Acoustic metasurfaces for scattering-free anomalous reflection and refraction

A formalism is developed to describe the propagation along a slowly varying magnetic field of purely transverse cyclotron waves. By an expansion of the coupled set of Vlasov-Maxwell equations, a one-dimensional wave equation is derived, which is applied to the case where the field configuration is a magnetic mirror with small field variation which includes points of cyclotron resonance where the local gyrofrequency is equal to the wave frequency. An investigation is made of the processes whereby particles trapped in the mirror field can cause anomalous transmission and reflection of the wave by a nonlocal mechanism. It is found that the nonlocal processes are most significant when the function which gives the total phase difference observed by a trapped particle on its orbit between the point of damping of the incident wave and that of excitation of the transmitted or reflected wave is stationary with respect to both the energy and magnetic moment of the particle.

Acoustic metasurfaces provide a way to manipulate wavefronts at anomalous reflection or refraction angles through subwavelength structures. Here, based on the generalized Snell's refraction law for acoustic metasurfaces and the classical acoustic phased array (PA) theory, a broadband acoustic PA with a subwavelength active tube array has been proposed to form a special acoustic beam and to determine the directivity characteristics of the acoustic source. Theoretical analysis shows that the dispersionless wavefront manipulation can be realized by the gradient model of the active tube array, and a wide working frequency band can be obtained in practical applications from the simulated and experimental results. The numerical results of forming a special acoustic beam and establishing an acoustic focus model with an arbitrary focal position are consistent with the theoretical predictions. The experimental results agree well with the simulated results in the model of forming the acoustic beam of 45°. By combining acoustic metamaterials and conventional acoustic PA, the model of the active tube array paves a way to design a composite acoustic PA with high radiation efficiency and system robustness without the need for any complex circuit control system. This design concept is expected to be used in the design of ultrasonic therapy devices and high-efficiency transducers.

The error resulting from using the well known paraxial approximation instead of Snell's law of refraction is visualized geometrically.

Optics is an important branch of physics and a required foundational course for students majoring in physics, optical engineering, and optoelectronics, among others. Snell's law and Fresnel's formulas are crucial topics in optical teaching, but recent research has revealed anomalous reflection and refraction phenomena at non-uniform interfaces, rendering traditional Snell's law obsolete. While researchers have derived the generalized Snell's law using Fermat's principle to calculate reflection and refraction angles at non-uniform interfaces, the generalized Fresnel formula for calculating the reflection coefficients has remained unexplored. In this paper, we derive the generalized Snell's law and Fresnel's formulas using Maxwell's equations and boundary conditions, providing a comprehensive framework for describing the relationships between reflection and refraction angles at both uniform and non-uniform interfaces, as well as calculating the efficiency of reflection and refraction. The theoretical formulas derived align with simulation results, confirming the correctness of the generalized Snell's law and Fresnel's formulas. This work presents a valuable attempt at innovating the teaching content of optics in universities.

The diffuse scattering from neutron-irradiation-produced defects in copper was measured in anomalous transmission and near the 111 Bragg reflection. The results were related through the theory of Dederichs, and the intensities and forms of the scattering curves obtained from the two measurements were found to be in good agreement over a wide range of defect concentrations and sizes. It was shown that the intercept of a plot of the diffuse scattering intensity Is (q0) vs In (q0) is at q0=e1/2/R for defects of uniform radius R and at q0 ≌1/R0 e for an exponential size distribution of average size R0 .

A novel 2-D single-layer reflective phase gradient metasurface (RPGM) with polarization-independent property is proposed based on the generalized Snell's law of reflection. The well optimized RPGM consists of 24×24 suitably selected elements with paraboloidal phase distribution along x direction and −45° phase gradient along y direction, respectively. Pure focusing effect and anomalous reflection are unambiguously observed by illuminating with different polarizations to afford physical insight into the principle of the RPGM. For demonstration and potential applications, a polarization-controlled wideband reflective device with radiation pattern selectivity is proposed based on the specially designed RPGM for the first time. Numerical and experimental results coincide well, indicating that the designed reflective device can work as a reflectarray antenna under excitation of horizontal polarization, and operate as a beam reflector under vertical polarization. More importantly, the reflective device advances in many aspects such as bifunctional radiation patterns, quite broad bandwidth of more than 5GHz (10–15GHz), and also a simple fabrication process based on the convenient print circuit board (PCB) technology. The finding opens up a new avenue to design bifunctional devices in a wide spectrum ranging from microwave to optical.

