Linear Phase Research Articles

Synthesizing polarization singularity lattices using phase ramps

In this paper, a novel methodology for generating polarization singularity lattices using ramp phase structures in a polarization interferometer is presented. By applying differential tilts to distinct regions within the wavefront using a spatial light modulator, a phase-discontinuity line separating the two regions is formed. During propagation along this line, phase vortices are formed at discrete points about which the phase difference on either side of the ramp is π. This wavefront with phase vortices is superimposed with a plane wave in orthogonal polarization in a polarization interferometer, giving rise to polarization singularities. A common-path polarization interferometer is constructed using a spatial light modulator to reduce errors and complexity. Polarization fringes instead of intensity fringes obtained in this interferometer host polarization singularities. Lattices made up of a linear chain of polarization singularities—unusually of the same index polarity—are found here. Experimental results corroborate the theoretical predictions. This study shows that singularities can be produced with non-spiral phase plates by using linear phase ramps. The method discussed in this paper may find potential applications in optical trapping and particle steering.

New algorithm on linearization-discretization solving systems of nonlinear integro-differential Fredholm equations

This article deals with a new strategy for solving a certain type of nonlinear integro-differential Fredholm equations with a weakly singular kernel. We build our new algorithm starting with the linearization phase using Newton's iterative process, then with the discretization phase we apply the Kantorovich's projection method. The discretized linear scheme will be approximated by the product integration method in the weak singular terms, and the other regular integrals will be approximated by the Nyström method. The process of convergence of our new algorithm is carried out under certain predefined and necessary conditions. Finally, we give practical examples where, the results show the efficiency of our new algorithm for solving systems of weakly singular nonlinear integro-differential equations.

High reflectivity, ultraflat-spectrum chirped fiber Bragg grating written using low energy UV femtosecond pulses

Chirped fiber Bragg gratings (CFBGs) have been extensively used in applications such as ultrafast lasers, fiber sensors, and fiber communications. This work presents a comprehensive investigation of CFBG written using a 257 nm femtosecond laser and a linear chirped phase mask. The CFBG, written on a hydrogen-loaded polarization-maintaining fiber, exhibited a center wavelength of 1031.7 nm and a bandwidth of 11.97 nm. The CFBG achieved an average reflectivity of 98.2 % within its bandwidth, demonstrating an ultrahigh flatness of the reflection spectrum with a low spectral reflectivity variance of 0.00003 (σ2). The high group velocity dispersion (GVD) of 60.7 ps2 signifies its potential in fiber chirped pulse amplification systems and dispersion compensation system. Meanwhile, the fs-laser + PM writing method shows advantages of high efficiency and low energy consumption (as low as 2 nJ), owing to the high photosensitivity of the fiber to the UV band, which holds significant promise in fiber grating inscription.

Reversible Redox‐Driven Crystallization in a Paracyclophane Monolayer at a Solid–Liquid Interface

AbstractThe development and integration of cyclophanes into future functional materials require a detailed understanding of the physicochemical principles that underlie their properties, phase behavior, and in particular the relationship between structure and function. Here, electrochemically switchable crystallization of a ferrocene‐bearing 3D Janus tecton (M‐Fc) at the interface between highly oriented pyrolytic graphite (HOPG) and an electrolyte solution is demonstrated. The M‐Fc adlayer is successfully visualized under both ambient and electrochemical conditions using scanning tunneling microscopy. Voltammetric measurements show a surface‐confined redox process for the M‐Fc modified surface that drives the phase transition between a visible 2D ordered linear phase (M‐Fc0, with ferrocene in the neutral state) and an invisible gas‐like adsorption layer with high mobility when ferrocene is oxidized, M‐Fc+, and a “square scheme” mechanism explains the data. Analogous experiments in a ferrocene‐free tecton adlayer show no phase transition and confirm that the dynamics in M‐Fc are redox‐driven. On‐surface 3D nanoarchitectures are also demonstrated by forming inclusion complexes between M‐Fc and β‐cyclodextrin and device behavior through electrochemical scanning tunneling spectroscopy (STS). These results showcase the functional potential of this class of cyclophanes, which can find use in actuators, optical crystals, and other smart materials.

Benefits of Zero-Phase or Linear Phase Filters to Design Multiscale Entropy: Theory and Application.

