Refraction Phenomena Research Articles

Simulation of hyperbolic type solitary waves based on velocity parameter for (3 + 1)-dimensional the B-type Kadomtsev–Petviashvili–Boussinesq equation

In this paper, we investigate solutions to the [Formula: see text]-dimensional B-type Kadomtsev–Petviashvili–Boussinesq (B-KPB) equation, which has strong nonlinearity feature by using sub-equation and the modified [Formula: see text]-expansion methods. Using these analytical methods, dark soliton, trigonometric oscillation, singular soliton, algebraic and hyperbolic type oscillating traveling wave solutions are presented. By giving special values to the parameters in the obtained traveling wave solutions, 3D, 2D and contour graphs representing the solitary waves are drawn. The advantages and disadvantages of both analytical methods are presented in comparison with each other. In addition, the changes of the solutions of the B-KPB equation according to the velocity parameter and the refraction phenomenon are supported by simulation. In addition, the solutions of the equation discussed are first discussed in detail, physical interpretations. Secondly, the geometric interpretations of the traveling wave solutions are analyzed and it is shown that the graphs of the solutions correspond to flat hyper-surfaces. It is argued that these hyper-surfaces can be leveled on a hyperplane without distortion.

Selection Optimal Method of Evaporation Duct Model Based on Sensitivity Analysis

Abstract The evaporation duct is an abnormal refractive phenomenon with wide distribution and frequency occurrence at the boundary between the atmosphere and the ocean, which directly affects electromagnetic wave propagation. In recent years, the use of meteorological and hydrological data to predict the evaporation duct height has become an emerging and promising approach. There are some evaporation duct models that have been proposed based on the Monin–Obukhov similarity theory. However, each model adopts different stability functions and roughness length parameterization methods, so the prediction accuracies are different under different environmental conditions. To improve the prediction accuracy of the evaporation duct under different environmental conditions, a model selection optimization method (MSOM) of the evaporation duct model is proposed based on sensitivity analysis. According to the sensitivity of each model to input parameters analyzed by the sensor observation accuracy, curve graph, and Sobol sensitivity, the model input parameters are divided into several intervals. Then the optimization model is selected in different intervals. The model was established using numerical simulation data from local areas in the South China Sea, and its accuracy was verified by the observational data from the offshore observation platform located in the South China Sea. The results show that the MSOM can effectively improve the prediction accuracy of the evaporation duct height. Under unstable conditions, the maximum relative error is reduced by 7.1%, and under stable conditions, the relative error is reduced by 10.7%. Significance Statement The evaporation duct height has a significant effect on marine radar or wireless apparatus applications. To obtain the evaporation duct height, there are some evaporation duct models that have been proposed. However, different evaporation duct models are applicable to different meteorological and hydrological environments. A single model cannot achieve accurate evaporation duct height predictions in all environments. We propose a model selection optimization method of the evaporation duct model based on sensitivity analysis. This method can dynamically select the optimal model according to different meteorological and hydrological environment, and improve the prediction accuracy of the evaporation duct height. Under unstable conditions, the maximum relative error is reduced by 7.1%, and under stable conditions, the relative error is reduced by 10.7%.

Determination of Diffusion Coefficient of Palm Oil in n-Hexane Using Laser Deflection Method and Image Processing