A single-layer reflecting element is proposed based on the principle of linear-to-circular polarization conversion focusing metasurface, which can independently control the phases of x-polarized and y-polarized reflecting waves and operate in a broadband of 10-14 GHz. Following the generalized Snell's laws of reflection, a super cell is designed with a phase-gradient of -60 for x-polarized waves and 60 for y-polarized waves, and the simulation results show the well wideband anomalous reflection as expected. In the design of the multifunctional metasurface, the 1313 unit cells are used to satisfy the parabolic profile and the focal-distance-to-diameter ratio is set to be 0.5. The phase compensation for forming a constant aperture phase is provided by the individual reflected elements with different structure parameters and x-y=90 is used to realize polarization conversion. The designed sample is simulated in CST Microwave Studio and the results show that both of the x-polarized and y-polarized plane waves are well focused through the reflection of the focusing metasurface in a broadband of 10-14 GHz. Traditionally, multi-layer element is used to broaden phase coverage and bandwidth, the single-layer design in this paper greatly reduces the cost, processing difficulty and thickness of the lens. For further application, a linearly polarized Vivaldi antenna with a highest gain of 10 dB is located at the focal point of metasurface and the angle included between its polarization direction and x-axis is 45 in order to acquire right-handed circularly polarized reflecting wave. According to the reversibility principle of electromagnetic wave propagation, the spherical wave radiated by the feed antenna is converted into plane wave by the reflection of the focusing metasurface so that the antenna gain is remarkably enhanced. Simultaneously, the linearly polarized wave can be transformed into circularly polarized wave. Finally, the feed antenna and the metasurface are fabricated, assembled and measured. Numerical and experimental results are in good agreement with each other, which shows that the -1 dB gain bandwidth of the high-gain antenna is 24% (11-14 GHz) and the 3 dB axial ratio bandwidth is 29.8% (10-13.5 GHz). In addition, the gain at 12 GHz reaches a highest value of 19.6 dBic, and the aperture efficiency is more than 54%. The good performances indicate that the proposed broadband high-gain circularly polarized antenna has a well promising application in various communication systems. It is worth noting that the horizontally polarized, vertically polarized, right-handed circularly polarized and left-handed circularly polarized high-gain antenna can be realized with the rotation of feed antenna. In this case the idea is more versatile and valuable for designing the polarization reconfigurable antenna systems.

The act of performing a sequential trigonometric ray trace through an optical system is as simple as applying Snell's Laws of refraction and reflection, along with some form of the grating equation, to the geometric description of the lenses and mirrors which can comprise that system. The orderly incorporation of these physical laws into an algorithm, which at the same time incorporates all possible geometries which may occur in this optical system, will be the result of this paper. The ray/surface equations and other useful numerical techniques will be spelled out in detail so that this paper can be used as a starting point for their own ray tracing program when commercial optical design codes are either not available or inappropriate.

Modelling plays a major role in the evolution of scientific knowledge and is an objective for students' literacy in science. The emergence of accessible and powerful computational technologies imposes the development of a specific curriculum focusing on the study of science by computer modelling. This paper presents the results of investigating the possibilities of integration of computational modelling activities in Physics lessons, at high school level. Through the activities we propose here we will highlight the generality and transferability of models, by applying a unique mathematical model to solve problems that, at first sight, have nothing in common. The simulations we built with GeoGebra software and VPython programming language can be tailored both to the study of optical phenomena such as inferior or higher mirage, and to solving the famous problem of the brachistochrone. The interdisciplinary learning context, based on problem solving, calls for the application of knowledge from various fields: trigonometric and algebraic calculus, Euclidian geometry elements, Snell's law of refraction, energy conservation law, knowledge of programming and use a graphical software in modelling. The problem which students start from when investigating requires determining the fastest path between two points, separated by strips in which the propagation speeds are different. Using the achieved models, students can infer that in the case of the non-friction sliding motion, the cycloid is the fastest path. The simulations of motions were performed with GeoGebra, based on the kinematic equations, and with the VPython programming language, using the dynamic equations. The proposed modelling activities foster the development of students' transversal and transferable skills in mathematics, physics and computational technology.