In various applications, multiscale entropy (MSE) is often used as a feature to characterize the complexity of the signals in order to classify them. It consists of estimating the sample entropies (SEs) of the signal under study and its coarse-grained (CG) versions, where the CG process amounts to (1) filtering the signal with an average filter whose order is the scale and (2) decimating the filter output by a factor equal to the scale. In this paper, we propose to derive a new variant of the MSE. Its novelty stands in the way to get the sequences at different scales by avoiding distortions during the decimation step. To this end, a linear-phase or null-phase low-pass filter whose cutoff frequency is well suited to the scale is used. Interpretations on how the MSE behaves and illustrations with a sum of sinusoids, as well as white and pink noises, are given. Then, an application to detect attentional tunneling is presented. It shows the benefit of the new approach in terms of p value when one aims at differentiating the set of MSEs obtained in the attentional tunneling state from the set of MSEs obtained in the nominal state. It should be noted that CG versions can be replaced not only for the MSE but also for other variants.

Titanium/FRP hybrid sandwich: in-plane flexural behaviour of short beam specimens

Adopting novel sandwich structures with FRP (Fibre Reinforced Polymer) skins and a metallic lattice core, both of which have high specific strength and stiffness, is one way to achieve better mechanical performance while remaining lightweight. Flexural stress is a load pattern that frequently occurs in the structural frame components of automobiles; nonetheless, while the in-plane load scheme has scarcely been examined, the out-of-plane load one has. As a result, the former configuration received consideration in this work. Moreover, short beam specimens were taken into account. The mechanical response of specimens with three different kinds of composite materials as skin material was analysed. The skins were made of CFRP (Carbon Fiber Reinforced Polymer), with two different weaving styles, and AFRP (Aramid Fiber Reinforced Polymer). All-titanium specimens were studied, too. Similar maximum loads and maximum displacement at break were recorded for both CFRP and AFRP specimens, while the all-titanium one resulted stronger. In terms of the load-displacement curves, the first section featured an initial linear phase, followed by a minor load drop, likely attributed to the breakage of fibres. The CFRP specimens showed a sharp fracture of the skin fibres, while for the AFRP, a fraying was observed.

Polygonal Laguerre-Gauss beams

We demonstrate that Laguerre-Gauss (LG) beams can have a polygonal distribution with the radial and azimuthal components, the so-called polygonal Laguerre-Gauss beams. These light beams are generated with a linear and trigonometric phase function of the angular coordinate which transform the Perfect LG beams with a lens. The polygonal Laguerre-Gauss beams preserve their distribution within a maximum propagation distance without diffraction similar to that used in the propagation-invariant light fields. We expect that these polygonal Laguerre-Gauss beams will be a method for creating any distribution controlling the radial and azimuthal components; moreover, they can be a proposal to control the number of the ring structures of the light beams.

Extension mechanism of fracturing in liquid nitrogen fractured coal rock dominated by phase change expansion pressure

In this paper, the liquid nitrogen (LN2) fracturing test research using LN2 phase expansion instead of N2 pressurization was carried out in response to the neglected high phase expansion rate characteristic of LN2, an anhydrous fracturing medium. Expansion pressure measurements, infrared temperature measurements, DIC full-field strain measurements and acoustic emission (AE) signal measurements were used as measurement means. The phase change gas expansion pressure, specimen end-face field, internal fracture signal and end-face temperature changes during the fracturing process were explored. The experimental results show that there was a significant difference in the performance of LN2 cold shock damaged specimens and undamaged specimens during fracturing. The change rule of LN2 phase change expansion pressure under no peripheral pressure went through linearly increasing first and then stabilizing, the slope of the linear phase was 0.029 MPa/s, the expansion pressure in the stabilizing phase was 1.2 MPa and lasted for 12s, and then the specimen ruptured. The initiation pressure of the gas fractured specimen was 2.2 MPa. The surface strain of the specimen was significantly increased during the stabilization stage of expansion pressure, and the maximum values of transverse strain and longitudinal strain were 0.059% and 0.071%, respectively, which were increased by 43.9% and 73.2% within 12 s. At the same time, the number of AE localization points increased from 12 to 78, and the location of the localization points gradually expanded from the two sides of the horizontal slot to the top of the horizontal slot and the outer wall of the specimen. There was a low-temperature zone with obvious temperature gradient in the extended area and no such change existed in the gas fractured specimens. Therefore, the fracture initiation pressure of the damaged specimen is lower than that of the undamaged specimen, and the cracks are more likely to expand and become continuous during the fracturing process, thus producing complex cracks. The use of LN2 with high phase change expansion rate can replace the high-pressure pumping of N2, which is of great significance for the reduction of the implementation time and cost of the LN2 fracturing process.

