Wave Plate Research Articles

Modeling of free vibrations and resonant frequencies of simply-supported submerged horizontal plate.

A theoretical approach was applied to study the vibration of simple-supported submerged horizontal plate. The derived analytical solution was used to determine natural frequencies for a horizontal plate vibrating in fluid. The investigations were conducted for a very wide range of material density and elasticity modulus covering all materials used in engineering practice. Analysis shows that plate vibration frequency decreases with increasing plate width and draft, and decreases with decreasing plate thickness. Moreover, the results show that a substantial effect on vibration of submerged plate has mass of water above plate. The results also show that plate vibration frequency decreases with increasing plate material density and decreases with decreasing elasticity modulus. The dominant factors affecting the vibration of the submerged plate are the plate width, the plate thickness, and elasticity modulus. For moderate and low values of elasticity modulus, vibration frequency is becoming lower than frequency of water waves. This is very important because wave frequencies overlap with the natural plate vibration frequencies, which may lead to resonance and failure of a structure. The problem is that the overlap of plate vibration frequencies and wave frequencies occurs for very wide range of wave and plate parameters. Laboratory experiments confirm theoretical results.

Dual-channel polarization-modulated metasurface

Metasurfaces provide excellent design flexibility, allowing for the creation of versatile integrated designs with significant potential for practical applications. This paper proposes a dual-channel polarization-modulated metasurface, which realizes the modulation of line-polarized light (LP) to circularly polarized light (CP) with opposite rotation. The polarization state of the dual channels can be changed by adjusting the polarization angle of the line-polarized light. Through the reasonable selection of element atoms, the function of the quarter waveplate is combined with the wavefront control of the general metalens, and the spiral phase can be arbitrarily added to the two channels to realize the simultaneous generation of multi-mode vortex beams. This work achieves functional integration on a single-layer metasurface, enabling its application in polarization imaging and other areas. This work achieves functional integration on a single-layer metasurface, enabling its application in polarization imaging and other areas.

Analytical solutions for single and multiple scattering from rib-stiffened plates in water.

The interaction of an acoustic plane wave with a pair of plates connected by periodically spaced stiffeners in water is considered. The rib-stiffened structure is called a "flex-layer" because its low frequency response is dominated by bending stiffness. The quasi-static behavior is equivalent to a homogeneous layer of compressible fluid, which we identify as air for the purposes of comparison. In this way, an air layer is acoustically the same as a pair of thin elastic plates connected by a periodic spacing of ribs. At discrete higher frequencies, the flex-layer exhibits perfect acoustic transmission, the cause of which is identified as fluid-loaded plate waves propagating back and forth between the ribs. Both the low and finite frequency behavior of the flex-layer are fully explained by closed-form solutions for reflection and transmission. The analytical model is extended to two flex-layers in series, introducing new low and high frequency phenomena that are explained in terms of simple lumped parameter models.

Momentum mismatch driven bound states in the continuum and ellipsometric phase singularities

In this paper, we elucidate the formation of bound states in the continuum (BICs) in compound grating waveguide structures from the perspective of momentum mismatch. As the complex lattice reduces to a simple lattice, the excitable guided resonance turns into an unexcitable BIC due to momentum mismatch. Herein, we refer to this state as momentum mismatch driven BIC. Interestingly, as the incidence changes from normal to oblique, the single momentum mismatch driven BIC splits into dual momentum mismatch driven BICs due to the nonzero tangential momentum of the incident light. Distinct from conventional symmetry-protected and accidental BICs, momentum mismatch driven BICs lie in sections of photonic bands. Consequently, factors of momentum mismatch driven quasi-BICs exhibit angular robustness far beyond conventional symmetry-protected and accidental quasi-BICs. Empowered by the momentum mismatch driven BIC, a pair of ellipsometric phase singularities emerge. Enabled by the drastic ellipsometric phase change, ultrasensitive refractive index sensing can be achieved. These results not only provide unique insights into the relation between momentum, BICs, and ellipsometric phase, but also offer a recipe for developing high-performance phase-based optical devices, such as ultrasensitive sensors, wave plates, and spatial light modulators. Published by the American Physical Society 2024

Wavelength continuously tunable and wavelength spacing variable comb filter based on a High-Birefringence fiber loop mirror

