Arbitrary Angle Of Incidence Research Articles

Broadband absorption with gradient metasurfaces

A metasurface with appropriately designed transverse spatial inhomogeneities can provide the desired phase redistribution in response to an incident wave with arbitrary incident angle. This property of gradient metasurfaces has been used to modify light propagation in unusual manners, to transform the impinging optical wavefront with large flexibility. In this work, we show how gradient metasurfaces can be tailored to offer high absorption in thin absorptive layers, and how to design realistic metasurfaces for this purpose using dielectric materials.

Tangential Network Transmission Theory of Reflective Metasurface With Obliquely Incident Plane Waves

In this paper, a tangential network transmission theory is established for the reflective metasurface composed of periodic subwavelength metallic elements and a perfect electrical conductor (PEC)-backed substrate. The theory is divided into two parts. The first part shows that the oblique incidence can be handled the same way as a normal incidence for a PEC-backed substrate in terms of tangential components of electric fields and a normal wave vector. Therefore, the network transmission theory is extended from the PEC-backed substrate to the reflective metasurface, whose total tangential reflection matrix depends on the induction matrix of the metallic elements in the air–substrate interface. The second part deals with the conversion of the induction matrices of different metallic elements into equivalent circuits, whose electrical parameters can be theoretically calculated or extracted from numerical simulations. Based on the obtained electrical parameters, the theory can be used to analyze or design reflective metasurfaces. Finally, the theory is verified by a metasurface, which is composed of periodic double-L shaped elements. The analytical results agree with the simulated ones for arbitrary substrate and incidence angle. The measured results further validate the proposed theory.

Theory of relativistic radiation reflection from plasmas

We consider the reflection of relativistically strong radiation from plasma and identify the physical origin of the electrons' tendency to form a thin sheet, which maintains its localisation throughout its motion. Thereby, we justify the principle of relativistic electronic spring (RES) proposed in [Gonoskov et al., Phys. Rev. E 84, 046403 (2011)]. Using the RES principle, we derive a closed set of differential equations that describe the reflection of radiation with arbitrary variation of polarization and intensity from plasma with an arbitrary density profile for an arbitrary angle of incidence. We confirm with ab initio PIC simulations that the developed theory accurately describes laser-plasma interactions in the regime where the reflection of relativistically strong radiation is accompanied by significant, repeated relocation of plasma electrons. In particular, the theory can be applied for the studies of plasma heating and coherent and incoherent emissions in the RES regime of high-intensity laser-plasma interaction.

Seismic Response for Wave Propagation across Joints with Equally and Unequally Close‐Open Behaviours

The interaction between rock joints and seismic waves is critical in rock engineering when rock mass is suffered from human‐induced or natural earthquakes. Stress wave propagation across rock joints is usually dependent on the seismic response of the joints. Wave propagation may cause joints close or open under the in situ stress. In this paper, the seismic response for wave propagation with an arbitrary incident angle impinging on joints is studied. Both reflection and transmission usually occurring at the two interfaces of the joint are considered, respectively. Wave propagation equations with equally and unequally close‐open behaviours are deduced firstly, which can be applied for the general cases of arbitrary incident P‐ or S‐wave. Then, wave propagation across joints with normal and oblique incident P‐ and S‐waves is analyzed by considering the equally and unequally close‐open behaviours and verified by comparing with the existing methods. Finally, several parametric studies are conducted to evaluate the effect of in situ stress on transmitted waves, the effect of the incident frequency on the maximum deformation of joints, and the effect of the incident angle on the maximum deformation of joints. The wave propagation equations derived in the study are more feasible and can well analyze the seismic response of wave propagation for the most general cases of different incident waveforms.

