Nonspecular Reflection Research Articles

Utilizing non-specular reflection of bounded ultrasonic beams for assessing damage in solid plates

This paper investigates the potential of utilizing non-specular reflection of a bounded ultrasonic beam in a liquid-solid-liquid structure as a method for assessing damage in solid plates. The study focuses on understanding the acoustic field formulation resulting from this type of reflection, as well as examining the impact of incident angles and material damage (indicated by reduced Young's modulus) on the non-specular reflection field. To quantify the effects of non-specular reflections, the specular reflection coefficient (SRC) proposed by the authors is employed (Wang and Deng, 2023) [1]. A finite-element (FE) model is developed to analyze the SRC response concerning the incident angle and material damage. Through FE simulations involving obliquely incident bounded ultrasonic beams at different angles, the research reveals a significant, monotonically increasing sensitivity of the SRC change rate at the S0 critical angle to the level of material damage. This finding offers a precise approach for accurately evaluating material damage in plates. Experimental tests are conducted on a water-aluminum sheet-water structure, which validates the theoretical predictions and FE simulation results. The experimental results consistently demonstrate an increased change rate of the SRC at the S0 critical angle in response to the fatigue cycle, confirming the effectiveness of using non-specular reflection of a bounded ultrasonic beam at the S0 critical angle as a method for evaluating material damage in plates.

Filter-based solutions for finite and infinite edge diffraction

Sound diffraction occurs at (building) corners, objects and openings, prominently affecting occluded and reflected sounds. Here, a physically-based, parametric filter model for diffraction at arbitrary wedges is presented. The model connects existing high-frequency asymptotic and exact solutions in geometrical acoustics using up to four half-order low-pass filters. Compact expressions for the transfer function and impulse response of the singly diffracted field are derived, with errors below 0.1 dB. A filter modification is suggested to account for the exact solution at low frequencies. The filter solution is further simplified to approximate the spectral effects of diffraction from finite wedges and objects composed thereof, referred to as universal diffraction filter approximation (UDFA). A computationally highly-efficient recursive filter implementation is presented and it is demonstrated that diffraction from flat finite objects like plates or apertures can be closely approximated. To account for effects of higher-order diffraction at the object, a heuristic filter extension is suggested. The presented filter-based diffraction solution is suited for the prediction and simulation of sound propagation including non-specular reflections in architectural acoustics. For virtual acoustics, UDFA provides an efficient and accurate approximation of edge diffraction to account for perceptually relevant frequency-dependent attenuation, extendable to arbitrary objects.

All-dielectric carpet cloaks with three-dimensional anisotropy control

Abstract In this article, we propose all-dielectric carpet cloaks composed of jungle gym shaped dielectric unit cells and present a design strategy for three-dimensional (3-D) anisotropy control based on the transformation optics. The carpet cloaks are 3-D printable and operate with polarization independent incident waves in arbitrary incident angles due to the 3-D anisotropy control. Realizable anisotropic permittivities of cubic and rectangular unit cells are numerically studied based on the relative permittivity and loss tangent of ɛ r = 2.9 and tan δ = 0.02 of ultra-violet curing resin measured at the microwave frequency. It is shown that the unit cell has little frequency dependence even with the anisotropy in the low frequency range where the effective medium approximation is valid. A carpet cloak is designed based on the design method with a quasi-conformal coordinate transformation and implemented with the unit cells taking into account its realizable anisotropy. Polarization independent 3-D cloaking operations of the designed cloak are confirmed numerically. The designed cloak is fabricated by stereolithography 3-D printing technology and its cloaking performances are evaluated experimentally at 10 GHz. It is shown that non-specular reflections are well suppressed by the carpet cloak for both TE and TM incident waves with different incident angles of 30, 45, and 60°. Frequency independent cloaking operations are also shown experimentally in the X-band. The measured near-field distributions and bistatic radar cross sections are in good agreement with simulated predictions and the validity of the design method is confirmed.

