Variation Of Phase Difference Research Articles

Anisotropic Sensing Performance in a High-Sensitivity Surface Plasmon Resonance Sensor Based on Few-Layer Black Phosphorus.

Few-layer black phosphorus (FLBP) is a highly promising material for high sensitivity label-free surface plasmon resonance (SPR) sensors due to its exceptional electrical, optical, and mechanical properties. FLBP exhibits inherent anisotropy with different refractive indices along its two main crystal orientations, the zigzag and armchair axes. However, this anisotropic property is often overlooked in FLBP-based sensors. In this study, we conducted a comprehensive investigation of the SPR reflectivity and phase in a BK7-Ag-FLBP structure to understand the influence of the stacking sequence and the number of FLBP layers on the sensing performance. Clear resonant angle shifts caused by different stacking sequences of FLBP could be observed both theoretically and experimentally. In the theoretical study, the highest reflective and phase sensitivities were achieved with a 12-layer black phosphorus (BP) structure. The reflectivity sensitivity reached 287.9°/refractive index units (RIU) with the zz stacking 12-layer BP film exhibiting a sensitivity 76°/RIU higher than the ac stacking structure. Similarly, the phase sensitivity reached 1162°/RIU with the zz stacking 12-layer BP structure showing a sensitivity 276.9°/RIU higher than the ac stacking structure. The electric field distribution of the 12-layer BP structure with four different stacking sequences has also been analyzed. In the experiment study, the well-known Attenuated Total Reflection (ATR) θ-2θ SPR setup is utilized to detect the reflectivity and phase of BK7-Ag-FLBP structures. The FLBP samples with the same thickness but different stacking sequences show significant resonant angle shift (0.275°) and maximum phase difference variation (34.6°). The FLBP sample thickness and crystal orientations have been demonstrated using the angular-resolved polarized Raman spectroscopy (ARPRS). These theoretical and experimental results provide strong evidence that the stacking sequences of FLBP have a significant impact on the sensing performance of SPR sensors. By harnessing the anisotropic properties of materials like FLBP, novel structures of anisotropic-2D material-based SPR sensors could open up exciting possibilities for innovative applications.

Three-Dimensional Nano-displacement Measurement by Four-Beam Laser Interferometry

A 3D nano-displacement measurement method, where the difference in phase between the beams in a four-beam laser interference is changed, is proposed. Simulation results demonstrate that the variation of phase difference causes the deviation of the interference pattern in the laser interference system. Based on this theory, we design and build a four-beam laser interference system. The corner cube prism in the optical path is shifted, and the phase of the beam is changed by applying different voltages to a piezoelectric stage. The phase difference is obtained by analyzing the lattice pattern with subpixel precision, and then the displacement is determined by correlation operation. The experimental measurement results are consistent with the theoretical analysis, thereby verifying the feasibility of this measurement method.

Manipulating the Generation of Photonic Moiré Lattices Using Plasmonic Metasurfaces.

The generation of moiré lattices by superimposing two identical sublattices at a specific twist angle has garnered significant attention owing to its potential applications, ranging from two-dimensional materials to manipulating light propagation. While macroscale moiré lattices have been widely studied, further developments in manipulating moiré lattices at the subwavelength scale would be crucial for miniaturizing and integrating platforms. Here, we propose a plasmonic metasurface design consisting of rotated nanoslits arranged within N + N' round apertures for generating focused moiré lattices. By introducing a spin-dependent geometric phase through the rotated nanoslits, an overall lens and spiral phase can be achieved, allowing each individual set of round apertures to generate a periodic lattice in the focal plane. Superimposing two sets of N and N' apertures at specific twist angles and varying phase differences allows for the superposition of two sublattices with different periods, leading to the formation of diverse moiré patterns. Our simulations and theoretical results demonstrate the feasibility of our proposed metasurface design. Due to their compactness and tunability, the utilization of metasurfaces in creating nanoscale photonic moiré lattices is anticipated to find extensive applications in integrated and on-chip optical systems.