Determination of diffusion coefficient using the Wiener method has shown a high level of agreement with literature in previous studies, particularly for liquids with a mass of less than hundreds of amu and a small molecule-sized order of Angstrom (atomic mass unit). This method involves a laser beam deflection and refraction phenomenon on the inter-diffusion zone of two fluids with different refractive indexes. Palm oil, vegetable oil with a composition and structure that is quite complicated and size relatively large molecule, has abundantly available and has become one of the primary raw materials for biodiesel production and cooking. This study used the method to examine the diffusivity of palm oil in n-hexane, which is still rare and hard to find, so challenging to be studied. A camera is used to catch the trace of a deflected laser beam on a screen after it passes through a diffusion cell in the measurement. This image was then corrected, made grey, and digitized to extract the laser image coordinate data. An averaging window algorithm is used in digitizing. The digitized results are then processed to calculate the diffusion coefficient. Measurements were made three times to test the consistency of the results. Camera and digitizing techniques are used here to speed up and facilitate measurement. The measured value of diffusion coefficient of palm oil in n-hexane is 2.18×10-4 ± 5.05×10-5 cm2/minute. The results showed consistency in measure, i.e., precision with a maximum error range of 10.6%, but not good suitability value with literature data, i.e., accuracy was less than 10%. These results found that the measurement system that applied the laser deflection method and the image processing of averaging window could not measure the diffusion coefficient of large molecules and complexes such as palm oil quite well.

3D DIGITIZATION OF TRANSPARENT AND GLASS SURFACES: STATE OF THE ART AND ANALYSIS OF SOME METHODS

Abstract. In the field of industrial metrology, there is a rising need for 3D information at a very high resolution for micro-measurements and quality control of transparent objects such as glass bottles (beer, wine, cola, cosmetics, etc.). However, such objects are particularly challenging for optical-based 3D reconstruction methods and systems such as photogrammetry, photometric stereo, structured light scanning, laser scanning, typically resulting in poor metrological performances. Indeed, these methods require the surface of the object to diffusely reflect the incoming light, which is not the case with the glass material where refraction and absorption phenomena do not permit their use. Over the years, various methods have been investigated and developed to avoid the coating (or powdering) treatment often used to make transparent objects opaque and diffusely reflecting. Most of the approaches require either some a priori knowledge of the transparent object or assumptions about how light interacts with the surface. This paper provides a general overview of state-of-the-art 3D digitization methods for optically non-cooperative surfaces featuring absorption, scattering, and refraction. The paper reviews research works summarizing them into four categories including shape-from-X, direct ray measurements, hybrid, and learning-based approaches. Moreover, we provided some 3D results to better highlight the advantages and disadvantages of each method in practice when dealing with transparent objects.

Newton’s Theory of Light and Wave-Particle Duality

The long history of the dispute among physicists as to whether matter is composed of particles or waves is reviewed. A turning point came at the dawn of the 20th century in the form of the de Broglie momentum-wavelength and Bohr/Planck energy frequency relations. It was on this basis that Schrödinger developed a quantum mechanical differential equation whose solution came to be known as a wave function. The Born Interpretation of these functions holds that their absolute square constitutes a probability distribution which has been used successfully to make predictions of the properties of the system under discussion. It is pointed out that the phenomenon of light refraction played a key role in the development of both Newton’s corpuscular theory of light and the competing theory of Huygens which looks upon light as consisting exclusively of waves. It is shown that Newton’s failure to predict the decrease in the speed of light as it passes from air into water was not because of his belief in the particle composition of light, but rather because he not did anticipate that the mass of a photon changes upon entering a medium of higher index of refraction n. By assuming that the energy E of light is equal pc/n, where p is the momentum of the photons and c is the speed of light in free space, it is shown that the experimental dependence of the speed the light on its wavelength as it passes through a transparent medium is derived successfully through the use of Hamilton’s Canonical Equations and Newton’s Second Law of Kinetics. It is suggested that the relationship between particles and waves can be understood by noting that the localized properties of matter exhibit themselves in experiments such as the photoelectric effect where attention can be concentrated on the behavior of a single particle. The corresponding wave properties occur when large numbers of particles are observed under exactly similar circumstances, as for example in electron diffraction. ...........