We demonstrated an all-fiber comb filter that can continuously tune the wavelength for four switchable wavelength spacings. The comb filter consists of a fiber loop mirror (FLM) that is inserted with three polarization maintaining fibers (PMFs) and three polarization controllers (PCs). The transmission characteristics of the comb filter was theoretically analyzed. The output characteristics of the comb filters shows a dependence of the orientation angles of the PCs. With the angles being optimally set, the comb filter with four different wavelength spacings can be achieved. The wavelength continuously tunable and wavelength spacing variable mechanisms are elaborated. The three PCs are employed to enable the tunable and switchable functions. The two PCs between the PMFs serve as a polarization rotator to align the birefringent axes of the PMFs for varying the wavelength spacing while the PC adjacent to the optical coupler can be used for wavelength tuning function. When the two quarter-waveplates (QWPs) of the PC are optimally set at π/4 and - π/4, the half-waveplate (HWP) acts as a wavelength tuning element, and when the QWPs are set at zero degrees, the HWP serves as an amplitude tuning element. The center wavelength of the comb filter could be linearly tuned with the rotation angle of the HWP, and a π/2 change in the rotation angle leads to a wavelength change in one free-spectral-range (FSR). A π/4 change in the rotation angle could bring the normalized peak transmission from its maximum at 1 to minimum at 0. The proposed tunable technique has been verified by our experimental results. We experimentally demonstrated the comb filters can switch among FSRs of 0.75 nm, 1.01 nm, 1.51 nm, and 3.1 nm with tunable functions.

Acoustic shadow zone of the guided wave in a variable thickness plate

This paper calculates the acoustic shadow zone of the guided wave in a variable thickness plate. The variable thickness plate has a wide range of applications in bridges, ships, etc., and the guided wave is often used for its nondestructive testing. The velocity gradient induced by thickness variations will deflect the guided wave towards lower phase velocities. Both frequency and thickness variation play crucial roles in determining the extent of path bending. In particular, the guided wave can undergo reverse propagation at the non-boundary of the plate. This curved propagation path results in an acoustic shadow zone, inaccessible to direct waves. This article calculates and experimentally verifies the curved propagation path of dispersive guided waves. Experiments show that the degree of propagation path bending increases with the increase of frequency in a certain frequency range. On the path that varies along the thickness, the experiment observes an acoustic shadow zone that accounts for nearly 25% of the total path. Additionally, a practical case study involving a guided wave with a curved path is presented. Consideration of the curved path improves the positioning accuracy, offering insights into damage location in variable thickness plates. This research on the propagation path and acoustic shadow zone contributes to advancing the understanding of guided wave propagation characteristics and enhancing their application in nondestructive testing for variable thickness structures.

Transmission of Lamb wave in a micro-mechanically piezoelectric fiber-reinforced composite plate

The present work addresses the propagation characteristics of Lamb wave in a piezoelectric fiber-reinforced composite material plate. The considered plate is micro-mechanically modeled using the analytical techniques of the Strength of Materials and Rule of Mixtures. Secular equations are deduced for symmetric and antisymmetric modes of Lamb wave by employing suitable boundary conditions. The data of two distinct PFRC materials are taken into account, viz. PZT-5A-epoxy and CdSe-epoxy with different fiber volume fractions to investigate the latent characteristics of Lamb wave propagation. The amplitudes of dilatation and electrical potential of considered material are examined numerically and manifested graphically for both kinds of modes, i.e., symmetric and antisymmetric modes. The obtained graphical results are also compared for both kinds of modes. A comparative study has been carried out to exhibit the concealed characteristics of Lamb wave propagation for various distinct cases of considered structure for both symmetric and antisymmetric modes. The determined analytical results are in well agreement with the results present in the existing literature.

Excitation of Odd Harmonics of SH0 Mode Ultrasonic Guided Waves Using Magnetostriction-Based EMAT: Theoretical Modeling

ABSTRACT Magnetostriction-based electromagnetic acoustic transducer (M-EMAT) is a promising tool for generating fundamental shear-horizontal (SH0) mode guided waves in plate. Though the M-EMAT possesses high-order harmonics excitation ability in nature, its conventional way can only generate a fundamental component of SH0 mode. The analytical modeling was performed in this study to releasing the ability of M-EMAT in generating odd harmonics of SH0 mode. First, the inaccurate conditions of magnetic fields for relative permeability calculation in the existing model are corrected in the proposed model. Second, the error of the existing model in predicting the spectrum of the SH0 mode generated in Nickel plate is estimated. Third, numerical solutions are provided by the improved model to examine the key factors governing the ability of M-EMAT in generating odd harmonics of SH0 mode. The conclusions demonstrated that the intensity ratio (H S /H D ) of static and dynamic magnetic fields is adjusted below 1 and the ability of M-EMAT in generating odd harmonics of SH0 mode can be activated. The normalized amplitude of 3rd harmonics decays exponentially with the increase of H S /H D , which is independent of geometrical parameters of M-EMAT. The improved model can effectively optimize excitation parameters of M-EMAT and generate odd harmonics of SH0 mode in plate.