Evaluation of material damage using non-specular reflection of a bounded ultrasonic beam at a liquid-solid interface

This paper proposes an effective method for evaluating the level of material damage using the non-specular reflection of a bounded ultrasonic beam at a liquid-solid interface. Non-specular reflection occurs when a bounded ultrasonic beam is obliquely incident from a liquid onto a solid surface. This paper formally formulates the acoustic field of the non-specular reflection of a bounded ultrasonic beam and analyzes the influences of some factors such as the incident angle and the level of material damage (characterized by a decrease in Young's modulus) on the non-specular reflection field. To characterize the effect of the non-specular reflection of a bounded ultrasonic beam, this paper defines a specific parameter called the specular reflection coefficient (SRC) of a bounded ultrasonic beam. A finite-element (FE) model is established to quantitatively observe the response of the defined SRC to the incident angle and the level of material damage. The FE simulations are conducted for the bounded ultrasonic beam obliquely incident at longitudinal, transverse, and Rayleigh critical angles, respectively. The simulations demonstrate that the change rate of SRC at the Rayleigh critical angle exhibits a monotonically sensitive response to the level of material damage, providing an effective means for accurately evaluating it. To validate this method, we conducted an experiment with oblique incidence testing of the bounded ultrasonic beam at the Rayleigh critical angle of the water-aluminum interface. The experimental results are consistent with the FE simulations, and show that the change rate of SRC at the Rayleigh critical angle has a monotonous and sensitive response to the level of material damage. The consistency of theoretical predictions, FE simulations, and experimental results confirms the feasibility of using the non-specular reflection of a bounded ultrasonic beam incident at the Rayleigh critical angle as an effective method for evaluating the level of material damage.

Experimental observation of diffractive retroreflection from a dielectric metasurface

The non-specular reflection scenario is considered important for many practical applications of gratings because this regime corresponds to the maximum efficiency of diffraction. Retroreflection is a particular case of a non-specular scenario when a grating returns a large portion of the incident light back to its source. We propose a detailed quasi-optic (microwave) experimental study of the retroreflection phenomenon in dielectric metasurfaces. Our study is supplemented by an analytical description and full-wave numerical simulation. The experimental sample of the metasurface is constructed as an array of disk-shaped low-loss ceramic resonators inserted in a host with air-like material properties. To ensure efficient reflection, the metasurface is coated on one side with a metallic foil. The conditions of retroreflection for any direction and polarization of an incident wave are demonstrated in both far-field and near-field experiments. The main contribution to the non-specular reflection of the Mie-type (HE 11) mode of the disk-shaped resonators forming the metasurface is revealed. The high efficiency of retroreflection in both TE (transverse electric) and TM (transverse magnetic) polarizations allows us to consider our metasurface as a prototype of planar grating rulers for high-precision displacement measurements.

Deflection of a reflected intense spatiotemporal optical vortex beam.

In this Letter, we reveal a new deflection effect in the reflection of an intense spatiotemporal optical vortex (STOV) beam. When a STOV beam with relativistic intensities (>1018 W cm-2) impacts on an overdense plasma target, the reflected beam deviates from the specular reflection direction in the incident plane. Using two-dimensional (2D) particle-in-cell simulations, we demonstrated that the typical deflection angle is of a few milliradians and can be enhanced by using a stronger STOV beam with tightly focused size and higher topological charge. Though similar to the angular Goos-Hänchen effect, however, it is worth emphasizing that the deviation induced by a STOV beam exists, even in normal incidence, revealing an essentially nonlinear effect. This novel effect is explained from the viewpoint of angular momentum conservation, as well as the Maxwell stress tensor. It is shown that an asymmetrical light pressure of the STOV beam breaks the rotational symmetry of the target surface and leads to nonspecular reflection. Unlike the shear press of an Laguerre-Gaussian beam, which only acts in oblique incidence, the deflection caused by the STOV beam exists more widely, including in normal incidence.

