Law Of Refraction Research Articles

Design of a metalens for beam collimation and angular amplification in optical phased array devices

We present an analytical design for increasing the beam sharpness (collimation) and field of view (FOV) of an optical phased array (OPA) device. In this work, a cylindrical metalens is used for collimation, while a set of metalens, with both concave and convex phase profiles, are incorporated to increase the FOV. Following the generalized vector law of reflection or refraction, the trajectories of the reflected or transmitted rays corresponding to the phase profile of phase gradient metasurfaces/metalens are obtained. Through the ray tracing method, the elliptical beam from the OPA device with a vertical beam (fast axis) width of 21 mm was collimated to a sharp spherical beam of width 1.5 mm by a metalens with a cylindrical phase profile. In addition, the incorporation of angular amplifier metalens with a 64-channel OPA device has shown an increased in FOV by almost threefold i.e., from 15 o to 41.96 o . Our results suggest that the use of metasurfaces/metalens can enhance the quality of output beam and provide significant advantages for compact on-chip integration with OPA devices in solid-state LiDAR applications.

An Economic, Compact Apparatus to Verify the Laws of Reflection and Refraction

An Economic, Compact Apparatus to Verify the Laws of Reflection and Refraction

Time dilation and time reversal with the multiple-wavelengths range-gated active imaging principle

The possibility of realizing time dilation and time reversal of events taking place in a scene by using the multiple-wavelengths range-gated active imaging (WRAI) principle in superimposed style was studied. Both temporal behaviors could be analyzed as a function of time since the WRAI principle allows different positions of the object in the image to be frozen at different moments according to the wavelengths. As the speed of the photons varies in the function of the refraction law of the crossed medium, different media were used to intervene in the time of the events recorded by the camera. Different wavelengths were used to select these media. By increasing the refractive index of the crossed medium as a function of time, the scene events arrived chronologically with an increasing delay compared to the events seen in the open, giving the impression of slowing down time. Similarly, by decreasing the refractive index of the crossed medium as a function of time, the scene events arrived chronologically in the opposite direction compared to the events seen in the open, giving the impression of going back in time. Experimental test results validated the theoretical part and the possibility of observing these different temporal behaviors with the multiple-wavelengths range-gated active imaging principle in superimposed style.

To a dispersion law of an electromagnetic wave in a medium having a double anisotropy

Dispersion relations for a transverse electromagnetic wave in a hypothetical medium having a low crystalline symmetry and double anisotropy are formulated phenomenological based on the general concepts of Maxwell's equations. Formalism for electrical and magnetic ordering of a medium is represented by tensor coefficients of the second rank in a general coordinate system corresponding to an external problem of incidence, reflection and refraction of a transverse wave at the interface. Based on the obtained dispersion law, the Snell law of refraction for the wave vector is displayed, as well as, some special cases for a section of a wave surface and a ray surface in the plane of incidence. Following Fresnel approach as usual, two characteristic types of linear polarization of an electric induction vector of a propagating wave are considered for a wave entering a double anisotropic medium at an arbitrary angle to the interface. Based on a character of a cross-section of a wave surface and of a ray surface for the plane of incidence, the degree of influence of anisotropy on a propagating field is discussed in terms of external/internal conic refraction of ordinary/extraordinary waves in a transparent medium. Following to initially general form of the permittivity ε^ and the magnetic permeability μ^ tensors some particular cases of a more favorable choice of coordinate system are analyzed to decrease a number of non-zero components in mentioned tensors, as well as to decrease in the number of elements in vector relations.

Study on dynamic response characteristics of the scanning angle in a liquid crystal cladding waveguide beam scanner

This paper studies the dynamic response characteristics of the scanning angle in a liquid crystal cladding waveguide beam scanner. Based on liquid crystal dynamic theory, finite element analysis and vectorial refraction law, a dynamic response calculation model of scanning angle is constructed. The simulation results show that the dynamic responses of the scanning angle during the electric field-on and field-off processes are asymmetric, and exhibit “S”-shape and “L”-shape changing trends, respectively. In addition, by comparing with the bulk phase modulation response process of traditional liquid crystal devices, the intrinsic physical reason for the rapid light regulation of the liquid crystal cladding waveguide beam scanner is clarified to be that the liquid crystal close to the core layer has a faster rotation speed during the electric field-off process. Moreover, the liquid crystal cladding waveguide beam scanner is experimentally tested, and the experiment results are in good agreement with theoretical simulations.