Controlling the time shape of terahertz pulses from two-color plasma by combining wavelength dispersion and laser chirp

Using a two-color plasma in air or gas allows for the generation of ultra-broadband and highly intense terahertz (THz) pulses. Precisely controlling the shape of THz pulses, particularly the carrier envelope phase, is crucial for a wide range of technological and scientific applications. Recent research has revealed that the phase difference between the fundamental laser wave and its second harmonic influences the shape of the emitted THz pulse. However, the combined impact of laser chirp and the air-dispersion-induced phase difference between the two colors has not been explored in detail. This study aims to fill this gap. The results show that both of these factors have a significant impact on the THz waveform and emitted pulse energy. Positive and negative chirps lead to distinct effects on the pulse shape. A positively chirped pump laser produces a THz waveform with a negative monopolar shape, while a negatively chirped pump laser results in a positive THz pulse shape. Additionally, our findings indicate that the relationship between THz pulse energy and chirp changes with variations in the specific phase difference between the first and second harmonics. These results underscore the importance of carefully tuning both parameters to achieve maximum generation efficiency for a given waveform.

A 3.58 nJ/Node Dual Cross Correlation Analog-Front-End Circuit With ADC for Mutual Capacitive Panel

This article presents a dual cross correlation analog-front-end (DCC-AFE) circuit for a mutual capacitive panel. The DCC-AFE circuit solves the problem of reduced recognition ability owing to the phase difference variation between the transmitted and received signals for a large load panel. A sparse collection algorithm is adopted to reduce the number of analog-to-digital converter (ADC) collections and microcontroller unit (MCU) operations in the proposed touch system. Only a 12-bit successive-approximation-register voltage-controlled-oscillator (SAR-VCO) ADC could meet the requirement. Based on this algorithm, both the power consumption and die area of the proposed analog-front-end (AFE) are significantly reduced. Moreover, we propose a calibration algorithm to improve the accuracy of the ADC. The proposed state-of-art touch integrated circuit (IC) was fabricated via a 110 nm CMOS process. The proposed AFE achieves 46.1 and 50.2 dB signal-to-noise ratio (SNR) with 384 and 128 Hz frame rates, respectively. The active area of the 64-channel AFE with ADC on the chip is 0.988 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{2}$</tex-math> </inline-formula> , which only occupies a small area. The touch IC has an energy consumption of 3.58 nJ/node.

Robustness and stability of doubly periodic patterns of the focusing nonlinear Schrödinger equation.

The nonlinear Schrödinger equation possesses doubly periodic solutions expressible in terms of the Jacobi elliptic functions. Such solutions can be realized through doubly periodic patterns observed in experiments in fluid mechanics and optics. Stability and robustness of these doubly periodic wave profiles in the focusing regime are studied computationally by using two approaches. First, linear stability is considered by Floquet theory. Growth will occur if the eigenvalues of the monodromy matrix are of a modulus larger than unity. This is verified by numerical simulations with input patterns of different periods. Initial patterns associated with larger eigenvalues will disintegrate faster due to instability. Second, formation of these doubly periodic patterns from a tranquil background is scrutinized. Doubly periodic profiles are generated by perturbing a continuous wave with one Fourier mode, with or without the additional presence of random noise. Effects of varying phase difference, perturbation amplitude, and randomness are studied. Varying the phase angle has a dramatic influence. Periodic patterns will only emerge if the perturbation amplitude is not too weak. The growth of higher-order harmonics, as well as the formation of breathers and repeating patterns, serve as a manifestation of the classical problem of Fermi-Pasta-Ulam-Tsingou recurrence.