Topological rainbow trapping of elastic waves in two-dimensional valley phononic crystal plates

Rainbow trapping is a significant strategy for capturing waves of different frequencies at different spatial positions. It offers significant potential for multi-frequency on-chip nanophotonic devices in the era of big data and has attracted much interest recently, and topological rainbow trapping that is immune to disorder has been observed in optics and acoustics. Reported here is the topological rainbow trapping of elastic waves using gradient valley phononic crystal plates (PCPs) with a hexagonal lattice, based on valley edge states that are localized at the boundary between two PCPs with opposite valley topological phases. The gradient valley PCPs are achieved by gradually adjusting the height of the scatterers or the thickness of the PCPs. The topological rainbow trapping of elastic waves is shown by applying vertical vibration to the studied gradient PCPs, which are simple in structure and easily fabricated, providing a good solution for manipulating and trapping elastic waves.

Quarter-Wave Plate Metasurfaces for Generating Multi-Channel Vortex Beams.

Metasurfaces of quarter-wave plate (QWP) meta-atoms have exhibited high flexibility and versatile functionalities in the manipulation of light fields. However, the generation of multi-channel vortex beams with the QWP meta-atom metasurfaces presents a significant challenge. In this study, we propose dielectric metasurfaces composed of QWP meta-atoms to manipulate multi-channel vortex beams. QWP meta-atoms, systematically arranged in concentric circular rings, are designed to introduce the modulations via the propagation phase and geometric phase, leading to the generation of co- and cross-polarized vortex beams in distinct channels. Theoretical investigations and simulations are employed to analyze the modulation process, confirming the capability of QWP meta-atom metasurfaces for generating the multi-channel vortex beams. This study presents prospective advancements for the compact, integrated, and multifunctional nanophotonic platforms, which have potential applications in classical physics and quantum domains.

Anti-reflection coating with mullite and Duroid for large-diameter cryogenic sapphire and alumina optics.

We developed a broadband two-layer anti-reflection (AR) coating for use on a sapphire half-wave plate (HWP) and an alumina infrared (IR) filter for the cosmic microwave background (CMB) polarimetry. Measuring the faint CMB B-mode signals requires maximizing the number of photons reaching the detectors and minimizing spurious polarization due to reflection with an off-axis incident angle. Sapphire and alumina have high refractive indices of 3.1 and are highly reflective without an AR coating. This paper presents the design, fabrication, quality control, and measured performance of an AR coating using thermally sprayed mullite and Duroid 5880LZ. This technology enables large optical elements with diameters of 600mm. We also present a thermography-based nondestructive quality control technique, which is key to assuring good adhesion and preventing delamination when thermal cycling. We demonstrate the average reflectance of about 2.6% (0.9%) for two observing bands centered at 90/150 (220/280) GHz. At room temperature, the average transmittance of a 105mm square test sample at 220/280GHz is 83%, and it will increase to 90% at 100K, attributed to reduced absorption losses. Therefore, our developed layering technique has proved effective for 220/280GHz applications, particularly in addressing dielectric loss concerns. This AR coating technology has been deployed in the cryogenic HWP and IR filters of the Simons Array and the Simons observatory experiments and applies to future experiments such as CMB-S4.

Polarimeter–interferometer diagnostic using terahertz solid-state sources for fluctuation measurements on Keda Torus eXperiment (KTX)

A multi-channel polarimeter–interferometer has been developed on the Keda Torus eXperiment (KTX) for the study of equilibrium dynamics and internal magnetic fluctuations. A three-wave technique based on terahertz solid-state sources (~650 GHz) is applied for simultaneous measurements of electron density and Faraday rotation angle. The output power of the microwave source is 2 mW. Faraday rotation effect using a rotating wave plate is tested with phase noise less than 0.8°, and the density phase noise is less than 0.9°. Measurement of Faraday rotation angle and density for discharges on KTX have demonstrated high sensitivity to internal MHD activities.

