Tunability for anomalous refraction of flexural wave in a magneto-elastic metasurface by magnetic field and pre-stress

This letter reports the design of a magneto-elastic metasurface composed of arrayed Terfenol-D pillars deposited on a homogeneous Aluminum plate, aiming to realize the tunability of flexural wave anomalous propagation without altering the structure. Considering the magneto-mechanical coupling of magnetostrictive materials, the phase shift and transmission of functional unit can be calculated. The anomalous refraction of incident flexural wave (i.e., negative refraction) can be accomplished by adjusting magnetic field and pre-stress properly, the refraction angle is remarkably affected by magnetic distribution. The proposed metasurface provides a method for flexible tunability of elastic wave in the fields of vibration/noise control.

A simple and comprehensive electromagnetic theory uncovering the complete picture of light transport in birefringent crystals

Birefringence production of light by natural birefringent crystal has long been studied and well understood. Here, we develop a simple and comprehensive rigorous electromagnetic theory that allows one to build up the complete picture about the optics of crystals in a friendly way. This theory not only yields the well-known refraction angle and index of ellipse for birefringence crystal, but also discloses many relevant physical and optical quantities that are rarely studied and less understood. We obtain the reflection and transmission coefficient for amplitude and intensity of light at the crystal surface under a given incident angle and show the electromagnetic field distribution within the crystal. We derive the wavefront and energy flux refraction angle of light and the corresponding phase and ray refractive index. We find big difference between them, where the phase refractive index satisfies the classical index of ellipse and Snell’s law, while the ray refractive index does not. Moreover, we disclose the explicit expressions for the zero-reflection Brewster angle and the critical angle for total internal reflection. For better concept demonstration, we take a weak birefringent crystal of lithium niobate and a strong birefringent crystal tellurium as examples and perform simple theoretical calculations. In addition, we perform experimental measurement upon z-cut lithium niobate plate and find excellent agreement between theory and experiment in regard to the Brewster angle. Our theoretical and experimental results can help to construct a clear and complete picture about light transport characteristics in birefringent crystals, and may greatly facilitate people to find rigorous solution to many light-matter interaction processes happening within birefringent crystals, e.g., nonlinear optical interactions, with electromagnetic theory.

Refraction of Flexural Waves by Ultra-broadband Achromatic Meta-slab with Wavelength-dependent Phase Shifts

Great progress has been made in modulating flexural waves by elastic metasurfaces. Most of the proposed elastic metasurfaces suffer from chromatic aberration, limited in a narrow bandwidth around the designed frequency. In this paper, overcoming the chromatic aberration, an ultra-broadband achromatic meta-slab (UAM) with subunits of gradient thickness is proposed to realize the refraction angle unchanged with the incident frequency. Based on the phase compensation principle, wavelength-dependent phase shifts for the UAM that realize achromaticity are obtained. In order to verify the effectiveness of the theoretical design, the transmitted wavefields are solved according to the phased array theory, and the results correspond with those obtained by the finite element (FE) simulations and experiments, which show that the refraction angle is unchanged for incident frequencies from 2 kHz to 8 kHz. Besides, the UAM is extended into a periodic meta-slab, and multifrequency achromaticity is realized. Our designed meta-slabs overcome the chromatic aberration by simple configurations, which have significance in the applications of vibration control, vibrational energy harvesting, and health monitoring.

All-Dielectric Phase-Gradient Metasurface Performing High-Efficiency Anomalous Transmission in the Near-Infrared Region

We propose and numerically demonstrate a phase-gradient metasurface with high anomalous transmission efficiency and a large anomalous refraction angle that consists of discontinuous regular hexagonal nanorods supported by a silica substrate. The metasurface achieves high anomalous transmission efficiency and a full 2$$\pi$$ π phase shift for the wavelength range of 1400–1600 nm. At a central wavelength of approximately 1529 nm, the total transmission efficiency reaches 96.5%, and the desired anomalous transmission efficiency reaches 96.2%, with an anomalous refraction angle as large as 30.64. With the adjustment of the period and the number of nanorods per periodic interval, the anomalous transmission efficiency exceeds 69.6% for a large anomalous refraction angle of 68.58. The superior performance of the proposed design may pave the way for its application in optical wavefront control devices.