Active multifunctional composite metamaterials with negative effective mass density and negative effective modulus

In this paper, a new composite metamaterial structure with negative effective mass density, negative effective modulus, and an ultralarge Poisson’s ratio is designed for vibration isolation, wave filtering, programmable construction of waveguides and negative refraction. This metamaterial can achieve vibration isolation in different frequency ranges using the shunting circuits. In two-dimensional metamaterial plate, a negative longitudinal modulus can be achieved by designing a model with an ultralarge Poisson’s ratio. This metamaterial can serve as wave filter when both shear and longitudinal waves are presented simultaneously. Wave propagation in the metamaterial can be controlled by switching of the shunting circuits. In this way, waveguides can be created programmatically. The phenomenon of negative refraction is also achieved in this metamaterial. Through control of the shunting circuits, this multifunctional metamaterial can be applied to vibration isolation, wave filtering, programmable waveguide construction, and negative refraction without changing its geometric structure.

Solving ultrasonic ray tracing in parts with multiple material layers through Root-Finding methods

Ultrasonic testing has been used for material analysis and inspection since 1930′s. Nevertheless, the applicability of ultrasonic waves to new complex cases is still growing, thanks to the availability of powerful electronics and software. However, the complication that slows down the deployment of ultrasonic inspection to geometric complex parts and structures arises from the wave refraction phenomenon. A clear understanding of the ultrasound wave propagation, impacted by refractions, is crucial to interpret the data obtained from the inspection of multi-layered/multi-medium test subjects as it is not always possible to assume that mechanical waves travel in straight lines. This work presents suitable approaches for solving the ray-tracing problem in multi-layered structures. Accurate benchmarking shows that the use of the Newton-Raphson root-finding method allows a threefold reduction of the computation time, when compared to the bisection-based root-finding methods. An effective combination of the Newton-Raphson methods with bisection-type iterations is also proposed and discussed. Although the work repeatedly refers to the field of ultrasonic inspection, the presented findings are relevant and applicable to areas beyond material inspection.

Nonlinear Optical Limiting and Radiation Shielding Characteristics of Sm2O3 Doped Cadmium Sodium Lithium Borate Glasses.

Strong nonlinear absorption (NLA), reduced optical limiting (OL) thresholds, and high radiation shielding parameters are required for the effective use of glasses in the laser radiation and nuclear radiation protecting materials. In view of this, the efficacy of Sm2O3 on the nonlinear optical (NLO) and OL properties were ascertained (at 532 nm) along with radiation shielding characteristics. The open and closed aperture Z-scan profiles revealed the presence of positive NLA and nonlinear refraction (NLR) phenomena respectively. OL measurements showed the existence of limiting behavior in the studied glasses. The NLA and NLR coefficients were improved while the OL thresholds were decreased as the doping of Sm2O3 elevated to a higher doping level. These improvements in NLA, NLR coefficients and OL efficiencies were attributed to the non-bridging oxygens and high polarizable Sm3+ ions. The NLA and OL results clearly suggest the high (5 mol %) Sm2O3 doped glass (Sm5CNLB) glass is beneficial to protect the delicate devices and human eye by suppressing the high energy laser light. The theoretical linear attenuation coefficients (LAC) values of the presented SmxCNLB glasses were obtained with the help of Phy-X software between 0.284 and 1.333 MeV. At 0.284 MeV, the maximum values occur and take values between 0.302 (for Sm0CNLB) and 0.409 cm−1 (for Sm5CNLB). We found that the LAC for the presented SmxCNLB glasses is a function of Sm2O3 content, where the LAC tends to increase, corresponding to the high probabilities of interaction, as the content of Sm2O3 changes from 0 to 5 mol %. The effective atomic number (Zeff) for the presented SmxCNLB glasses was examined between 0.284 and 1.333 MeV. As the amount of Sm2O3 is added, the Zeff increases, and this was observed at any energy.

Refraction of space-time wave packets in a dispersive medium.

Space-time (ST) wave packets are a class of pulsed optical beams whose spatiotemporal spectral structure results in propagation invariance, tunable group velocity, and anomalous refractive phenomena. Here, we investigate the refraction of ST wave packets normally incident onto a planar interface between two dispersive, homogeneous, isotropic media. We formulate a new, to the best of our knowledge, refractive invariant for ST wave packets in this configuration, from which we obtain a law of refraction that determines the change in their group velocity across the interface. We verify this new refraction law in ZnSe and CdSe, both of which manifest large chromatic dispersion at near-infrared frequencies in the vicinity of their band edges. ST wave packets can thus be utilized in nonlinear optics for bridging large group-velocity mismatches in highly dispersive scenarios.