Stacked Polarizing Elements for Controlling Parameters of Surface Relief Gratings Written in Photosensitive Materials.

Photosensitive materials are widely used for the direct fabrication of surface relief gratings (SRGs) without the selective etching of the material. It is known that the interferometric approach makes it possible to fabricate SRGs with submicron and even subwavelength periods. However, to change the period of the written SRGs, it is necessary to change the convergence angle, shift a sample, and readjust the interferometric setup. Recently, it was shown that structured laser beams with predetermined, periodically modulated polarization distributions can also be used to fabricate SRGs. A structured laser beam with the desired polarization distribution can be formed with just one polarizing optical element-for example, the so-called depolarizer, a patterned micro-retarder array. The use of such stacked elements makes it possible to directly control the modulation period of the polarization of the generated laser beam. We show that this approach allows one to fabricate SRGs with submicron periods. Moreover, the addition of q-plates, elements effectively used to generate cylindrical vector beams with polarization singularities, allows the efficient formation of fork polarization gratings (FPGs) and the fabrication of higher-order fork-shaped SRGs. Full control of the parameters of the generated FPGs is possible. We demonstrate the formation of FPGs of higher orders (up to 12) by only adding first- and second-order q-plates and half-wave plates to the depolarizers. In this work, we numerically and experimentally study the parameters of various types of SRGs formed using these stacked polarizing elements and show the significant potential of this method for the laser processing of photosensitive materials, which often also serve as polarization sensors.

Measurement of Kerr rotation and ellipticity in magnetic thin films by MOKE magnetometry

When polarized light is incident on a magnetic material, the magneto-optical Kerr effect (MOKE) rotates the polarization and induces ellipticity in the reflected light, which allows the magnetization direction to be probed optically. The Kerr rotation and ellipticity determine the magnitude of the effect and are usually measured using dedicated ellipsometers. Here, we demonstrate a simple method for extracting Kerr rotation and ellipticity in magnetic thin films using a conventional MOKE magnetometer consisting of two polarizers and a quarter waveplate. Using this technique, we report the longitudinal Kerr angle of BiYIG, GdCo, and TbCo. We additionally observe a linear decrease in polar complex Kerr angle magnitude in 3 nm GdCo films as the atomic fraction of Gd is increased.

Terahertz bi-functional polarization converter based on interference mechanism supported by diatomic metasurfaces

Polarization manipulation based on the Jones matrix facilitates the enhancement of light-matter interactions. Recently, arbitrarily tailorable polarization states generated with the assistance of a diatomic metasurface effectively reduce the complexity of the system. Nevertheless, a single polarization switching behavior hinders the application of meta-platforms in cryptographic imaging. Here, we theoretically propose and design a single-layer diatomic all-dielectric metasurface working in the terahertz band, which can efficiently realize bi-functional polarization switching according to the Jones matrix. Such a meta-platform is assembled from two anisotropic silicon pillars with carefully optimized lateral dimensions and in-plane twist angles. Benefiting from the flexible assembly of half-wave plate and quarter-wave plate, the polarization states generated by the constructed metasurfaces in the transmission mode can be arbitrarily tailored. The feasibility of this diatomic metasurface is further validated by a broadband near-field imaging device, paving the way for broader system applications in cryptographic imaging, data storage, and chiral sensing.

Sagnac-interferometer-based multiwavelength SOA fiber laser assisted by an intensity-dependent loss mechanism.

We demonstrate a Sagnac-interferometer-based multiwavelength fiber laser with an intensity-dependent loss (IDL) mechanism in the L-band region using a semiconductor optical amplifier (SOA) as the gain medium. The IDL mechanism flattens and stabilizes the multiwavelength spectrum. We also investigate the effect of rotation angles of polarization controllers (PCs) at different polarization devices on multiwavelength performance. At best settings, 31 lasing lines within 3dB uniformity were generated with an extinction ratio (ER) of 17dB. Adjusting the half-wave plate of PC1 and PC2 from 0° to 90° shifted the multiwavelength output by 0.01nm and 0.072nm, respectively. PC2 adjustment also affects the multiwavelength flatness as compared to PC1. Furthermore, the number of lasing lines and the ER were directly influenced by the SOA current.

