Law Of Reflection Research Articles

Flat mirrors, virtual rear-view cameras, and camera-mirror calibration

Flat mirrors are useful to generate virtual cameras and capture a scene from multiple viewpoints. However, the resultant camera-mirror setup is cumbersome to calibrate because of the mirror image reversion. The typical calibration flaws are omitting the checkerboard symmetry and assuming that virtual cameras are front-view. This paper explains the rear-view abstraction and its usefulness in calibrating a camera-mirror setup to obtain the equivalent mirrorless configuration. The underlying theory is reviewed, including camera imaging, the calibration process, and the laws of reflection. The proposed approach is illustrated by calibrating a camera-mirror setup and then using the calibrated camera to generate mirror images synthetically. This work offers a practical insight into calibrating more sophisticated systems such as mirrored camera-projector profilometers.

Investigating the consistency of the shape and flux of X-ray reflection spectra in the hard state with an accretion disk reaching close to the black hole

The observed spectra from black hole (BH) X-ray binaries (XRBs) typically consist of two primary components. A multitemperature blackbody originating from the accretion disk in the soft X-ray, and a power law-like component in the hard X-ray, due to the Comptonization of soft photons by the hot corona. The illumination of the disk by the corona gives rise to another key component known as reflection. A fraction of the incident hard X-ray radiation is naturally absorbed and re-emitted as a blackbody at lower energies and referred to as the ``reprocessed blackbody''. For densities relevant to XRBs and typical ionization values, the reprocessed blackbody may become significant in the soft X-ray region (approximately 0.1-1.0 keV) and should be noticeable in the observed spectra as a consequence of reflection. The absence of any blackbody component in the low/hard state of a BH XRB may not be consistent with the reflection of highly irradiating flux, observed as a power law from an appropriately dense disk of XRB. We focus on the low/hard state of the BH XRB MAXI J1820+070. In contrast to previous works, we simultaneously fit the shape and flux of the reflection spectra. This allowed us to estimate the correct density and ionization of the slab as well as the corresponding reprocessed blackbody. Our fitting of the representative observation of the BH XRB low/hard state suggests that the disk may, in principle, extend very close to the BH, even though the reprocessed thermal emission (due to disk illumination) remains cold (and thus low) enough to be consistent with the data in contrast to the results of a previous study. The inner reflection component is highly ionized and its fit is primarily driven by its contribution to the continuum, rather than by the shape of the relativistic iron line. The reprocessed blackbody cannot help determine whether the disk extends close to the BH or not in the hard state. For this specific observation, the flux in inner reflection component turns out to be quite low with respect to the outer reflection or power law. The outflowing slab corona covering the inner region of the disk could be the plausible geometry of the source, with the underlying disk approaching near to the BH.

Extended transfer matrix method for electron transmission in anisotropic 2D materials: Interplay of strain and (a)periodicity of potentials

We extend the conventional transfer matrix method to include anisotropic features for electron transmission in two-dimensional materials, such as breaking reflection law in pseudo-spin phases and wave vectors, which are not usually considered appropriately in the literature. This method allows us to study transmission properties of anisotropic and stratified electrostatic potential media from a wide range of tunable parameters, which include strain tensor and gating. We apply the extended matrix method to obtain the electron transmission, conductance, and Fano factor for the interplay of a uniaxially strained graphene sheet with external one-dimensional aperiodic potentials. Our results suggest the possibility of visualizing this interplay from conductance measurements.

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

Highly sensitive CH4-TDLAS sensor based on 3D-printed multi-pass cell

In this paper, a highly sensitive methane (CH4) sensor based on tunable diode laser absorption spectroscopy (TDLAS) with 3D-printed multi-pass cell (MPC) is reported. A MPC design model based on ray tracing mathematical method with the law of reflection in vector form was established. The designed MPC has an optical path length (OPL) of 37.8 m and a ratio of optical path length to volume (RLV) of 13.9 cm−2 to enhance the optical absorption. The 3D-printed gas chamber equipped with the MPC and fiber-coupled input greatly simplifies optical alignment. A minimum detection limit (MDL) of the constructed CH4-TDLAS sensor based on fiber-coupled 3D-printed MPC with dense spot pattern was determined to be 30.93 ppb. It can be further improved to 11.79 ppb when the averaging time of the system was 300 s according to the Allan deviation analysis.