Analysis of Methods for Determining Shallow Waterbody Depths Based on Images Taken by Unmanned Aerial Vehicles.

Hydrographic surveys enable the acquisition and processing of bathymetric data, which after being plotted onto nautical charts, can help to ensure safety of navigation, monitor changes in the coastal zone, and assess hydro-engineering structure conditions. This study involves the measurement of waterbody depth, identification of the seabed shape and geomorphology, the coastline course, and the location of underwater obstacles. Hydroacoustic systems mounted on vessels are commonly used in bathymetric measurements. However, there is also an increasing use of Unmanned Aerial Vehicles (UAV) that can employ sensors such as LiDAR (Light Detection And Ranging) or cameras previously not applied in hydrography. Current systems based on photogrammetric and remote sensing methods enable the determination of shallow waterbody depth with no human intervention and, thus, significantly reduce the duration of measurements, especially when surveying large waterbodies. The aim of this publication is to present and compare methods for determining shallow waterbody depths based on an analysis of images taken by UAVs. The perspective demonstrates that photogrammetric techniques based on the SfM (Structure-from-Motion) and MVS (Multi-View Stereo) method allow high accuracies of depth measurements to be obtained. Errors due to the phenomenon of water-wave refraction remain the main limitation of these techniques. It was also proven that image processing based on the SfM-MVS method can be effectively combined with other measurement methods that enable the experimental determination of the parameters of signal propagation in water. The publication also points out that the Lyzenga, Satellite-Derived Bathymetry (SDB), and Stumpf methods allow satisfactory depth measurement results to be obtained. However, they require further testing, as do methods using the optical wave propagation properties.

The absolute photonic band gaps and all-angle negative refraction phenomenon of two-dimensional photonic crystals composed of multi-ring scatterers

A new novel of scatterers which is in the form of a multi-ring shape is proposed in this paper. The circular scatterers in the two-dimensional (2D) photonic crystals (PCs) have been replaced by the multi-ring ones based on the honeycomb and Kagomé lattices, and the effects of the number of layers (N), the refractive index (n), and the ring width (W) for the multi-ring scatterers on the photonic band gaps (PBGs) are also researched. After that, the relative properties of the absolute PBGs and all-angle negative refraction (AANR) phenomenon in two different types of inserted scatterers have been probed into. The band structure diagrams of those two lattices and equifrequency contours (EFCs) for two different inserted scatterers are acquired through the plane wave expansion (PWE) method. Through comparison, it is qualified for being figured out that, if the scatterer structure is varied from circular rode to multi-ring one, the bandwidths of some absolute PBGs can be expanded or the number of absolute PBGs can be added. Then, through the diagrams of EFCs and the band structures, the phenomenon that the AANR range shrank after the change has been discovered, and verify it by calculation.

Three-dimensional coupled-mode model and characteristics of low-frequency sound propagation in ocean waveguide with seamount topography

Large-scale topography, such as a seamount, substantially impacts low-frequency sound propagation in an ocean waveguide, limiting the application of low-frequency acoustic detecting techniques. A three-dimensional (3D) coupled-mode model is developed to calculate the acoustic field in an ocean waveguide with seamount topography and analyze the 3D effect. In this model, a correction is introduced in the bottom boundary, theoretically making the acoustic field satisfy the energy conservation. Furthermore, a large azimuth angle calculation range is obtained by using the operator theory and higher-order Padé approximation. Additionally, the model has advantages related to the coupling mode and parabolic equation theory. The couplings corresponding to the effects of range-dependent environment are fully considered, and the numerical implementation is kept feasible. After verifying the accuracy and reliability of the model, low-frequency sound propagation characteristics in the seamount environment are analyzed. The results indicate lateral variability in bathymetry can lead to out-of-plane effects such as the horizontal refraction phenomenon, while the coupling effect tends to restore the abnormal sound field and produces acoustic field diffraction behind the seamount. This model effectively considers the effects of the horizontal refraction and coupling, which are proportional to the scale of the seamount.