Non-specular reflection of a narrow spatially phase-modulated Gaussian beam.

The lateral and angular Goos-Hänchen shifts undergone upon reflection on a dielectric plate by a spatially phase-modulated Gaussian beam are derived. It is shown that the amplitude and direction of both lateral and angular shifts are very sensitive to the degree of spatial phase modulation of the incident beam, so that such modulation thus provides a means to control those shifts. It is also shown that the modulation incurs some beam reshaping upon reflection. Analytical calculations of the lateral shift are found to be in good agreement with numerical simulations of beam propagation before and after reflection. In these simulations, the required spatial transverse phase modulation is achieved by focusing a microwave Gaussian beam onto the dielectric plate with a non-spherical lens or a flat-surfaced thin lamella exhibiting a suitable gradient of its refractive index. The optimal parameters governing the spatial phase modulation are discussed to achieve: (i) enhancement of the lateral shift of a spatially phase-modulated beam in comparison to that of a non-modulated beam and (ii) simultaneous large values of reflectivity and of the lateral shift, while keeping the reshaping of the reflected beam to a minimum.

Beam- and Band-Width Broadening of Intelligent Reflecting Surfaces Using Elliptical Phase Distribution

Reflectarray surfaces (RASs) can be useful as passive repeaters or intelligent reflecting surfaces (IRSs) in communication networks by providing nonspecular reflection of an incident wave. To provide adequate signal at a given location, the radar cross section (RCS), and therefore physical size, of the RAS needs to be maximized. This inevitably reduces the beamwidth and bandwidth of the RCS pattern, severely limiting their practical implementation. This article considers a shaped reflector profiled as a truncated ellipse that can give a widened “equi-ripple” beam that addresses these problems. It is shown that by careful selection of the phase profile, the beamwidth can be expanded by a factor of 3.5 (or even 7.5 if lower roll-off in the RCS pattern is allowed) with a corresponding increase in the useable bandwidth. The tradeoff is a reduction in the peak RCS. By increasing the physical size of the reflector, this loss of RCS can be compensated for, still resulting in at least 1.8 times the beamwidth of a flat reflector. The shaped reflector can be realized as an RAS using a closed-form expression. A typical design at 28 GHz is considered. In principle a 22 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times22$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.4\lambda $ </tex-math></inline-formula> spaced array offers illumination from 40° to 50° over 26–32 GHz, considerably better than the unshaped beam.

Accounting for Lambertian reflection in the assimilation of microwave sounding radiances over snow and sea‐ice

AbstractThis article investigates two aspects aimed at an increased use of surface‐sensitive microwave sounding radiances for numerical weather prediction (NWP), namely the assimilation of humidity‐sounding radiances from the Advanced Technology Microwave Sounder (ATMS) over snow, as well as the use of Lambertian reflection in radiative‐transfer modelling over snow and sea‐ice surfaces for temperature‐ and humidity‐sounding radiances. The Lambertian characteristics are modelled through a parameterisation of the effective zenith angle used to calculate the downwelling radiation in the radiative‐transfer model. Using Lambertian rather than specular reflection improves the forward modelling significantly for 183‐GHz humidity‐sounding channels over snow and sea‐ice in comparisons with observations, including a reduction of significant zenith‐angle‐dependent biases. For temperature‐sounding channels in the 50‐GHz band, comparisons between observations and background equivalents also suggest improvements from treating snow and sea‐ice surfaces as Lambertian or semi‐Lambertian, but the characteristics appear more variable and there are indications of other sources of error, such as biases in the skin temperature. For both spectral regions, the improvement from using nonspecular reflection is clearest for snow‐covered land surfaces. Assimilation experiments show that the addition of 183‐GHz humidity‐sounding channels from ATMS over snow‐covered land leads to a slight positive impact over higher latitudes in winter. On top of this, replacing the specular surface assumption over snow and sea‐ice with a fully Lambertian one for 183‐GHz channels on ATMS and semi‐Lambertian one for 50‐GHz channels on ATMS and the Advanced Microwave Sounding Unit–A (AMSU‐A) means that more observations pass quality control, giving a neutral to slightly positive impact at higher latitudes in winter. Combining the two changes leads to small forecast benefits that are statistically significant up to day 3 at higher latitudes.