Eigenwave analysis of vortex-induced vibrations on long cylinders in sheared flows

The vortex-induced vibration of long cylinders in sheared flows is usually a mixture of standing and traveling waves. Understanding how the waveform is developed is of significant scientific and engineering interest. However, the interference between the traveling wave components makes the response patterns hard to interpret. Therefore, a spatial–temporal domain decomposition may offer a new perspective for the problem. This paper presents an eigenwave analysis method based on two-dimensional singular value decomposition, aiming to discover the hidden spatial–temporal modes. The application to experimental data shows its capability to separate the traveling and standing wave components, revealing the alternating dominance of these two waveforms along the span. It can also decompose the motion into two intrinsic traveling waves propagating in opposite directions, evolving and interacting in space and time. Based on the amplitude profiles of these waves, we locate the power-in/out regions and evaluate the lock-in range of reduced velocity as 4.73 to 7.68. It also reveals that the varying phase difference between multi-frequency modes, instead of the mode transition, is the main reason for the envelope fluctuation. The findings suggest that the proposed method is a useful data-driven technique extending the current toolkit for research on related topics.

Hybrid metasurface using graphene/graphitic carbon nitride heterojunctions for ultrasensitive terahertz biosensors with tunable energy band structure

Integrating novel materials is critical for the ultrasensitive, multi-dimensional detection of biomolecules in the terahertz (THz) range. Few studies on THz biosensors have used semiconductive active layers with tunable energy band structures. In this study, we demonstrate three THz biosensors for detecting casein molecules based on the hybridization of the metasurface with graphitic carbon nitride, graphene, and heterojunction. We achieved low-concentration detection of casein molecules with a 3.54 ng/mL limit and multi-dimensional sensing by observing three degrees of variations (frequency shift, transmission difference, and phase difference). The favorable effect of casein on the conductivity of the semiconductive active layer can be used to explain the internal sensing mechanism. The incorporation of protein molecules changes the carrier concentration on the surface of the semiconductor active layer via the electrostatic doping effect as the concentration of positively charged casein grows, which alters the energy band structure and the conductivity of the active layer. The measured results indicate that any casein concentration can be distinguished directly by observing variations in resonance frequency, transmission value, and phase difference. With the heterojunction, the biosensor showed the highest response to the protein among the three biosensors. The Silvaco Atlas package was used to simulate the three samples’ energy band structure and carrier transport to demonstrate the benefits of the heterojunction for the sensor. The simulation results validated our proposed theoretical mechanism model. Our proposed biosensors could provide a novel approach for THz metasurface-based ultrasensitive biosensing technologies.

Generation of Circularly Polarized High Harmonics with Identical Helicity in Two-Dimensional Materials

Generation of circularly polarized high harmonics with the same helicity to all orders is indispensable for chiral-sensitive spectroscopy with attosecond temporal resolution. Solid-state samples have added a valuable asset in controlling the polarization of emitted harmonics. However, maintaining the identical helicity of the emitted harmonics to all orders is a daunting task. In this work, we demonstrate a robust recipe for efficient generation of circularly polarized harmonics with the same helicity. For this purpose, a nontrivial tailored driving field, consisting of two co-rotating laser pulses with frequencies $\ensuremath{\omega}$ and $2\ensuremath{\omega}$, is utilized to generate harmonics from graphene. The Lissajous figure of the total driving pulse exhibits an absence of rotational symmetry, which imposes no constraint on the helicity of the emitted harmonics. Our approach to generating circularly polarized harmonics with the same helicity is robust against various perturbations in the setup, such as variation in the subcycle phase difference or the intensity ratio of the $\ensuremath{\omega}$ and $2\ensuremath{\omega}$ pulses, as rotational symmetry of the total driving pulse remains absent. Our approach is expected to be equally applicable to other two-dimensional materials, among others, transition-metal dichalcogenides and hexagonal boron nitride, as our approach is based on the absence of rotational symmetry of the driving pulse. Our work paves the way for establishing compact solid-state chiral extreme ultraviolet sources, opening a realm for chiral light-matter interaction on its intrinsic timescale.

Vibration phase difference analysis of long-span suspension bridge during flutter

The research on vibration characteristics of long-span bridges is of great importance to flutter analysis, yet the literature is limited which concerns the phase difference characteristic of the full bridge. This study thus aims to investigate the vibration phase difference characteristics and mechanism along the main span during flutter. The time-domain flutter analysis was conducted in a long-span suspension bridge. The results manifest that the vibration in different directions at the same position and the vibration in the same direction at different positions of the main girder and the main cable all exist phase difference, which varies along the main span. The deduced phase difference equation reveals that the variable of the distance from mid-span is in cosine term of the denominator, making the increasing of the distance resulting in the growth of phase difference. Due to the variation of phase difference, the vibration of the main girder and main cable along the span is asynchronous. The motion trajectories of individual points are elliptic and vary along the main span. These findings can help understand the flutter performance and mechanism of long-span bridges.