All-angle total reflection and negative refraction realized with uniaxial hyperbolic materials by manipulating the orientation of the optic axis

Uniaxial hyperbolic materials possess some distinctive electromagnetic properties and thus have received extensive investigations. However, unique reflection and refraction phenomena related to uniaxial hyperbolic materials in hyperbolic bands have not been investigated thoroughly. In this paper, we theoretically and numerically studied the reflection and refraction of a natural hyperbolic material calcite with in-plane anisotropy. Our results show that when the optic axis (OA) of the material is parallel or perpendicular to the incidence plane, all-angle total reflection (ATR) can happen in both Types Ⅰ and Ⅱ hyperbolic bands, while all-angle negative refraction (ANR) can appear only in Type Ⅱ hyperbolic band. Based on the findings, we proposed novel design of fibers and filters. Our findings may extend the understanding of reflection and refraction involved with uniaxial hyperbolic materials and offer new theoretical guidance for design of optical devices.

Electromagnetic Signal Modulation by Chromatic Dispersion in Phase Gradient Metasurface

Chromatic dispersion in phase gradient metasurface and its impact on the scattered electromagnetic signals are studied in this paper. Due to its intrinsic material dispersion and special spatial arrangement of unit cells, phase gradient metasurface possesses large chromatic dispersion for the scattering waves, resulting in anomalous reflection and refraction phenomena. Moreover, from the perspective of signal domain, the scattered waves no longer carry the whole information of the incident wave especially for the wideband ones, because different frequencies are scattered in different directions due to the large chromatic dispersion. This progress is equivalent to a signal modulation in each scattering direction. Here we proposed a simple calculation method to achieve the direction-related spectral response characteristic for a given metasurface using 2D Fourier transform of the 2D phase pattern. Furthermore, a typical wideband radar signal was adopted to give a visualized display of the modulation effect. The simulated results showed that the scattered signals were greatly distorted, causing the correlation reduction and range deviation in radar detection. This work opens a new possibility for metasurface to manipulate the signal characteristic of electromagnetic waves and may prompt new applications in antennas, communication and radar systems.

The Sinking of the R.M.S. Titanic: A Case Study in Thermal Inversion and Atmospheric Refraction Phenomena

On April 14, 1912, the British passenger liner R.M.S. Titanic struck an iceberg. The ship sank in a fraction of the time designers had estimated following a worst case scenario. The purpose of this article is to examine the atmospheric refractive phenomena that might have played a significant role in obscuring the iceberg from Titanic’s two lookouts. We describe a way in which these phenomena can easily and inexpensively be brought to students in our introductory physics classrooms.

Facet-Based Hybrid Method for Electromagnetic Scattering From Shallow Water Waves Modulated by Submarine Topography

This article presents a mechanism model of synthetic aperture radar (SAR) remote sensing imaging of submarine topography in shallow areas. According to the shallow water effect and complex geographical factors, a 3-D geometric model of multiscale wave is generated by combining sea spectrum separation and phase superposition methods. It has the advantage of reflecting the random fluctuation characteristics of waves and the refraction phenomenon influenced by submarine topography. In addition, the modulation relationship among submarine topography, tidal current, and sea surface microroughness is established. This constitutes hydrodynamic modulation. The facet-based hybrid method that combines the geometry optics (GO) and the integral equation method (IEM) is adopted to solve the electromagnetic (EM) scattering of super electrically large sea surface. This contains tilt modulation. The effectiveness of the proposed model is demonstrated through the comparisons with the measured results. The influence of the parameters of radar, sea state, water depth, and tidal current direction on the scattering intensity of sea surface is studied as well. It is revealed that the shallower the water depth, the more significant the hydrodynamic and tilt effect. In addition, the velocity bunching (VB) modulation is a special modulation method in SAR imaging. According to the simulated results, the contributions of tilt, hydrodynamic, and VB modulation in SAR imaging mechanism are compared. The VB is the main factor, hydrodynamic is second, and tilt is the least.