A generalized theory of thin film growth

This paper reports a theory of thin film growth that is generalized for arbitrary incidence angle during physical vapor deposition in two dimensions. The accompanying kinetic Monte Carlo simulations serve as verification. A special theory already exists for thin film growth with zero incidence angle, and another theory also exists for nanorod growth with a glancing angle. The theory in this report serves as a bridge to describe the transition from thin film growth to nanorod growth. In particular, this theory gives two critical conditions in analytical form of critical coverage, ΘI and ΘII. The first critical condition defines the onset when crystal growth or step dynamics stops following the wedding cake model for thin film growth. The second critical condition defines the onset when multiple-layer surface steps form to enable nanorod growth. Further, this theory also reveals a critical incidence angle, below which nanorod growth is impossible. The critical coverages, together with the critical incidence angle, defines a phase diagram of thin growth versus nanorod growth.

Extrinsic and intrinsic acoustical cross-sections for a viscous fluid particle near a planar rigid boundary: circular cylinder example

The objective of this investigation is to derive closed-form partial-wave series expansions for the extrinsic and intrinsic acoustical scattering, extinction and absorption cross-sections of a fluid viscous cylindrical particle of arbitrary geometrical cross-section, located nearby a flat rigid boundary. Plane progressive waves with arbitrary incidence angle are considered in a non-viscous fluid. The multiple scattering between the particle and the boundary is described using the multipole expansion in cylindrical coordinates, the method of images and the translational addition theorem. The extrinsic cross-sections are determined by integrating the associated power flow densities over a virtual surface of large radius enclosing the object and its image, stemming from far-field expressions of the incident and scattered pressure fields. The expressions for the intrinsic cross-sections are established after defining an effective acoustic field incident on the particle, which includes the primary incident field, the reflected waves from the boundary and the scattered field from the image object. Subsequently, the incident effective field is used with the scattered field from the object to derive closed-form analytical expressions for the intrinsic cross-sections, based on a far-field scattering approach, which does not introduce any approximation in the evaluation of the expressions. The obtained expressions involve the angle of incidence, the expansion coefficients of the scatterer and its image, and the distance from the center of mass of the particle to the boundary. Numerical examples for a viscous fluid circular cylindrical cross-section are considered, and computations illustrate the analysis with particular emphasis on varying the size of the particle, the angle of incidence and the particle-wall distance. The results find potential applications in the quantitative predictions of the acoustical cross-sections from fluid/soft/compressible objects nearby a boundary, such as contrast agents in biomedicine, oceanography, sonochemistry, marine science, and (borehole) geophysical applications to name a few examples.

Optimization of the Artificially Anisotropic Parameters in WCS-FDTD Method for Reducing Numerical Dispersion

A 3-D artificial anisotropy weakly conditionally stable finite-difference time-domain (AA-WCS-FDTD) method is presented to reduce the dispersion error without introducing additional computational cost and complexity. The motivation is to equal the speed of light in the numerical simulation to the physical speed through manipulating the permittivity and permeability. The proposed AA-WCS-FDTD algorithm achieves the reduced dispersion error for the arbitrary incident angles, different time-step sizes, and wideband frequency. The analyses of the stability and dispersion indicate that the proposed algorithm is WCS, and the Courant–Friedrich–Levy condition is slightly changed. The numerical example demonstrates that the proposed method has a reduced dispersion error and high accuracy as compared to the WCS-FDTD method.

Seismic dispersion and attenuation in saturated porous rocks with aligned fractures of finite thickness: Theory and numerical simulations — Part 2: Frequency-dependent anisotropy