Optically tunable and broadband terahertz coherent perfect absorption based on coupled toroidal dipole excitation

ABSTRACT In this paper, we present a multiple dumbbell-shaped aperture metasurface (MDSAM) combined semiconductors to force implementation of tunable broadband coherent perfect absorption (CPA) in the terahertz (THz) region, thus manipulating the interaction between electromagnetic wave and matter. Utilizing the variation of phase difference between two back-propagation beams, on the one hand, the coherent absorptivity at 2.73–4.04 THz can be tailored successively from greater than 90% to as low as 11.7%. On the other hand, exciting the semiconductor germanium (Ge) through a pump power, the realization of quadruple-band, dual-band, and broadband CPA switching is demonstrated. Numerical simulations reveal that the CPA of the reported MDSAM is attributed to the destructive interference originating from two anti-parallel toroidal dipole moments. Our findings offer a novel platform to design tunable broadband CPA and comprehend the underlying mechanism with electromagnetic response for toroidal dipole.

Experimental demonstration of thermophones in vibro-acoustic noise cancellation scenario for varying gaseous media

The paper focuses on an analytical and experimental study of global noise cancellation between two co-planar thermo- and vibro-acoustic sources in varying gaseous media. To address the experimental uncertainty in thermophone thermal boundary condition, the previously developed theoretical model is expanded to consider oscillating temperature at the solid-fluid interface, beyond the previously studied oscillating heat flux boundary. The results of the analysis indicate that at the point of optimal cancellation, the ratio of acoustic sources’ powers correlates to the specific heat ratio γ of the surrounding media through γ/(γ−1) relation. Then, a thermophone device is designed using commonly available materials and is deposited on a conventional vibro-acoustic loudspeaker, which acts as the noise source. Both acoustic sources are placed in a sealed acoustic chamber and are experimentally studied in several fluid media with different specific heat ratio values (argon, nitrogen, carbon dioxide and norflurane). The constructive and destructive interferences of the two emitters are analyzed at an exemplary frequency for varying phase differences, and global noise cancellation is demonstrated in all gases using microphone measurements in different spatial locations. The empirical results are observed to fully agree with the theoretical predictions.

Structured Vector Field Manipulation of Terahertz Wave along the Propagation Direction Based on Dielectric Metasurfaces

AbstractThe generation and manipulation of vector light fields are of great significance for both fundamental research and industrial applications of polarized optics. In recent years, the spatial domain control of structured vector fields has gradually expanded from two‐ to three‐dimensional, including traditional optics and meta‐optics. Here, a new method to generate and manipulate structured vector light fields along the propagation direction is proposed, and the functionality in terahertz band using all‐silicon metasurfaces is demonstrated. The coherent superposition of orthogonal circularly polarized terahertz waves through long focal depth and multifocal metalens is completed, and varying phase differences between them in the propagation direction via path accumulation or initial phase design are introduced, thereby continuous variation or independently designed vector polarization distributions in multiple planes are obtained. It is worth mentioning that the proposed scheme is not only for the design of transverse electric field components, but also shows a strong ability for manipulation of the longitudinal component. This scheme realizes the polarization distribution designs of three‐dimensional vector fields in three‐dimensional space, and provides a new inspiration for the generation and manipulation of vector beams based on meta‐optics.