Refraction of electromagnetic waves in pseudo-passive media

The problem of reflection and refraction of a plane monochromatic wave is considered in the most general formulation for a flat interface of two isotropic pseudo-passive media using the vector covariant approach of F.I. Fedorov. The generalized Fresnel coefficients for the perpendicular and parallel polarizations turn out to be complex values, except for cases when the phase difference of the permeabilities of the two media is zero or 180 degrees. The critical Brewster angles also turn out to be complex quantities. The phenomenon of total reflection, in contrast to passive transparent media, is not realized in pseudo-passive media. The energy coefficients of reflection and transmission are calculated and analyzed. Restrictions imposed on the values of the material parameters of the problem are indicated, which should be taken into account when studying refractive wave phenomena involving pseudo-passive metamaterials.

A Hybrid Parallel Numerical Model for Wave-Induced Free-Surface Flow

An advanced numerical model is presented for the simulation of wave-induced free-surface flow, utilizing an efficient hybrid parallel implementation. The model is based on the solution of the Navier–Stokes equations using large-eddy simulation of large-scale coastal free-surface flows. The three-dimensional immersed boundary method was used for the enforcement of the no-slip boundary condition on the bed surface. The water-air interface was tracked using the level-set method. The numerical model was effectively validated against laboratory measurements involving wave propagation over a flatbed with an elliptical shoal, whose presence induces combined wave refraction and diffraction phenomena. The parallel implementation of the model enabled the efficient simulation of depth-resolved, wave-induced, three-dimensional, free-surface flow; the model parallel efficiency and strong scaling are quantitatively demonstrated.

Refraction of space-time wave packets: II. experiments at normal incidence.

The refraction of space-time (ST) wave packets offers many fascinating surprises with respect to conventional pulsed beams. In the first paper in this sequence [J. Opt. Soc. Am. A38, 1409 (2021)10.1364/JOSAA.430105], we theoretically described the refraction of all families of ST wave packets at normal and oblique incidence at a planar interface between two nondispersive, homogeneous, isotropic dielectrics. Here, in this second paper in the sequence, we present experimental verification of the refractive phenomena predicted for baseband ST wave packets upon normal incidence on a planar interface. Specifically, we observe group velocity invariance, normal and anomalous refraction, and group velocity inversion leading to group delay cancellation. These phenomena are verified in a set of optical materials with refractive indices ranging from 1.38 to 1.76, including MgF2, fused silica, BK7 glass, and sapphire. We also provide a geometrical representation of the physics associated with anomalous refraction in terms of the dynamics of the spectral support domain for ST wave packets on the surface of the light cone.

Refraction of space-time wave packets: III. experiments at oblique incidence.

The refraction of space-time (ST) wave packets at planar interfaces between non-dispersive, homogeneous, isotropic dielectrics exhibits fascinating phenomena, even at normal incidence. Examples of such refractive phenomena include group-velocity invariance across the interface, anomalous refraction, and group-velocity inversion. Crucial differences emerge at oblique incidence with respect to the results established at normal incidence. For example, the group velocity of the refracted ST wave packet can be tuned simply by changing the angle of incidence. In the third paper, we present experimental verification of the refractive phenomena exhibited by ST wave packets at oblique incidence that were in the first paper of this sequence [J. Opt. Soc. Am. A38, 1409 (2021)10.1364/JOSAA.430105]. We also examine a proposal for "blind synchronization," whereby identical ST wave packets arrive simultaneously at different receivers without a priori knowledge of their locations except that they are all located at the same depth beyond an interface between two media. A first proof-of-principle experimental demonstration of this effect is provided.