Collisionless Shocks in the Heliosphere: Foot Width Revisited

Abstract For single-point measurements of quasi-perpendicular shocks, analytical measurements of the foot width are often used to evaluate the velocity of the shock relative to the satellite. This velocity is of crucial importance for in situ observations because it enables the identification of the spatial scale of other regions of the shock front such as a magnetic ramp for which the comprehensive understanding of their formation is not yet achieved. Knowledge of the spatial scale is one of the key parameters for the validation of theoretical models that are developed to explain the formation of these regions. Previously available estimates of the foot width for a quasi-perpendicular shock are based on several simplifications such as zero upstream ion temperature and specular ion reflection by the cross-shock electrostatic potential. The occurrence of specular reflection implies high values of the cross-shock electrostatic potential that significantly exceed the values obtained from in situ measurements. In this paper the effects of nonzero ion temperature and nonspecular ion reflection on the foot width are investigated. It is shown that in the case of nonspecular reflection the foot width can be as small as half of the size of the standard widely used estimate. Results presented here enable more reliable identification of the shock velocity from single-point observations.

On the role of spatial dispersion in boundary conditions for perfect non-specular reflection

Exact solutions for perfect anomalous reflection through metasurfaces have been recently developed in terms of both ideal nondispersive impenetrable boundary conditions (BCs) and penetrable BCs on top of a grounded slab. The second model is more accurate for the description of metasurfaces realized in PCB technology. Focusing on this particular class of metasurfaces, this paper investigates the connection between the two solutions, with the aim to clarify the role of spatial dispersion. It is shown that the two solutions can be related through an equivalent transmission network where transmission lines with different wavenumbers are associated to the incident and reflected waves. Finally, numerical analyses are carried out to assess the impact of neglecting spatial dispersion, as it is done in designs based on a linear phase gradient of the local reflection coefficient.

Broadband Channel Characterization in Wooded Environment in the 26 GHz Band

The present work describes the use of a simulation model based on asymptotic methods (ray tracing) on the propagation of ultra-wideband radio signals in a densely-arborized urban channel. The model was previously validated and adjusted using data obtained from measurement campaigns in the millimeter-wave band in locations different from the one to be analyzed here. The simulation uses deterministic methods to predict the received power, cross-polar discrimination, root mean square delay spread, and mean delay in a channel with a high density of scatterers (trees, buildings, and poles). Simulated signals were transmitted in the vertical and horizontal polarizations, considering non-specular reflections caused by rough surfaces and the effect of the transmitter’s height variation in outdoor channels.

Exploiting eutectic formation and phase separation to produce plasmonic metamaterials

Novel Au mesostructures with a polyhedron shape, henceforth referred to as pyramids, are produced by annealing in vacuo an Au thin film on a Si(100) substrate. Gold diffusion and incorporation into pyramids is a function of the thickness of the Au film, the annealing temperature, and the vacuum pressure. The Au pyramids have unique surface morphologies due to the presence of channels and plateaus, where channels are cut into the surface of the pyramids and plateaus are the surfaces between adjacent channels. The bulk of the pyramids consists of Au with cavities that are devoid of Au or Si. Normalized energy dispersive spectroscopy of intact regions of the surface are 98.1 wt. % Au and 1.9 wt. % Si, while the bottom of the channels are 85.7 wt. % Au and 14.3 wt. % Si. Therefore, one step in the growth process is the formation of an Au–Si eutectic. The low concentration of Si in the solid regions of the pyramid and its high concentration in the walls of the cavities are indicative of phase separation of the Au–Si eutectic. The pyramids are oriented in the same direction relative to one another and are a consequence of eutectic formation-induced etching of the Si(100) surface. The scattering spectrum (non-specular reflectivity) of the Au pyramids consists of two very strong surface plasmon polariton states that correspond to excitation from the Au d-bands to the sp conduction bands. The surface morphology produces linearly polarized reflected light.

