Snell's Law of Refraction (Wave Fronts)

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

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.

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.

Manipulation of acoustic wavefronts by thin and planar devices, known as metasurfaces, has been extensively studied, in view of many important applications. Reflective and refractive metasurfaces are designed using the generalized reflection and Snell's laws, which tell that local phase shifts at the metasurface supply extra momentum to the wave, presumably allowing arbitrary control of reflected or transmitted waves. However, as it has been recently shown for the electromagnetic counterpart, conventional metasurfaces based on the generalized laws of reflection and refraction have important drawbacks in terms of power efficiency. This work presents a new synthesis method of acoustic metasurfaces for anomalous reflection and transmission that overcomes the fundamental limitations of conventional designs, allowing full control of acoustic energy flow. The results show that different mechanisms are necessary in the reflection and transmission scenarios for ensuring perfect performance. Metasurfaces for anomalous reflection require non-local response, which allows energy channeling along the metasurface. On other hand, for perfect manipulation of anomalously transmitted waves, local and non-symmetric response is required. These conclusions are interpreted through appropriate surface impedance models which are used to find possible physical implementations of perfect metasurfaces in each scenario. We hope that this advance in the design of acoustic metasurfaces opens new avenues not only for perfect anomalous reflection and transmission but also for realizing more complex functionalities, such as focusing, self-bending or vortex generation.

Refraction holodiagrams and Snell's law

T. G. Muir et al. observed experimentally that the maximum of the received sound pressure in the sediment insonified by a parametric array departed significantly from the prediction of Snell's law. The wave fronts penetrated more steeply into the sediment and the attenuation with depth was less than predicted by plane-wave theory at the postcritical incidence. It was found that, due to the variation of the length of the parametric array and the variation of the attenuation in the sediment, the maximum of the received sound pressure occurs at the line-of-sight between the projector and the hydrophone. It has been proved both theoretically and experimentally that Snell's law is still valid when the length of the parametric array and the attenuation in the sediment are kept constant. Due to the contribution of the secondary sources close to the boundary, the postcritical penetration of the parametric array can be deeper. The lateral wave should be considered at the postcritical incidence.

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.