Numerous theoretical models have been proposed for computing seismic wave dispersion and attenuation in rocks with aligned fractures due to wave-induced fluid flow between the fractures and the embedding background. However, all these models rely on certain assumptions, for example, infinitesimal fracture thickness or dilute fracture concentration, which rarely hold in real reservoirs and, thus, limit their applicability. To alleviate this issue, theoretical models for periodically or randomly spaced planar fractures and penny-shaped cracks were recently extended by the authors to the case of finite fracture thickness for P-waves propagating perpendicular to the fracture plane. Theoretical predictions under low and relatively high fracture density were then assessed by comparing with corresponding numerical simulations. However, the case of arbitrary incidence angles as well as the behaviors of S-waves remained unexplored. In this work, we therefore extended the prediction results to the full stiffness matrix through two theoretical approaches. The first approach uses an interpolation between the low- and high-frequency limits using a relaxation function obtained from the normal-incidence solution. The second approach is based on the linear slip theory with a frequency-dependent fracture compliance. Both derivations rely on the fact that all the stiffness coefficients are controlled by the same relaxation function. With the full stiffness matrix, anisotropic seismic properties can then be studied. P- and S-wave velocities and attenuations at different frequencies and incidence angles and also corresponding anisotropy parameters are calculated for one synthetic 2D rock sample. The results indicate that the predictions provided by the two theoretical approaches are in good agreement with each other and also indicate a good agreement with the corresponding numerical simulations. The extended theoretical models presented in this work are easy to apply and computationally much cheaper than numerical simulations and, hence, can be used in the seismic characterization of fractured reservoirs.

Acoustic attraction, repulsion and radiation force cancellation on a pair of rigid particles with arbitrary cross-sections in 2D: Circular cylinders example

The acoustic radiation forces arising on a pair of sound impenetrable cylindrical particles of arbitrary cross-sections are derived. Plane progressive, standing or quasi-standing waves with an arbitrary incidence angle are considered. Multiple scattering effects are described using the multipole expansion formalism and the addition theorem of cylindrical wave functions. An effective incident acoustic field on a particular object is determined, and used with the scattered field to derive closed-form analytical expressions for the radiation force vector components. The mathematical expressions for the radiation force components are exact, and have been formulated in partial-wave series expansions in cylindrical coordinates involving the angle of incidence, the reflection coefficient forming the progressive or the (quasi)standing wave field, the addition theorem, and the expansion coefficients. Numerical examples illustrate the analysis for two rigid circular cross-sections immersed in a non-viscous fluid. Computations for the dimensionless radiation force functions are performed with emphasis on varying the angle of incidence, the interparticle distance, the sizes of the particles as well as the characteristics of the incident field. Depending on the interparticle distance and angle of incidence, one of the particles yields neutrality; it experiences no force and becomes unresponsive (i.e., “invisible”) to the linear momentum transfer of the effective incident field due to multiple scattering cancellation effects. Moreover, attractive or repulsive forces between the two particles may arise depending on the interparticle distance, the angle of incidence and size parameters of the particles. This study provides a complete analytical method and computations for the axial and transverse radiation force components in multiple acoustic scattering encompassing the cases of plane progressive, standing or quasi-standing waves of arbitrary incidence by a pair of scatterers. Potential applications concern the prediction of the forces used in acoustically-engineered metamaterials with reconfigurable periodicities, cloaking devices, and liquid crystals to name a few examples.

Optimizing Weak Measurements to Detect Angular Deviations

AbstractWe analyze and compare the angular deviations for an optical beam reflected by and transmitted through a dielectric triangular prism. The analytic expressions derived for the angular deviations hold for arbitrary incidence angles. For incidence approaching the internal and external Brewster angles, the angular deviations transverse magnetic waves present the same behavior leading to the well‐known giant Goos‐Hänchen angular shift. For incidence near the critical angle a new region of large shift is seen both for transverse magnetic and transverse electric waves. While a direct measuring procedure is better in the vicinity of the Brewster region, a weak measurement breaks off the giant Goos‐Hänchen effect, preserving the amplification in the critical region. We discuss under which conditions it is possible to optimize the amplification and we also determine when a weak measurement is preferred to a direct measuring procedure.

Optical bound states in the continuum in a single slab with zero refractive index

We have investigated theoretically the reflectivity, quality factor, and eigenfrequency for a single slab with zero refractive index. We demonstrate that optical bound states in the continuum can be achieved by the various zero-refractive-index slabs made of epsilon-near-zero, impedance-machted zero-index, or mu-near-zero materials. Moreover, by analytically investigating the frequency of the resonant reflection and resonant transmission, when the quality factor becomes infinity, these two frequencies are precisely equal. For the mu-near-zero slab, the bound states in the continuum are observed at arbitrary incident angles by analyzing the behaviors of complex eigenfrequencies. Our findings may lead to unprecedented high-quality resonators in metamaterials.