Perfect non-specular reflection with polarization control by using a locally passive metasurface sheet on a grounded dielectric slab

This paper investigates the conditions for a perfect anomalous reflection through a modulated metasurface consisting of a metallic cladding printed over a grounded slab. Differently to what has been previously published, the problem is rigorously addressed by modeling the metallic cladding through an equivalent penetrable impedance and accounting for the grounded slab through the problem's Green's function. It is shown that without polarization transformation, the exact solution exists only for the special case of retroreflection, and, in that case, it can be done simultaneously for the two orthogonal polarizations, with an arbitrary phase shift among the two. On the other hand, changing the polarization of the reflected wave allows one to find an exact solution for arbitrary combinations of incidence and reflection angles. The exact solution is found by imposing that the induced currents radiating with the Green's function of the background problem simultaneously create the desired reflected beam and cancel the specular reflection from the grounded slab. This approach leads to the derivation of a closed-form expression for the homogenized penetrable impedance profile providing perfect anomalous reflection, i.e., ensuring the vanishing of all the coefficients of the waves associated with unwanted diffraction orders, including the specular reflected wave and the evanescent waves. This result is of great practical interest, since the derived penetrable impedance profile can be readily implemented through a simple distribution of metallic patches. The feasibility of this approach is verified through full wave simulations of both the ideal impedance and the patch-based structure, which confirm the effectiveness of the proposed solution.

Nonspecular Reflection of Droplets.

The bouncing of droplets on super-repellent surfaces normally resembles specular reflection that obeys the law of reflection. Here, the nonspecular reflection of droplet impingement onto solid surfaces with a dimple for energy-efficient, omnidirectional droplet transport is reported. With the dimple of the radius being comparable to that of the droplet, all the symmetries in the law of reflection can be broken down so that the droplet is endowed with a translational velocity finely tunable in both its direction and magnitude simply by varying the radii of the droplet and the dimple, the impinging position, and droplet Weber number. Tailoring the initial and translational velocity of impinging droplets would steer their reflected trajectories at will, thus enabling versatile droplet manipulation including trapping, shedding, antigravity transport, targeted positioning, and on-demand coalescence of droplets.

Non-specular scattering of carriers from surface defects in thin metal interconnects

Non-specular scattering of carriers, despite being one of the key contributors to metal film resistivity, is conveniently characterized by a single parameter p (referred to as specularity parameter) in the literature without providing a means to separate out relative contributions of surface defects to it. In this work, we report a theoretical formalism to predict contributions to (non-specular) reflection (scattering) of carriers from different types of chemical and structural defects on the film surface. Establishing specular reflection as a special case of the more generalized reflection from the surface, we show that elastic scatterings contribute to the non-specular reflections by randomizing the forward momentum along the transport direction. We predict density and angle-dependent specularity coefficient for various types of defects and show that large angle reflections tend to be non-specular in the presence of isotropic surface defects. Using this formalism, we predict the probability of specular reflection for technologically relevant metal–metal and metal–insulator interfaces. Calculated specularity coefficients are in agreement with values obtained from experimental measurements. Our methodology will help in designing next generation interconnects and engineering the interfaces with minimal diffuse reflection.