Direct detection Φ-OTDR based on UWFBG array using linear-phase-modulated double-pulse

We propose what we believe to be a novel direct detection phase-sensitive optical time-domain reflectometry (Φ-OTDR) based on ultra-weak fiber Bragg grating (UWFBG) array to achieve distributed vibration measurements with exceptional sensitivity and remarkable stability. Our system employs a pulse modulator to generate a double pulse and achieves linear phase modulation of one pulse by one cycle through a phase modulator. The phase change can be quantitatively demodulated using our proposed N-step phase-shifted demodulation algorithm. This method effectively mitigates the influence of phase noise of the laser and the pulse modulator, while also eliminating fluctuations in the half-voltage of the phase modulator. Compared with the existing phase modulation methods, our method avoids stringent requirements for the stability and precision of phase modulation. Moreover, we propose a phase-shifted approximation method, breaking the limitation of sensing length on the traditional differential approximation method and improving the accuracy significantly. The technique's effectiveness is experimentally demonstrated on a 1 km UWFBG array with a reflectivity of −40 dB to −45 dB and a spatial resolution of 10 m. Vibrations with different amplitudes are measured quantitatively with good linearity. The low-frequency self-noise is greatly suppressed and the overall self-noise is −54.3 dB rad2/Hz.

The Effect of Spatially Varying Collision Frequency on the Development of the Rayleigh–Taylor Instability

The Rayleigh–Taylor (RT) instability is ubiquitously observed, yet has traditionally been studied using ideal fluid models. Collisionality can vary strongly across the fluid interface, and previous work demonstrates the necessity of kinetic models to completely capture dynamics in certain collisional regimes. Where previous kinetic simulations used spatially and temporally constant collision frequency, this work presents five-dimensional (two spatial, three velocity dimensions) continuum-kinetic simulations of the RT instability using a more realistic spatially varying collision frequency. Three cases of collisional variation are explored for two Atwood numbers: low to intermediate, intermediate to high, and low to high. The low-to-intermediate case exhibits no RT instability growth, while the intermediate-to-high case is similar to a fluid-limit kinetic case with interface widening biased toward the lower-collisionality region. A novel contribution of this work is the low-to-high collisionality case that shows significantly altered instability growth through an upward movement of the interface and damped spike growth due to increased free-streaming particle diffusion in the lower region. Contributions to the energy flux from the non-Maxwellian portions of the distribution function are not accessible to fluid models and are greatest in magnitude in the spike and regions of low collisionality. Increasing the Atwood number results in greater RT instability growth and reduced upward interface movement. Deviation of the distribution function from Maxwellian is inversely proportional to collision frequency and concentrated around the fluid interface. The linear phase of RT instability growth is well described by theoretical linear growth rates accounting for viscosity and diffusion.

Investigation of CO2 measurement of ZIF-8-based F–P interferometric optical fiber sensor

In this paper, a set of ZIF-8 (Zeolitic Imidazolate Framework-8)-based Fabry-Perot (F–P) interferometric optical fiber sensor was designed to measure the carbon dioxide gas with different concentrations. The optical path difference of our sensing element was mainly caused by the F–P cavity filled with ZIF-8 instead of gas cavity. We analyzed the operating principle and verified the feasibility of the sensor. We gave the exact relation between the concentration of carbon dioxide and each parameter of the F–P cavity. The experimental results show that the spectrum will be red-shifted with the increase of the adsorption of carbon dioxide by ZIF-8 at a certain concentration of carbon dioxide. In addition, after applying Fourier transform to the spectrum, the frequency spectrum displayed two main peaks which changed to the lager value with the increase of concentration of carbon dioxide. The sensor has linear wavelength and phase sensitivities with the concentration of carbon dioxide under 5 × 104 ppm. Besides, the response time becomes shorter as the concentration of carbon dioxide decreases. To sum up, we presented a fiber optic gas sensor that is both simple to manufacture and has high selectivity, making it an effective method for measuring carbon dioxide.

A dual-stage correction approach for high-precision phase-shifter in Fizeau interferometers

This paper proposes a dual-stage correction approach for a high-accuracy phase-shifter in Fizeau laser interferometers, effectively reducing the phase shift errors in PSI (Phase-Shifting interferometry) and improving the precision of surface profile measurements. The precision of PSI depends on the displacement accuracy of the reference mirror, and the function of the phase shifter is to drive the reference mirror to generate wavelength-level displacements with nanometer-level accuracy. The first-stage correction aims to reduce the nonlinearity error of the reference mirror by ULPS (Ultra-High Linearity Phase Shifter). The second-stage correction aims to reduce the average velocity error and plane velocity uniformity error of the reference mirror by AVIC (Auto Velocity Iterative Correction). The experimental results indicate that, after the first-stage correction, ULPS exhibits a 0.05 % nonlinearity, a 2.5 nm repeatability, and a 0.2 nm resolution under a load of 20 kg, and its nonlinearity surpassing all phase-shifters documented in the literature. After the second-stage correction, the average velocity error and plane velocity uniformity error of the reference mirror are reduced to 0.07 %.