Analysis of forward scattering of an acoustical zeroth-order Bessel beam from rigid complicated (aspherical) structures

The forward scattering from rigid spheroids and endcapped cylinders with finite length (even with a large aspect ratio) immersed in a non-viscous fluid under the illumination of an idealized zeroth-order acoustical Bessel beam (ABB) with arbitrary angles of incidence is calculated and analyzed in the implementation of the T-matrix method (TTM). Based on the present method, the incident coefficients of expansion for the incident ABB are derived and simplifying methods are proposed for the numerical accuracy and computational efficiency according to the geometrical symmetries. A home-made MATLAB software package is constructed accordingly, and then verified and validated for the ABB scattering from rigid aspherical obstacles. Several numerical examples are computed for the forward scattering from both rigid spheroids and finite cylinder, with particular emphasis on the aspect ratios, the half-cone angles of ABBs, the incident angles and the dimensionless frequencies. The rectangular patterns of target strength in the (β, θs) domain (where β is the half-cone angle of the ABB and θs is the scattered polar angle) and local/total forward scattering versus dimensionless frequency are exhibited, which could provide new insights into the physical mechanisms of Bessel beam scattering by rigid spheroids and finite cylinders. The ray diagrams in geometrical models for the scattering in the forward half-space and the optical cross-section theorem help to interpret the scattering mechanisms of ABBs. This research work may provide an alternative for the partial wave series solution under certain circumstances interacting with ABBs for complicated obstacles and benefit some related works in optics and electromagnetics.

Sound Source Localization Using Non-Conformal Surface Sound Field Transformation Based on Spherical Harmonic Wave Decomposition

Spherical microphone arrays have been paid increasing attention for their ability to locate a sound source with arbitrary incident angle in three-dimensional space. Low-frequency sound sources are usually located by using spherical near-field acoustic holography. The reconstruction surface and holography surface are conformal surfaces in the conventional sound field transformation based on generalized Fourier transform. When the sound source is on the cylindrical surface, it is difficult to locate by using spherical surface conformal transform. The non-conformal sound field transformation by making a transfer matrix based on spherical harmonic wave decomposition is proposed in this paper, which can achieve the transformation of a spherical surface into a cylindrical surface by using spherical array data. The theoretical expressions of the proposed method are deduced, and the performance of the method is simulated. Moreover, the experiment of sound source localization by using a spherical array with randomly and uniformly distributed elements is carried out. Results show that the non-conformal surface sound field transformation from a spherical surface to a cylindrical surface is realized by using the proposed method. The localization deviation is around 0.01 m, and the resolution is around 0.3 m. The application of the spherical array is extended, and the localization ability of the spherical array is improved.

On the orientational dependence of drag experienced by spheroids

The flow around different prolate (needle-like) and oblate (disc-like) spheroids is studied using a multi-relaxation-time lattice Boltzmann method. We compute the mean drag coefficient$C_{D,\unicode[STIX]{x1D719}}$at different incident angles$\unicode[STIX]{x1D719}$for a wide range of Reynolds numbers ($\mathit{Re}$). We show that the sine-squared drag law$C_{D,\unicode[STIX]{x1D719}}=C_{D,\unicode[STIX]{x1D719}=0^{\circ }}+(C_{D,\unicode[STIX]{x1D719}=90^{\circ }}-C_{D,\unicode[STIX]{x1D719}=0^{\circ }})\sin ^{2}\unicode[STIX]{x1D719}$holds up to large Reynolds numbers,$\mathit{Re}=2000$. Further, we explore the physical origin behind the sine-squared law, and reveal that, surprisingly, this does not occur due to linearity of flow fields. Instead, it occurs due to an interesting pattern of pressure distribution contributing to the drag at higher$\mathit{Re}$for different incident angles. The present results demonstrate that it is possible to perform just two simulations at$\unicode[STIX]{x1D719}=0^{\circ }$and$\unicode[STIX]{x1D719}=90^{\circ }$for a given$\mathit{Re}$and obtain particle-shape-specific$C_{D}$at arbitrary incident angles. However, the model has limited applicability to flatter oblate spheroids, which do not exhibit the sine-squared interpolation, even for$\mathit{Re}=100$, due to stronger wake-induced drag. Regarding lift coefficients, we find that the equivalent theoretical equation can provide a reasonable approximation, even at high$\mathit{Re}$, for prolate spheroids.