Tunable non-reciprocity of elastic waves in one-dimensional magnetoelastic phononic crystal plate with oblique incident angle

In this work, non-reciprocal A0 wave in a one-dimensional (1D) magnetoelastic phononic crystal (PC) plate is observed by adjusting the magnitude of the external static magnetic field and the angle of incidence of the elastic wave. This phenomenon arises from the both breaking of time-reversal and spatial-inversion symmetries. When the angle between the applied in-plane magnetic field and the wave vector direction is greater than 0°, the spin waves exhibit a small non-reciprocity. The non-reciprocal spin waves couples with the elastic wave to form a non-reciprocal bandgap, which is distinct from the asymmetric transmission of elastic waves in non-periodic structures. Our research provides robust way to manipulate the transmission characteristics of A0-Lamb waves and has potential application in the design of diodes in seismic exploration and material testing.

The Simons Observatory: Cryogenic half wave plate rotation mechanism for the small aperture telescopes.

We present the requirements, design, and evaluation of the cryogenic continuously rotating half-wave plate (CHWP) for the Simons Observatory (SO). SO is a cosmic microwave background polarization experiment at Parque Astronómico de Atacama in northern Chile that covers a wide range of angular scales using both small (⌀0.42m) and large (⌀6m) aperture telescopes. In particular, the small aperture telescopes (SATs) focus on large angular scales for primordial B-mode polarization. To this end, the SATs employ a CHWP to modulate the polarization of the incident light at 8Hz, suppressing atmospheric 1/f noise and mitigating systematic uncertainties that would otherwise arise due to the differential response of detectors sensitive to orthogonal polarizations. The CHWP consists of a 505mm diameter achromatic sapphire HWP and a cryogenic rotation mechanism, both of which are cooled down to ∼50K to reduce detector thermal loading. Under normal operation, the HWP is suspended by a superconducting magnetic bearing and rotates with a constant 2Hz frequency, controlled by an electromagnetic synchronous motor. We find that the number of superconductors and the number of magnets that make up the superconducting magnetic bearing are important design parameters, especially for the rotation mechanism's vibration performance. The rotation angle is detected through an angular encoder with a noise level of 0.07 μrad s. During a cooldown process, the rotor is held in place by a grip-and-release mechanism that serves as both an alignment device and a thermal path. In this paper, we provide an overview of the SO SAT CHWP: its requirements, hardware design, and laboratory performance.

The Simons Observatory: Development and Optical Evaluation of Achromatic Half-Wave Plates

The Simons Observatory (SO) experiment is a cosmic microwave background (CMB) experiment located in the Atacama Desert, Chile. The SO’s small aperture telescopes (SATs) consist of three telescopes designed for precise CMB polarimetry at large angular scales. Each SAT uses a cryogenic rotating half-wave plate (HWP) as a polarization modulator to mitigate atmospheric 1/f noise and other systematics. To realize efficient polarization modulation over the observation bands, we fabricated an achromatic HWP (AHWP) consisting of three sapphire plates with anti-reflection coatings. The AHWP is designed to have broadband modulation efficiency and transmittance. This paper reports on the design and the preliminary characterization of the AHWPs for SATs.

Phase-shifting determination and pattern recognition using a modified Sagnac interferometer with multiple reflections.

This work has implemented a diverse modification of the Sagnac interferometer to accommodate various measurement requirements, including phase shifting, pattern recognition, and a morphological analysis. These modifications were introduced to validate the adaptability and versatility of the system. To enable phase shifting using the multiple light reflection technique, a half-wave plate (HWP) was utilized with rotations at 0, π/8, π/4, and 3π/8radians, generating four interference patterns. It is possible to observe a distinct circular fringe width as the polarized light experiences diffraction at the interferometer's output as it travels through a circular aperture with various diameters ranging from 0.4 to 1mm. Further modifications were made to the setup by inserting a pure glass and a fluoride-doped tin oxide (FTO) transparent substrate into the common path. This modification aimed to detect and analyze a horizontal fringe pattern. Subsequently, the FTO substrate was replaced with a bee leg to facilitate morphology recognition. A deep learning-based image processing technique was employed to analyze the bee leg morphology. The experimental results showed that the proposed scheme succeeded in achieving the phase shift, measuring hole diameters with errors smaller than 1.6%, separating distinct transparent crystals, and acquiring the morphological view of a bee's leg. The method also has successfully achieved an accurate surface area and background segmentation with an accuracy over 87%. Overall, the outcomes demonstrated the potential of proposed interferometers for various applications, and the advantages of the optical sensors were highlighted, particularly in microscopic applications.