Research on Delamination Damage Quantification Detection of CFRP Bending Plate Based on Lamb Wave Mode Control.

The carbon-fiber-reinforced polymer (CFRP) bending structure is widely used in aviation. The emergence and spread of delamination damage will decrease the safety of in-service bending structures. Lamb waves can effectively identify delamination damage as a high-damage-sensitivity detection tool. For this present study, the signal difference coefficient (SDC) was introduced to quantify delamination damage and evaluate the sensitivity of A0-mode and S0-mode Lamb waves to delamination damage. The simulation results show that compared with the S0-mode Lamb wave, the A0-mode Lamb wave exhibits higher delamination damage sensitivity. The delamination damage can be quantified based on the strong correlation between the SDC and the delamination damage size. The control effect of the linear array PZT phase time-delay method on the Lamb wave mode was investigated by simulation. The phase time-delay method realizes the generation of a single-mode Lamb wave, which can separately excite the A0-mode and S0-mode Lamb wave to identify delamination damage of different sizes. The A0-mode Lamb wave was excited by the developed one-dimensional miniaturized linear comb transducer (LCT), which was used to conduct the detection experiment on the CFRP bending plate with delamination damage sizes of Φ6.0 mm, Φ10.0 mm, and Φ15.0 mm. The experimental results verify the correctness of the simulation. According to the Hermite interpolation results of the finite-element simulation data, the relationship between the delamination damage size and the SDC was fitted by the Gaussian function and Rational function, which can accurately quantify the delamination damage. The absolute error of the delamination damage quantification with Gaussian and Rational fitting expression does not exceed 0.8 mm and 0.7 mm, and the percentage error is not more than 8% and 7%. The detection and signal processing methods employed in the present research are easy to operate and implement, and accurate delamination damage quantification results have been obtained.

Acoustic metasurface development for transmitted wavefront manipulation using a level set-based topology optimization approach

A customized transmission-type metasurface design is developed for high-efficiency wavefront modulation by employing a level set-based topology optimization approach. The metasurface consists of periodically arranged supercells made of discrete unit cells aiming to form a precisely linear phase gradient of the transmitted wave ranging from 0 to 2π with high transmittances. The configuration of each unit is optimized to generate a desired phase and amplitude response of the transmitted wave at the interface. The transmitted wavefront steering realized by the phase-gradient metasurface is numerically and experimentally verified according to the diffraction theory, demonstrating that the level set-based topology optimization approach is a viable and effective technique for developing a transmitted phase-gradient metasurface. Afterwards, the designed optimal unit cells are elaborately arranged to form desired phase shift distributions for realizing fascinating acoustic functionalities, including acoustic energy focusing and acoustic Airy-like beam generation, further demonstrating the ability of the optimal units to achieve unprecedented transmitted wavefront control. This study presents a promising approach for customized transmission-type metasurface design based on the level set-based topology optimization, which is expected to be significantly valuable for acoustic device development.

Self‐equalized linear‐phase microstrip bandpass filter based on negative group delay parallel‐coupled three‐line units

AbstractA self‐equalized linear‐phase microstrip bandpass filter (BPF) utilizing negative group delay (NGD) parallel‐coupled three‐line (PCTL) units is presented in this letter. The NGD PCTL unit possesses an NGD valley in its frequency response of group delay (GD). By a combination of two or more NGD valleys, the sharp positive GD peaks at passband edges of a conventional coupled‐line BPF are counterbalanced, resulting in a linear phase response over the entire passband. A prototype of linear‐phase BPF in S‐band is designed by replacing two coupled‐line units in a three‐pole conventional BPF with the proposed NGD PCTL units. Measured passband GD fluctuation of the BPF utilizing NGD PCTL units is 0.5 ns while that of the BPF using conventional coupled‐line units is 1.7 ns, a considerable improvement of 70.5% is achieved with no increase in overall time delay. The out‐of‐band suppression is well retained, and the circuit size is 0.18 λg2.