Wideband LP to CP Converter Using a Reflectarray Based on Modulated Admittance Surfaces Capable of Wide‐Range Beam‐Scanning for Ku/K Band Applications

AbstractThis study provides the design and demonstration of a Ku/K band horn‐fed linear polarization (LP) to circular polarization (CP) converter using a reflectarray antenna based on the holographic technique and the generalized law of total reflection without any iterative algorithms. The proposed hologram performs wide‐range frequency beam scanning with minimum gain losses and cross‐polarization levels. It comprises 2,500 diagonal slotted octagonal subwavelength metasurfaces with a periodicity of 0.266λ0 = 4 mm at 20 GHz as the center frequency. Two equations are defined to compute Y11 of the proposed unit cell regarding its dimensions for TE(0,0) and TM(0,0) Floquet modes. They significantly simplify the coding procedure and reduce the computational time for synthesizing the hologram. The antenna is simulated using the CST software from 14 to 25 GHz. As a confirmation, a prototype is manufactured and measured at 16, 18, 20, 22, and 24 GHz to verify its performance. The simulated and measured results are well‐matched. The presented hologram achieves 40% 1.8‐dB axial ratio (AR) bandwidth (16–25 GHz), 40% 3.3‐dB gain bandwidth (16–24 GHz), and above 30% 2‐dB gain bandwidth (16–22 GHz). Moreover, the antenna can perform beam scanning from 42° to 24° by changing the frequency from 16 to 24 GHz with peak gain values greater than 20.33 dBi. The LHCP pencil beams are at least 24° off‐broadside, so the proposed hologram avoids the feed blockage. These achievements make the hologram one of the best candidates for satellite communications, radar applications, short‐range communication, and point‐to‐point communication.

Geometric properties of integrable Kepler and Hooke billiards with conic section boundaries

We study the geometry of reflection of a massive point-like particle at conic section boundaries. Thereby the particle is subjected to a central force associated with either a Kepler or Hooke potential. The conic section is assumed to have a focus at the Kepler center, or have its center at the Hookian center respectively. When the particle hits the boundary it is ideally reflected according to the law of reflection. These systems are known to be integrable.We describe the consecutive billiard orbits in terms of their foci. We show that the second foci of these orbits always lie on a circle in the Kepler case. In the Hooke case, we show that the foci of the orbits lie on a Cassini oval. For both systems we analyze the envelope of the directrices of the orbits as well.

Reflective anomalous beam splitter (RABS) metasurface for millimeter-wave (mm-Wave) frequency

Metasurfaces have gained a considerable amount of interest in the past decade for their capabilities to manipulate electromagnetic (EM) waves in different manners. They have offered multiple functionalities in terms of wave control depending on the given application. In terms of wave control, particularly EM beam splitting, it can be challenging compared to the given literature review, to achieve a wide number of beam-splitting reflections and coverage for multiple incident angles simultaneously. In this paper, we focus on the design of a metasurface based on the methodology of high periodicity supercell design (5.76λ) and impedance modulation to achieve a various number of beam-splitting angles, while maintaining the same coverage at multiple incident angles for millimeter-wave (mm-Wave) frequencies. Following the generalized phase law of reflection alongside proper optimization of the surface impedance, the proposed reflective anomalous beam splitter (RABS) metasurface is designed to be polarization independent, and high reflection efficiency is achieved with a wave beam split into 11 different directions while operating for multiple incident angles simultaneously, making it a promising candidate to overcome challenges for various mm-Wave communication applications, especially in expanding 5G coverage in non-line of sight regions at a 28 GHz frequency band. The performance of the RABS metasurface is evaluated using both full-wave simulations and experimental measurements, which demonstrate its effectiveness in achieving 11 efficient reflective anomalous beams with a reflection efficiency of up to 96.65% and 97.36% in TE and TM modes at 28 GHz.

Modelling and simulation for the investigation on the ultrasonic propagation mechanism in advanced microelectronic packages

The miniaturisation, ultra-thinness and high-density multi-layer structure of advanced microelectronic packages complicate the propagation mechanism of ultrasonic waves. In this paper, a finite element model is used to simulate ultrasonic wave propagation in flip chip packages, investigating the laws of transmission and reflection at the lamination boundaries. The acoustic field of ultrasonic transducers is simulated using MATLAB and Abaqus software. The angular spectrum method (ASM) based on the Fourier transform is adopted to more precisely reveal the distribution characteristics and attenuation relationship of near‐field ultrasonic waves. The influence of the frequency and size of the ultrasonic transducer on the propagation characteristics of ultrasonic waves is analysed. Based on an acoustic field map generated by the detection model, the waveform conversions of acoustic waves in a multi-layer structure are analysed. The results show that ultrasonic waves are mainly presented in the form of reflected and transmitted waves at the layered interface and the model with a perfectly matched layer (PML) has higher accuracy. Therefore, this method is applied to ultrasonic testing in a flip chip package, which cannot only effectively exclude interference from boundary reflection but also greatly improve the reliability of waveform conversions analysis.