Scattering in Feedback Delay Networks

Feedback delay networks (FDNs) are recursive filters, which are widely used for artificial reverberation and decorrelation. One central challenge in the design of FDNs is the generation of sufficient echo density in the impulse response without compromising the computational efficiency. In a previous contribution, we have demonstrated that the echo density of an FDN can be increased by introducing so-called delay feedback matrices where each matrix entry is a scalar gain and a delay. In this contribution, we generalize the feedback matrix to arbitrary lossless filter feedback matrices (FFMs). As a special case, we propose the velvet feedback matrix, which can create dense impulse responses at a minimal computational cost. Further, FFMs can be used to emulate the scattering effects of non-specular reflections. We demonstrate the effectiveness of FFMs in terms of echo density and modal distribution.

Sea Ice Transition Detection Using Incoherent Integration and Deconvolution

Currently, reflectometry-based sea ice detection methods rely on observables extracted from delay-Doppler maps (DDM)s, which are sensitive to ice in the specular zone. Due to the size of the glistening zone, the transition from open seas to sea ice in the specular zone can take up to 10 s for satellite platforms and no methods exist that can process this. In this article, using DDMs collected by TechDemoSat-1, we demonstrate that this transition is comprised of a response that is fixed in the spatial domain, at the ice edge, and moving in the delay-Doppler domain. This is the first observation of persistent nonspecular coherent reflections from sea ice. The delay-Doppler trajectory of the ice response is shown to correspond with a point that is located on the ambiguity free line. Furthermore, the response is point-like as it suffers from delay and Doppler walk suggesting that it originates from a small spatial footprint, i.e., the first (few) Fresnel zone(s). Exploiting these facts, we then propose a technique that integrates the ice response in the spatial domain after preprocessing. This results in the edges of the ice sheet being emphasized as all of the power received during the transition phase maps to the edge of the sheet. We also propose to compensate for the delay-Doppler walk during preprocessing by modifying Woodward's ambiguity function when deconvolution is performed.

Optically probing picometer-resolved photo-dynamics of solid surfaces

Optical probes for precisely studying laser-solid interactions are of utmost importance in various fields. Here we demonstrate a simple, single-lens interferometer for measuring time-resolved deformation of solid surfaces induced by optical excitation with about 150 pm (λ/4000) precision by analyzing the local intensity of the interference fringes in a self-referencing manner. We first show picometer-resolved deformation and relaxation of a smooth acrylic surface due to absorption of a sub-mW low-power laser pulse. We demonstrate the applicability of our approach to samples producing non-specular reflections, such as a dried drop of blood and a black rough surface of graphene oxide, prepared by drop-casting on a glass slide. We suggest that the thermo-mechanical deformation from our interferometer can be used to measure thermal effects (such as the local change in temperature) of different solid materials with high precision, which is needed in many applications such as in laser heating or cooling experiments. It will be interesting to extend our approach to study real-time thermal and non-thermal deformation in solids due to nanosecond or picosecond laser pulses.

Numerical Study of a Phased Array-Based Ultrasonic Polar Scan to Determine Plane-Wave Reflection Coefficients of Plates.

Numerical finite-element (FE) simulations and postprocessing analysis methods are presented for ultrasonic polar scan (UPS) measurements involving a circular phased array (C-PA) to determine the plane-wave reflection coefficient of plates. Apodization weights for the C-PA elements are determined to assure the generation of a quasi-plane wave upon excitation at the plate surface and to mitigate bounded beam effects on the assessed reflection coefficient. In addition, postprocessing of the reflection signals is performed via the synthetic plane-wave technique to further filter out any bounded beam effects. Reflection coefficients are presented for three cases namely, an aluminum, a unidirectional carbon epoxy, and a cross-ply carbon epoxy plate. For all three cases, comparison with the analytical plane-wave theory shows excellent agreement with the reflection coefficients obtained by the C-PA and the additional postprocessing steps for both the pulsed and harmonic signals. It is also shown that the agreement becomes considerably worse if the nonspecular reflection field is disregarded in the postprocessing treatment, thus enforcing the need to capture the full reflected field via the PA whenever plane-wave reflection coefficients are needed.