Meta‐atom design and communication prototype for wideband reconfigurable intelligent surface

AbstractExisting research on reconfigurable intelligent surfaces (RIS) has mainly focused on narrowband applications due to limitations in programmable metasurfaces and field prototype realization. This letter introduces a wideband RIS meta‐atom consisting of a single‐layer frequency selective surface supported by a dogbone‐shaped patch, ensuring a stable linear phase interval around the resonant frequency. A RIS communication prototype is constructed to evaluate its phase bandwidth upper limit and fundamental bandwidth properties. An equivalent circuit model is derived to predesign the wideband RIS meta‐atom, controlled by a varactor, and experimental validation in an anechoic chamber confirms its large bandwidth. Additionally, a wideband RIS‐assisted self‐contained prototype is demonstrated to illustrate the bandwidth characteristics and link gain enhancement at a system level. Test results indicate a researched bandwidth of up to 19.65%, with the 1‐bit RIS board achieving a 3‐dB gain bandwidth of about 8.62%.

Nonlinear phase estimation based on nonlinear interferometers with coherent and squeezed vacuum light

Nonlinear interferometers, also known as SU(1,1) interferometers, are unconventional interferometers deploying nonlinear elements. Previous studies showed that they can provide better sensitivity than conventional Mach-Zehnder interferometers regarding the linear phase estimation. In this paper, we make use of nonlinear interferometers with coherent and squeezed vacuum states to perform nonlinear phase estimation. We discuss the optimal phase sensitivities in the absence and presence of photon losses. For a lossless environment, the optimal phase sensitivity can reach the Heisenberg limit scaling of 1/N2. Even with an internal lossy rate of 30% or an external lossy rate of 70%, our scheme can still achieve sub-shot-noise-limited phase sensitivity. These results indicate that our scheme is practical due to high sensitivity and strong robustness.

Comparative analysis of digital holographic microscopy and digital lensless holographic microscopy for quantitative phase imaging

This study provides a detailed comparison of two widely used quantitative phase imaging (QPI) techniques: single-shot off-axis digital holographic microscopy (DHM) and digital lensless holographic microscopy (DLHM). The primary aim is to evaluate and contrast critical aspects of their imaging performance, including spatial phase sensitivity, phase measurement accuracy, and spatial lateral resolution. Employing typical configurations for both DHM and DLHM, the study utilizes a customized phase test target featuring linear phase changes introduced by a specially designed linear density attenuation filter. Ground truth data from an atomic force microscope is incorporated to validate the experimental findings. The comparative analysis reveals that DHM and DLHM exhibit nearly identical spatial phase sensitivity, with DHM demonstrating a minimal 3.2% measurement error compared to DLHM's 4% in height measurement accuracy. Notably, DHM achieves a finer spatial lateral resolution down to 3.1 µm, surpassing DLHM's 5.52 µm. While DHM outperforms DLHM in precision and resolution, the latter offers advantages in terms of portability and cost-effectiveness. These findings provide valuable insights for researchers and practitioners, aiding in the informed selection of QPI methods based on specific application requirements.

A Phase Correction Model for Fourier Transform Spectroscopy

In Fourier transform spectroscopy (FTS), the conventional Mertz method is commonly used to correct phase errors of recovered spectra, but it performs poorly in correcting nonlinear phase errors. This paper proposes a phase correlation method–all-pass filter (PCM-APF) model to correct phase errors. In this model, the proposed improved phase correlation method can correct linear phase errors, and all-pass filters are applied to correct the residual nonlinear phase errors. The optimization algorithm for the digital all-pass filters employs an improved algorithm which combines the subtraction-average-based optimizer (SABO) and the golden sine algorithm (Gold-SA). The proposed PCM-APF model demonstrates high correction precision, and the optimization algorithm for the filters converges faster than traditional intelligent optimization algorithms.

COMPARISON OF THE PHENOLIC COMPOUNDS CONTENT AND COMPOSITION IN SYNECHOCYSTIS SP. AND DESERTIFILUM THARENSE

The content and composition of phenolic compounds in Synechocystis sp. PCC 6803 GT-L and Desertifilum tharense were studied for the first time. A spectrophotometric method was used to determine the phenolic compounds content, thin-layer chromatography and UV spectrometry to study their composition. A higher accumulation of these secondary metabolites was found in Synechocystis sp., which was almost twice as high as that in Desertifilum tharense. In both cases, the higher content of phenolic compounds was observed in the linear phase of cyanobacteria growth (3 days). Synechocystis sp. and Desertifilum tharense characterized by the formation of phenolics (4 and 7 compounds, respectively), which contain p-oxybenzoic or p-coumaric acids – the initial stages’metabolites of the phenolic compounds biogenesis.