Angular Deviations, Lateral Displacements, and Transversal Symmetry Breaking: An Analytical Tutorial

The study of a Gaussian laser beam interacting with an optical prism, both through reflection and transmission, provides a technical tool to examine deviations from the optical path as dictated by geometric optics principles. These deviations encompass alterations in the reflection and refraction angles, as predicted by the reflection and Snell laws, along with lateral displacements in the case of total internal reflection. The analysis of the angular distributions of both the reflected and transmitted beams allows us to understand the underlying causes of these deviations and displacements, and it aids in formulating analytic expressions that are capable of characterizing these optical phenomena. The study also extends to the examination of transverse symmetry breaking, which is a phenomenon observed in the laser beam as it traverses the oblique interface of the prism. It is essential to underscore that this analytical overview does not strive to function as an exhaustive literature review of these optical phenomena. Instead, its primary objective is to provide a comprehensive and self-referential treatment, as well as give universal analytical formulas intended to facilitate experimental validations or applications in various technological contexts.

SPECIAL THEORY OF RELATIVITY IS ALSO FAILED TO EXPLAIN NULL RESULT OF MICHELSON AND MORLEY EXPERIMENT

Michelson and Morley conducted an experiment in the year 1887 to measure the speed of earth in luminiferous aether. In this experiment Michelson’s interferometer was used in which two waves are superimposed to generate interference fringes. Keeping in view known velocity of earth around the sun a fringe shift of 0.44 fringe was expected on the rotation of interferometer at an angle of 900, but surprisingly no fringe shift was observed. The experiment was conducted so many times and at so many places but always null results were obtained. The null result of MMX could not be explained by classical mechanics. A number of explanations for null results were submitted but no one was found to be correct. George Fitzerald and Hendrick Lorentz proposed length contraction hypothesis in the direction of motion of earth, but it was also rejected being an adhoc hypothesis. Albert Einstein submitted his famous theory “The special theory of relativity” in the year 1905. The second postulate of the STR states that speed of light is constant in all directions of inertial frames of reference irrespective of motion of source of light or the observer and states that no luminiferous aether exist as a medium, light waves do not require any medium to propagate. As light travels with constant velocity in both the arms of interferometer irrespective of motion of interferometer and there involves no time difference between the two rays hence null results of MMX were explained by special theory of relativity. Michelson and Morley experiment is based on the wave nature of light. In such experiments wavefront of light plays very important role but behaviour of wavefront of light was not taken into consideration while deriving the time taken by the light rays in the arms of interferometer due to motion of earth resulting into wrong derivation of time. The present article describes the principle and realization of role of wavefront of light in MMX. The time taken by light rays in the arms of the interferometer due to motion of earth depends upon the behaviour of wavefront of light. It has been established by results of Fizeau experiment and steller aberration of light that speed of light is not effected by velocity of moving medium. The derivation of time has been worked out keeping in view constancy of speed of light, wavefront of light and laws of reflection of light according to Huygen’s principle. Contrary to earlier beliefs the Lorentz length contraction hypothesis is not able to explain the null results of MMX. In the light of new facts it is established that there is no difference between theorectical results derived by classical mechanics and special theory of relativity. Special theory of relativity is also failed to explain the null result of MMX. The null result of Michelson and Morley experiment has again become a perplexing question for physicists.

Faraday rotation stimulated optical-rotation quasi-phase-matching technique to radiate a highly efficient elliptically polarized second harmonic

Faraday rotation has been employed to ensure efficient frequency conversion in the ultraviolet regime. The reported 36% efficiency of the radiated 372 nm, continuous-wave second harmonic of this paper has been numerically analyzed in the presence of a magnetic field in a thin-film-coated magneto-optic crystal using the total-internal-reflection-based optical-rotation quasi-phase-matching approach, considering the influence of surface roughness, absorption loss, and the nonlinear law of reflection.

Broken Ray Transform for Twisted Geodesics on Surfaces with a Reflecting Obstacle

We prove a uniqueness result for the broken ray transform acting on the sums of functions and 1-forms on surfaces in the presence of an external force and a reflecting obstacle. We assume that the considered twisted geodesic flows have nonpositive curvature. The broken rays are generated from the twisted geodesic flows by the law of reflection on the boundary of a suitably convex obstacle. Our work generalizes recent results for the broken geodesic ray transform on surfaces to more general families of curves including the magnetic flows and Gaussian thermostats.

A layered metastructure based on brewster angle for Janus ultra-wideband tunable directional thermal radiation

In this proposal, we introduce a Janus layered metastructure (JLM) composed of three distinct structures. The first and third structures (S1 and S3) are designed based on Brewster and Bragg reflection laws, which enable the selection of a specific incident angle of electromagnetic waves (EMWs) by adjusting the refractive indices of the materials. By matching the thickness of the dielectric layer to the optical wavelength, S1, and S3 operate across the 30–300 μm band, achieving angle selection (AS) of EMWs in the THz band. The second structure (S2) consists of a single layer of graphene and SiO2 arranged in quasi-periodic sequences, which absorbs EMWs in the THz band and achieves broadband absorption without angle sensitivity. By combining the characteristics of these three structures, we achieve a broadband directional thermal radiation covering the 30–300 μm band. Additionally, the adjustability of the AS of S1 and S3 and the absorption effect of S2 enable Janus ultra-wideband tunable directional thermal radiation at large angles depending on the specific needs.