Three-dimensional midwater camouflage from a novel two-component photonic structure in hatchetfish skin.

The largest habitat by volume on Earth is the oceanic midwater, which is also one of the least understood in terms of animal ecology. The organisms here exhibit a spectacular array of optical adaptations for living in a visual void that have only barely begun to be described. We describe a complex pattern of broadband scattering from the skin of Argyropelecus sp., a hatchetfish found in the mesopelagic zone of the world's oceans. Hatchetfish skin superficially resembles the unpolished side of aluminium foil, but on closer inspection contains a complex composite array of subwavelength-scale dielectric structures. The superficial layer of this array contains dielectric stacks that are rectangular in cross-section, while the deeper layer contains dielectric bundles that are elliptical in cross-section; the cells in both layers have their longest dimension running parallel to the dorsal–ventral axis of the fish. Using the finite-difference time-domain approach and photographic radiometry, we explored the structural origins of this scattering behaviour and its environmental consequences. When the fish's flank is illuminated from an arbitrary incident angle, a portion of the scattered light exits in an arc parallel to the fish's anterior–posterior axis. Simultaneously, some incident light is also scattered downwards through the complex birefringent skin structure and exits from the ventral photophores. We show that this complex scattering pattern will provide camouflage simultaneously against the horizontal radially symmetric solar radiance in this habitat, and the predatory bioluminescent searchlights that are common here. The structure also directs light incident on the flank of the fish into the downwelling, silhouette-hiding counter-illumination of the ventral photophores.

Geant4 simulations of the lead fluoride calorimeter

In this paper we simulate the charged particle interaction with complex structures, including the emission, with help of Geant4. We take into account Cherenkov radiation, transition radiation, bremsstrahlung, pair production and other accompanying processes. As an application we investigate the full size electromagnetic calorimeter for the muon g-2 experiment at Fermilab. A calorimeter module consists of a Delrin front panel for installation of the laser calibration system, 54 PbF2 Cherenkov crystals wrapped by black Tedlar paper, and silicon photo-multiplier sensors. We report here on results of a simulation of the radiation from positrons striking the calorimeter system. The Cherenkov radiation expansion when a positron moves down through the calorimeter at the arbitrary angle of incidence has been considered. Both spectral and angular distributions of Cherenkov optical photons in different parts of the calorimeter system was evaluated as well as the transition radiation and pre-shower distributions from both the Delrin panel and the Al vacuum chamber of the g-2 storage ring.

Acoustic radiation torques on a pair of fluid viscous cylindrical particles with arbitrary cross-sections: Circular cylinders example