Design of a dual hollow beam optical antenna based on a Fresnel lens-conical lens combination

To improve the transmission efficiency of Cassegrain antennas and enable the simultaneous transmission of signals with different wavelengths in the antenna system, this study introduces Fresnel lenses and conical lenses in front of the Cassegrain antenna at the transmitting end. Reflective mirrors and focusing lenses are introduced at the receiving end. A detailed description is provided of the design process for the Fresnel lens, as well as the impact of various parameters on the hollow radius when combined with the conical lens. Based on the laws of vector reflection and refraction, simulations are performed to track the propagation of light through the entire communication system and lens pairs, providing transmission efficiency plots of the antenna system under deflection and off-axis conditions. Taking into account practical factors such as lens chamfer, transmittance, Cassegrain antenna reflectance, and material dispersion, the transmission efficiency of the antenna system at 1550 nm wavelength can still reach 93.45%. The proposed method not only improves the transmission efficiency of Cassegrain antennas, but also enables the transmission of different information through the inner and outer layers of the antenna system.

Noise Reduction System Using Passive Bandpass Noise Filter on Podcast Microphone

The general properties of waves are refraction, reflection, bending (diffraction), interference and polarization. Sound is a form of wave and is in accordance with the law of wave refraction where waves coming from a less dense medium to a denser medium will be refracted closer to the normal line or vice versa. Sound waves easily experience diffraction because sound waves in air have wavelengths of around several centimeters to several meters. Then basically every room, whether you feel it or not, will always have sound. This is inversely proportional to light which has a wavelength of around 500 mm. Therefore, an interference reduction system using a passive bandpass interference filter on the podcast microphone is necessary to reduce interference. Test results carried out by filters used to reduce noise using Passive Band Pass. the waveform is still the original spectrum at 0 Hz – 120 Hz, the original sound conditions and does not cause interference, but interference occurs and filtering Category (Noise %) 10 – 40 low - 98 – 99 high.

Bringing metasurfaces to analytical lens design: stigmatism and specific ray mapping.

We propose a method to design the exact phase profile of at least one metasurface in a stigmatic singlet that can be made to implement a desired ray mapping. Following the generalized vector law of refraction and Fermat's principle, we can obtain exact solutions for the required lens shape and phase profile of a phase gradient metasurface to respect particular ray conditions (e.g., Abbe sine) as if it were a freeform refractive element. To do so, the method requires solving an implicit ordinary differential equation. We present comparisons with Zemax simulations of illustrative designed lenses to confirm the anticipated optical behaviour.

A new method for high-precision starlight refraction indirect horizon-sensing positioning of atmospheric flight vehicles

The starlight refraction indirect horizon-sensing positioning method is a new type of autonomous celestial navigation method with broad application prospects. In view of this method currently being limited to the spacecraft outside the atmosphere, this article derives and establishes a starlight refraction indirect horizon-sensing positioning model between the starlight refraction angle and the flight vehicle’s position inside the atmosphere. Based on this model, a new starlight refraction indirect horizon-sensing positioning method for the flight vehicle inside the atmosphere is proposed. According to the atmospheric refraction law and the spherical atmospheric model, the refracted optical path of starlight entering the atmosphere and reaching the flight vehicle is traced, so as to establish a starlight refraction positioning model that reflects the relationship between the refraction angle and the 3-D position of the flight vehicle inside the atmosphere. Subsequently, by employing star sensors on the flight vehicle to measure the starlight refraction angle, and combining the starlight refraction positioning model that maps the starlight refraction angle and the flight vehicle’s position, a starlight refraction indirect horizon-sensing autonomous celestial positioning method, tailored for the flight within the atmosphere, is proposed. Finally, the effectiveness of the proposed method is verified through ground semi physical experiments, and an analysis is conducted to explore the factors that affect the positioning accuracy of the starlight refraction indirect horizon-sensing positioning method within the atmosphere.