Electromagnetic Wave Scattering from a Moving Medium with Stationary Interface across the Interluminal Regime

This paper extends current knowledge on electromagnetic wave scattering from bounded moving media in several regards. First, it complements the usual dispersion relation of moving media, ω(θk) (θk: phase velocity direction, associated with the wave vector, k), with the equally important impedance relation, η(θS) (θS: group velocity direction, associated with the Poynting vector, S). Second, it explains the interluminal-regime phenomenon of double-downstream wave transmission across a stationary interface between a regular medium and the moving medium, assuming motion perpendicular to the interface, and shows that the related waves are symmetric in terms of the energy refraction angle, while being asymmetric in terms of the phase refraction angle, with one of the waves subject to negative refraction, and shows that the wave impedances of the two transmitted waves are equal. Third, it generalizes the problem to the case where the medium moves obliquely with respect to the interface. Finally, it highlights the connection between this problem and a spacetime modulated medium.

Numerical-analytical method for calculating the refraction of radio waves in a chaotic upper atmosphere

An operational method is proposed for calculating the refraction of decameter radio waves in a randomly-inhomogeneous upper atmosphere. The method is based on the numerical-analytical solution of stochastic equations of geometric optics. An integral expression is obtained for the dispersion of the refraction angle of a radio wave on the atmospheric path using the approximation of the perturbation method. For a quick calculation of the statistical moment of the refraction angle, the integral expression is reduced to an ordinary first-order differential equation. The joint numerical solution of the unperturbed ray equations and the equations for the statistical moment allows doing an operational estimate of beam width of radio waves arriving at the observation point. The results of numerical calculations of the standard deviations of the refraction angles of radio waves on paths of various lengths are presented.

All-dielectric Phase-gradient Metasurface Performing High-efficiency Anomalous Transmission in the Near-infrared Region

We propose and numerically demonstrate a phase-gradient metasurface with high anomalous transmission efficiency and great anomalous refraction angle, which consists of discontinuous regular hexagonal nanorods supported by a quartz substrate. The metasurface achieves high anomalous transmission efficiency and full 2 phase shift for the wavelength range of 1400-1600 nm. At the central wavelength around 1504 nm, the total transmission efficiency reaches 97.9%, and the desired anomalous transmission efficiency is up to 96.1% with an anomalous refraction angle as large as 30.09°. By adjusting the period and the number of nanorods in one unit cell, the anomalous refraction angle can reach 68.03°, and the anomalous transmission efficiency exceeds 60% within a bandwidth of 50 nm. Theresults are more excellent than those of most present phase-gradient metasurface structures. The superior performance of the proposed structure may pave the way for its application in wavefront control optical devices.

Teaching about Waves with Applications in Lenses

The paper examines ways of teaching wave pulses traveling on strings and wave fronts in two dimensional waves. The phenomena examined for pulses are: reflection, transmission and superposition. Two methods of finding the refracted wave fronts, the corresponding rays and the refraction angle are presented. Then the gradual change of the speed of propagation of a wave is presented. In the last part is examined the application of the concept of wave fronts in lenses and Huygens’ method of finding the shape of a perfect lens. The students’ difficulties with connection with all these subjects are presented.

Optimizing the Calibration Error of Refraction Angles in Ultrasonic Angle Beam Testing

Ultrasonic testing is a useful approach for quantifying the flaws in mechanical components. The height of the flaws in ultrasonic angle beam testing is closely related to the calibration value of the probe refraction angle. In order to reduce the calibration error, some ignored data during the traditional calibration process are reanalyzed and fused to determine the refraction angle. Both arithmetical measurement fusion method and weighted measurement fusion method are applied and compared. Monte Carlo simulation is used to estimate the probability distribution of the refraction angle and obtain the optimal refraction angle weights. Experiments were carried out to verify the results of Monte Carlo simulation. The applicability of data fusion on refraction angles is investigated. It was found in the study that the data fused with the refraction angle is helpful for measuring the height of flaws.

Сombined method of determining vertical refraction correction for electronic tacheometry

This article deals with issue of the vertical refraction effect on the results of trigonometric levelling. The possible affecting the results of EDM levelling by refraction is evaluated. A brief review of methods of correcting the refraction influence is executed. The conclusion is drawn that the accuracy capabilities of refraction correction methods lag behind the level of development of geodetic equipment. As a possible solution of the refraction account problem, a combined method is proposed. This way is based on a geodetic model of the atmosphere and complex gradient meteorological and geodetic measurements. The results of these measurements are the data for calculating the model parameters. The combined use of meteorological and geodetic measurements at several levels enables minimizing the volume of additional measurements, provides the determination of the refraction angle with geodetic accuracy. The results of field experiment are presented. They proved the actuality of the algorithm implementing the combined method of vertical refraction correction calculating, and made an opportunity of working out the proposed way methodically.