The numerical prediction of the radiation torques in acoustofluidics and fluid dynamics applications is essential for the design and the understanding of the underlying physics as it allows quantitative analyses. In this work, closed-form analytical expressions for the acoustic radiation torques arising from multiple scattering effects between a pair of fluid viscous cylindrical particles of arbitrary cross-sections are derived. Plane progressive waves with an arbitrary incidence angle are considered. The multipole expansion method in cylindrical coordinates is used to describe the multiple scattering effects as well as the addition theorem of cylindrical wave functions. An effective incident acoustic field on a particular object is determined and used with the scattered field to derive the analytical expressions for the torques. The mathematical expressions for the radiation torque on each particle are formulated using partial-wave series expansions in cylindrical coordinates involving the angle of incidence, the addition theorem for the cylindrical wave functions, and the expansion coefficients of the scatterers. The analysis shows that the radiation torque expressions depend on the coupled expansion coefficients of both scatterers in addition to an interference factor coupled to the interparticle distance. Numerical examples illustrate the analysis for two fluid viscous circular cylindrical cross-sections immersed in a non-viscous fluid. Computations for the dimensionless radiation torque functions are performed with particular emphasis on varying the angle of incidence, the interparticle distance, and the sizes of the circular particles. Depending on the interparticle distance and incidence angle, the particles can yield rotational neutrality; they become unresponsive (i.e., “invisible”) to the angular momentum transfer caused by multiple scattering and cancellation effects. Moreover, the radiation torque functions can be positive implying a direction of rotation in the counter-clockwise direction, and under some conditions determined by the interparticle distance, angle of incident and particle size, they reserve sign, indicating an opposite spinning in the clockwise direction. This study provides a complete analytical method and computations of the acoustic radiation torques in multiple acoustic scattering by a pair of fluid viscous scatterers. The results can be used as a priori information in the design of acoustofluidic devices and other applications involving particle rotation and handling.

Impact of incident angles of earthquake shear (S) waves on 3-D non-linear seismic responses of long lined tunnels

The incident direction of earthquake waves has significance on the seismic responses of long lined tunnels. In this study, based on the equivalent node force method and together with the viscous-spring artificial boundary, the 3-D input method of SV and SH-waves with arbitrary incident angles is studied firstly. The input method is introduced within the framework of ABAQUS software and is verified by two numerical examples. Consequently, the proposed input method is employed to investigate the impact of the incident angles of SV and SH-waves on the seismic responses of a long lined tunnel. The numerical results indicate that the non-linear seismic responses of long lined tunnels are highly affected by the incident angles of S-waves. As the incident directions of SV and SH-waves being not perpendicular to the tunnel longitude, non-uniform motions appear along the tunnel longitude, as well as the longitudinal internal forces. The plastic deformation and strain components along the tunnel cross-section are also influenced by the incident angles of SV and SH-waves. It is thus important to include the incident angles of earthquake waves in mapping the seismic risk of tunnels.

A compact permanent-magnet system for measuring magnetic circular dichroism in resonant inelastic soft X-ray scattering.

A compact and portable magnet system for measuring magnetic dichroism in resonant inelastic soft X-ray scattering (SX-RIXS) has been developed at the beamline BL07LSU in SPring-8. A magnetic circuit composed of Nd-Fe-B permanent magnets, which realised ∼0.25 T at the center of an 11 mm gap, was rotatable around the axis perpendicular to the X-ray scattering plane. Using the system, a SX-RIXS spectrum was obtained under the application of the magnetic field at an angle parallel, nearly 45° or perpendicular to the incident X-rays. A dedicated sample stage was also designed to be as compact as possible, making it possible to perform SX-RIXS measurements at arbitrary incident angles by rotating the sample stage in the gap between the magnetic poles. This system enables facile studies of magnetic dichroism in SX-RIXS for various experimental geometries of the sample and the magnetic field. A brief demonstration of the application is presented.

Propagation matrix of plane wave incident obliquely on stratified lossy chiral medium

The real and imaginary parts of the eigen complex wave vector in a stratified lossy chiral medium for the case of oblique incidence are derived by using the phase-matching condition. Due to the fact that the real and imaginary parts are nonparallel, the eigen wave propagating in the medium is inhomogeneous. Then the refraction angle of the eigen wave can be deduced via the real part of the wave vector. Finally the propagation matrix of the obliquely incident wave in a stratified lossy chiral medium is derived based on the boundary conditions and the field equations of eigen wave in each region. By using the proposed method, the reflection, transmission, and propagation characteristics of plane wave with arbitrary incident angle in a stratified chiral medium can be analyzed.