions of the CIE Standard Skies, which can be essential to a fast study for the solar energy potential as well as the thermal and daylight environments under different sky conditions.

Effect of Geomagnetic Field on Motion of Passive Conductive Satellites

In this paper we analyze theoretically the effect of geomagnetic field on rotation of passive conductive satellites of a spherical shape such as Russian-Australian satellite WESTPAC or Russian satellite Larets. The main cause of this effect is the generation of eddy currents and satellite magnetic moment, which interact with the Earth’s magnetic field. The analytical solutions have been derived for orbital and intrinsic magnetic moments of satellite, which result from a translatory motion of an Earth-orbiting satellite and from a satellite spin around axes passing through its center of mass. An arbitrary relation between skin layer depth and satellite radius is assumed. Both a torque acting on satellite in geomagnetic field and the changes in its angular velocity are derived. The satellite orbiting the Earth in a circular orbit with an arbitrary tilt of the orbital plane is studied having regard to rotation of the vector of geomagnetic dipole moment. A characteristic time it takes for the angular velocity of the satellite to decrease exponentially is estimated. Peculiarities of residual irregular vibrations of the satellite angular velocity are examined.

Estimating Solar Irradiance on Tilted Surface with Arbitrary Orientations and Tilt Angles

Photovoltaics modules are usually installed with a tilt angle to improve performance and to avoid water or dust accumulation. However, measured irradiance data on inclined surfaces are rarely available, since installing pyranometers with various tilt angles induces high costs. Estimating inclined irradiance of arbitrary orientations and tilt angles is important because the installation orientations and tilt angles might be different at different sites. The goal of this work is to propose a unified transfer model to obtain inclined solar irradiance of arbitrary tilt angles and orientations. Artificial neural networks (ANN) were utilized to construct the transfer model to estimate the differences between the horizontal irradiance and the inclined irradiance. Compared to ANNs that estimate the inclined irradiance directly, the experimental results have shown that the proposed ANNs with differential outputs can substantially improve the estimation accuracy. Moreover, the trained model can successfully estimate inclined irradiance with tilt angles and orientations not included in the training data.

Generalized Warped Disk Equations

Abstract The manner in which warps in accretion disks evolve depends on the magnitude of the viscosity. For small viscosity (α < H/R), the warp evolves in a wave-like manner; for large viscosity, H/R < α ≪ 1, it evolves diffusively. Here, α is the viscosity parameter and H/R is the disk aspect ratio. Currently there is no simple set of equations that describes the evolution in both regimes. In this paper, we describe a possible solution to this problem and introduce a set of one-dimensional equations that describe the evolution of a warped disk that are applicable in both high- and low-viscosity regimes for arbitrary tilts, but small warps.

Tilt-induced kink in the plasmon dispersion of two-dimensional Dirac electrons

The list of two dimensional Dirac systems with a tilt in their Dirac cone spectrum is expanding, and now in addition to organic system $\alpha$(BEDT-TTF)$_2$I$_3$ includes the two dimensional $8Pmmn$-borophene sheet, which allows for controlled doping by the gate voltage. We analytically calculate the polarization function of tilted Dirac cone for arbitrary tilt parameter, $0\le \eta <1$, and arbitrary doping. This enables us to find two interesting plasmonic effects solely caused by the tilt: (i) In addition to the standard plasmon oscillations, strong enough tilt, induces an additional linearly dispersing overdamped branch of plasmons, which is strongly Landau damped due to overlap with a large density of intra-band free particle-hole (PH) excitations. (ii) There appears a kink in the plasmon dispersion for any non-zero tilt parameter. The kink appears when the plasmon branch enters the inter-band continuum of PH excitations. This kink becomes most manifest for wave vectors perpendicular to the tilt direction and fades away by approaching the tilt direction. Experimental measurement of the wave vector and energy of the plasmonic kink, when combined with our analytic formula for the kink energy scale, allows for a direct experimental measurement of the tilt parameter.