Metasurfaces, planar metamaterials consisting of a single layer or several layers of artificial structures, not only form the basis for fundamental physics research but also have considerable technological significance. Metasurfaces can locally modify the optical property within a subwavelength range, which can facilitate device miniaturization and system integration. Metasurfaces have shown extraordinary capabilities in the local manipulation of the light's amplitude, phase, and polarization, leading to a plethora of novel applications such as generalized Snell's law of refraction and photonic spin Hall effect. This progress report is focused on the recent advancements in the fundamental research of geometric metasurfaces and their applications in ultrathin optical devices, including planar metalenses, helicity multiplexed holograms, functionality switchable devices, polarization beam splitters, vector beam generation, arbitrary polarization control, and so on. The compactness, ease of fabrication, and unusual functionalities of these devices render geometric optical metasurface devices very attractive for new applications such as encryption, imaging, anti‐counterfeiting, optical communications, quantum science, and fundamental physics. This paper aims to bring readers some new insights, and to broaden the applications of geometric metasurfaces in more research fields of science and technology.

In this paper, we present a semi-analytical simplified approach based on the ray tracing method to estimate radiated electric fields associated with lightning return strokes, taking into account ionospheric reflections. The field transfer function at each frequency and each grazing angle is determined by applying the generalized Snell's law of refraction, and the antenna radiation pattern concept is used to obtain the source illumination efficiency, from which the radiated field is derived. The proposed method is validated using as reference full-wave FDTD simulations.

We investigate the spectral reflectivity of photonic crystals assembled with silica spheres. The propagation of electromagnetic wave can be controlled by periodic structures known as photonic crystals. Therefore photonic crystals are anticipated for advanced control of thermal radiation beyond solid state properties. The close-packed photonic crystals well-defined thickness are rapidly made on a Si wafer by using self-assembly of colloidal silica spheres. We measure spectral reflectivities of the samples with an FT-IR (Fourier Transform - Infrared Spectroscopy). The spectral reflectivity is enhanced at specific wavelength designed with numerical analysis. The peak of spectral reflectivity shifts to shorter wavelength with increasing incident angle. The angular dependency of the spectral reflectivity can be roughly calculated by the modified Bragg's equation taking into account Snell's law of refraction. We show that the reflectivity in infrared range is well enhanced by using large photonic crystals assembled with silica micro-spheres.

The influence of surface roughness on the refraction effect for X-rays at gracing incidence was investigated using a set of brass samples with different surface roughnesses. For each sample Bragg peak positions were measured varying the incidence angle. The refraction effect at the sample surface was calculated and compared with theoretical values derived from Snell's law of refraction. Peak shift due to residual stress was also taken into account.

Light travels at different speeds through different materials causing it to bend according to Snells law Here light is represented by traveling wave fronts coming from a light source above the boundary between two materials

It is often advantageous to acquire pulse-echo ground-penetrating radar (GPR) measurements from antennas that are offset from the air-ground interface by a nonnegligible distance, either because the ground's surface is rough, or because measurements must be collected remotely. This paper describes the effects of incorrectly estimating the location of the air-ground interface on GPR images created with the plane-to-plane backpropagation (PPB) method. To compensate for a nonplanar air-ground interface, the wideband time-domain synthetic aperture method is reviewed and reformulated, using Snell's law of refraction, to account for measurements taken some distance above an undulating interface. A modification of the PPB algorithm that accounts for a nonplanar interface is also formulated, and examples of imaging with both methods are given to validate, the algorithms' performance for surface variations that are relatively smooth with respect to the radar waveform wavelengths. Additionally, a method for inferring the surface topography from the radar returns is described. Finally, the modified PPB is demonstrated by imaging buried targets sensed in field-acquired data.