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.

Towards design of a gradient locally resonant acoustic metasurface for negative reflection

Gradient acoustic metasurfaces are a class of subwavelength metamaterials that provide unprecedented opportunities to control the direction of reflected and refracted waves, including negative angles in accordance with the diffraction theory and generalized law of reflection. This opens new possibilities in designing metasurfaces for many practical applications in wave engineering. In this work, locally resonant acoustic metamaterials are considered as the building units of the metasurface, which owe their favorable properties to local resonances at the microstructural level. Non-trivial reflection angles are realized by introducing suitable phase modulations along the wave path. The required phase shift is achieved through the variation of geometrical and material parameters of the metamaterial unit cells. The negative reflection of ultrasound waves is demonstrated numerically by means of a finite-element analysis of a fluid-metasurface-solid structure. The results of this study provide new insights and detailed guidelines for designing metasurfaces for controllable acoustic wave reflection.

Design of auxiliary viewing mirror for filter centering drum in GD121-AF12 filter assembler

In order to solve the problem of observation blind area on the outer end face of the cigarette groove of the filter centering drum on the GD121—AF12 filter assembler, an auxiliary observation mirror was designed and installed on the inner wall nearby. According to the light reflection law, according to the space position the central position of the mirror , design the mirror surface support parts refer to the available screw holes on the mirror surface center and inner wall, and calculate the relative position and deflection angle of the support parts. Based on the above data, support parts are designed with Pro/E, and parts are made with 3D printer. After the improved equipment is blocked, the manual cleaning time is reduced to 3.2min/time, and the maintenance time is reduced by 67%, which effectively reduces the labor intensity of operators and improves the equipment efficiency.

Numerical Optimization of Metasurface Cells for Acoustic Reflection

Metamaterials and metasurfaces disclosed new degrees of freedom in controlling the acoustic field. Exploiting the generalized Snell law and the generalized law of reflection, the assembly of subwavelength unit cells is able to achieve extraordinary refraction and reflection by means of a controlled phase delay introduced in the field by the treated boundaries. The space-coiling design is one of the most powerful for cells in this metadevice class, providing effective low-thickness metasurfaces. However, space-coiling suffers from a narrow frequency operating range due to the intrinsic connection between the design operating wavelength and the characteristic dimensions of the metasurface. This work defines a procedure based on numerical optimization for designing space-coiling cells for modular acoustic metasurfaces, extending the frequency range in which the metasurface is effective. The set comprises eight different unit cells, each introducing a tailored phase shift in the reflected field that can be arranged to produce the desired acoustic effect. The broadband design is obtained by minimizing the dependency on the operating frequency of phase delay introduced by the cells, keeping the overall thickness below a quarter of the design wavelength. Results are shown for the benchmark problem of a metasurface modifying the reflection angle from a boundary.

Composite phase modulated beam steering controllable reflective metasurface

Terahertz metasurface functional devices as an effective method to control terahertz waves have attracted extensive attention from researchers. In order to enhance the functionality and flexibility of the metasurface and adapt to diverse application scenarios and demands, a beam-steering controllable reflective metasurface is designed by combining the Pancharatnam-Berry phase principle and the phase change material vanadium dioxide in this work. The metasurface unit consists of five layers, they being the top layer that is a metal patterned layer, the third layer that is made of vanadium dioxide and located between the dielectric layers with different thickness, the dielectric layer that is made of polytetrafluoroethylene (PTFE), and the bottom layer that serves as a metal reflective layer. The metasurface units are rotated based on the Pancharatnam-Berry phase principle to obtain four metasurface units with fixed phase differences in between, after which the metasurface units are arranged in two dimensions based on the generalized Snell reflection law to obtain the desired phase-gradient deflected reflection beam. The insulating state-metallic state transition of the vanadium dioxide layer on the metasurface can change the phase gradient of the preset metasurface, thereby realizing the on/off function of deflection. The simulation results show that when the vanadium dioxide is in the insulating state, the phase gradient of the designed metasurface appears, and the metasurface can deflect the vertically incident circularly polarized wave with specific angle anomalies in a operating band of 1.1–2.0 THz; when the vanadium dioxide is in the metallic state, for the same operating band of the same metasurface, the phase gradient of the metasurface disappears, and the metasurface mirror reflects the vertically incident circularly polarized waves, thereby realizing the function switching. This design provides new possibilities for modulating the terahertz reflected beam, which will have potential applications in terahertz wireless communication and radar systems.