A new procedure for locating free surfaces of complex unconfined seepage problems using fixed meshes

The main challenge in the analysis of unconfined seepage flow is that the position of free surfaces is unknown a priori, which needs to be determined through a series of iterative processes. The numerical manifold method (NMM) is a promising method which uses a dual cover system consisting of both mathematical and physical covers. Compared with those traditional methods, NMM is characterized by meshing convenience, approximation accuracy, and being capable of coping with free boundary value problems. Unlike the traditional NMM where the material interface participates in cutting the mathematical cover while forming the physical cover, the physical patches in this study can contain the material interface. The new weight functions for such physical patches are constructed using the refraction law, followed by the application to the analysis of unconfined seepage flow problems. By comparing with analytical or reference solutions of some classic examples, it is validated that the proposed method can accurately locate the free surface, demonstrating its accuracy and convenience in solving unconfined seepage problems.

Study on dynamic features and traveling wave solutions of perturbed nonlinear Biswas–Milovic equation combining Kudryashov's law of refractive index

This article mainly explores the Biswas–Milovic equation containing Kudryashov's refractive index law and nonlinear perturbation terms. We take the complete discrimination system for polynomial method and the trial equation method to implement qualitative and quantitative studies for the equation. We verify that the Hamiltonian of the dynamic system is conserved and apply the complete discrimination system of polynomial method to give the associated global phase diagrams, which are qualitatively analyzed to illustrate the presence of periodic solutions and solitons. In addition, we gain a classification of all single traveling wave solutions, provide optical wave patterns with specific parameters and validate the above findings.

Visualization of the optical spin Hall effect in out-of-plane refraction

The traditional law of refraction defines the incidence plane as the plane including the incident beam wavevector and the surface normal vector at the interface of two different optical media. The optical spin Hall effect (OSHE) refers to the spin-dependent transverse shift of the refracted beam perpendicular to the incidence plane. In this Letter, we demonstrate that OSHE in out-of-plane refraction can be detected and visualized in the far-field, even at small and normal incidence angles. The extent of spin-dependent photon spatial separation induced by anomalous refraction can be customized by manipulating the 2D additive momentum from the metasurface. Experimental visualization of the OSHE confirms the existence of a new, to the best of our knowledge, plane to describe the OSHE of the refracted beam outside the incidence plane.

Refraction laws for two-dimensional plasmons

Refraction laws for two-dimensional plasmons

Flexural gravity wave interaction with an articulated heterogeneous plate within the paradigm of blocking dynamics

Surface gravity waves interact with the flexural waves to generate the flexural gravity waves whose characteristics are triggered for higher values of lateral compressive stress to generate multiple propagating wave modes. This investigation examines the scattering of obliquely incident flexural gravity waves due to articulation in two semi-infinite heterogeneous floating elastic plates in finite water depth within a blocking dynamics regime. The dispersion curve demonstrates the existence of three propagating wave modes within the blocking limits. The canonical eigenfunction expansion method used for a single propagating mode is generalized to account for multiple propagating wave modes within the limits of blocking periods. The energy relation is established using the conservation of wave energy flux and Snell's law of refraction, which depends upon the angles and amplitude of the scattered waves along with the wave energy transfer rates. The amplitude of scattering coefficients (energy transfer rate) goes beyond the unit, where the corresponding energy transfer rate (scattering coefficients) diminishes for specific wave periods. Subsequently, complete wave reflection occurs for oblique waves beyond a critical angle of incidence for a fixed period and prior to a critical angle of incidence at a higher angle of incidence. Removable discontinuities occur at the blocking and saddle points, while a jump discontinuity appears due to a change in the incident wave mode in the scattering coefficients. Surface plots reveal the irregular pattern of plate deflection for the period within the blocking limits. Linear time-dependent plate displacement is simulated in two and three dimensions.

Chaotic dynamics in refraction galactic billiards

We prove the presence of topological chaos at high internal energies for a new class of mechanical refraction billiards coming from Celestial Mechanics. Given an open and bounded domain with smooth boundary, a central mass generates a Keplerian potential in it, while, in , a harmonic oscillator-type potential acts. At the interface, Snell’s law of refraction holds. The chaoticity result is obtained by imposing progressive assumptions on the domain, arriving to geometric conditions which holds generically in . The workflow starts with the existence of a symbolic dynamics and ends with the proof of topological chaos. Intermediate results will be the analytic non-integrability and the presence of multiple heteroclinic connections between different equilibrium saddle points. This work can be considered as the final step of the investigation carried on in De Blasi and Terracini (2022 Nonlinear Anal. 218 112766; 2023 Discrete Contin. Dyn. Syst. 43 1269–318).

Automatic Alignment Method of Underwater Charging Platform Based on Monocular Vision Recognition

To enhance the crypticity and operational efficiency of unmanned underwater vehicle (UUV) charging, we propose an automatic alignment method for an underwater charging platform based on monocular vision recognition. This method accurately identifies the UUV number and guides the charging stake to smoothly insert into the charging port of the UUV through target recognition. To decode the UUV’s identity information, even in challenging imaging conditions, an encryption encoding method containing redundant information and an ArUco code reconstruction method are proposed. To address the challenge of underwater target location determination, a target location determination method was proposed based on deep learning and the law of refraction. The method can determine the two-dimensional coordinates of the target location underwater using the UUV target spray position. To meet the real-time control requirements and the harsh underwater imaging environment, we proposed a target recognition algorithm to guide the charging platform towards the target direction. The practical underwater alignment experiments demonstrate the method’s strong real-time performance and its adaptability to underwater environments. The final alignment error is approximately 0.5548 mm, meeting the required alignment accuracy and ensuring successful alignment.

Optical axis determination method

To overcome the shortcomings of the existing optical axis determination method’s optical path is a complex, cumbersome operation with difficulty in identifying criteria. According to Huygens’ drawing principle, this paper establishes a mathematical model between incident light and the outgoing distance of o-light and e-light, analyzes the optical system between the incident angle and refraction angle, deduces the relationship between the incident angle and the distance between two beams of light, designs a distinction scheme between o-light and e-light, proposes a distance method to determine the optical axis based on the difference between the two optical mathematical models, and verifies that although e-light does not meet the refraction law in birefringence, its optical path is reversible. The designed optical axis determination method is simpler, easier to operate, and simpler in identifying criteria than the existing optical path. The validity of the analysis is verified by experiments.

Spin-textured neutron beams with orbital angular momentum

We present a rigorous theoretical framework underpinning the technique of spin-echo modulated small-angle neutron scattering (SEMSANS), and show how the technique can be extended in order to generate spin-textured neutron beams with orbital angular momentum (OAM) via birefringent neutron spin-polarization devices known as magnetic Wollaston prisms. Neutron OAM beams are mathematically characterized by a ``cork-screw'' phase singularity ${e}^{i\ensuremath{\ell}\ensuremath{\phi}}$ about the propagation axis where $\ensuremath{\ell}$ is the OAM quantum number. To understand the precise relationship between the emergent OAM state and the variety of spin textures realized by various setups, we have developed a path-integral approach that in the interferometric limit makes a judicious use of magnetic Snell's law. We show that our proposed technique produces a complex two-dimensional pattern of spin-OAM entangled states which may be useful as a probe of quantum magnetic materials. We compare our path-integral approach to the well-known single-path Larmor precession model and present a pedagogical derivation of magnetic Snell's law of refraction for both massive and massless particles based on Maupertuis's action principle.

Detailed derivation of the generalized Snell-Descartes laws from Fermat's principle.

Beginning with Fermat's principle, we provide a detailed derivation of the generalized laws of refraction and reflection for a geometry realizing a metasurface. We first solve the Euler-Lagrange equations for a light ray propagating across the metasurface. The ray-path equation is found analytically, and the results are supported by numerical calculations. We get generalized laws of refraction and reflection that have three main features: (i)They are relevant in gradient-index optics and in geometrical optics; (ii)A collection of rays emerges from the metasurface as a result of multiple reflections inside the metasurface; and (iii)The laws, although derived from Fermat's principle, differ from previously published results.

Variable discrete ordinates method for radiation transfer in concentric spherical variable index media

Radiation heat transfer in participating concentric spherical media with variable refractive index along the radial direction is solved by the variable discrete ordinates method. The radiative properties, including refractive index, are assumed to be constant in each volume element, such that a radiative ray travels along straight line in each volume element, and redirects by passing the interface of volume elements according to Snell's law of refraction, or specularly reflects back into the volume element. The radiative transfer equation in spherical coordinates system is solved for different number and direction of ordinates in each volume element. The performance of the present method is examined for two cases with medium's specified temperature and radiative equilibrium with continuous linear, continuous non-linear, and discontinuous profiles of refractive index. The accuracy of the present method is checked by comparing with benchmark solutions. For the cases where the exact solution is not available, the energy conservation criterion is used to validate the solution method. The effects of radiative properties, such as wall emissivities, optical thickness, single scattering albedo, and anisotropy factor are examined by some example problems.