Modeling and validation of eccentricity effects in fine angle signals of high precision angular sensors

High precision optical angular sensors are extensively used for detection and control of position and velocity in payload rotating mechanisms and spacecraft actuators. The accuracy and thus the performance of the encoder are significantly affected due to installation eccentricity. In this paper, a comprehensive study of the causes of installation eccentricity is done. The apportionment of the resultant eccentricity is attributed to variations in diametrical clearances, doweling error, gluing error of the glass disc and bearing wobble. The effect of eccentricity changes during rotation. A new 3-center variable eccentricity model is introduced which improves upon the existing 2-centered one in previous literature. This new 3-centered model is able to better predict the deviations in the fine angle signals in a practical system due to variable eccentricity effect. The efficacy of the mathematical model was validated through two independent experiments- 1) by analyzing the electrical signals from opposite read-heads and 2) by performing mechanical measurements- both done on an actual sensor assembly. The eccentricity value calculated from the maximum and minimum phase difference of the fine angle signals is able to exactly match with the total phase difference variation over one complete rotation. It is observed that the variation in the phase difference between the fine angle sinusoidal signals given by two opposite read-heads varies as a shifted sine over one complete rotation and not as a symmetric sine as shown in previous literature. The eccentricity value obtained from mechanical measurement and that computed using the 3-centered model was matching within 0.1 µm. Both the experimental results support the effectiveness of the 3-centered model.

Measurement of visibility and phase steps of a static wind imaging interferometer assisted by deep learning

In a static wind imaging Michelson interferometer we developed, one of the Michelson mirrors is divided into four quadrants, with coatings on the quadrants that provide small phase steps from one quadrant to another, realizing the four simultaneous sampling of the interferogram. Restricted by the coating process and interferometer adjustment, the instrument visibility and phase steps of the four quadrants will deviate from the design value. In the actual passive detection of the atmospheric wind field, quasi-real-time calibration is required, and the calibration will also be affected by the instrument noise. In this paper, we propose a deep-learning-based denoising algorithm that can quickly denoise the wind interferogram with no need to adjust parameters, combined with conventional least-squares fitting cosine curves to obtain the visibility and phase steps of four quadrants from a series of interferograms with varying phase differences. The proposed algorithm framework is verified by experiment, and the measurement of visibility and phase steps of the wind field interferogram is efficiently realized. It can provide a reference for the visibility and phase steps measurement of the wind imaging interferometer and may have applications in wind imaging interferometer calibration.

Influence of the hydrofoil trailing-edge shape on the temporal-spatial features of vortex shedding

Ocean energy is a kind of clean and valuable renewable resource, which can be efficient utilized through turbomachinery. The turbulent pulsation effect and unsteady flow regime will cause pressure pulsation which can destroy the stability of the unit, especially at the tailing edge of blade. This paper compares pressure field change in the downstream region with different trailing edge geometry by numerical simulation and the pulsation tracking network method. The reasons for weakening downstream pressure pulsation with the Donaldson modification and the propagation law of the pressure pulsation are clarified. By Donaldson modification, the main frequency of pressure pulsation becomes the frequency of vortex shedding (fvs) and the amplitude is reduced to 10% of the original value. The propagation law of pressure pulsation has changed and the scope of influence has been expanded. The position of vortex generation can be judged by the phase variation. The weakening of the fvs amplitude is due to the stable low-pressure region and the phase difference variation. The inhibition of the convergence effect of vortex causes the weakening of the 2fvs amplitude. This study provides an effective method and reference for understanding the downstream pressure pulsation variation of shedding vortex.

Vector Optical Beam with Controllable Variation of Polarization during Propagation in Free Space: A Review

The vector optical beam with longitudinally varying polarization during propagation in free space has attracted significant attention in recent years. Compared with traditional vector optical beams with inhomogeneous distribution of polarization in the transverse plane, manipulating the longitudinal distribution of polarization provides a new dimension for the expansion of the applications of vector optical beams in volume laser machining, longitudinal detection, and in vivo micromanipulation. Two theoretical strategies for achieving this unique optical beam are presented in the way of constructing the longitudinally varying phase difference and amplitude difference. Relevant generation methods are reviewed which can be divided into the modulation of complex amplitude in real space and the filtering of the spatial spectrum. In addition, current problems and prospects for vector optical beams with longitudinally varying polarization are discussed.

Dynamic range enhancement of the roll angle displacement measurement with birefringence using a polarization camera.

A roll angle displacement measurement technique with high resolution for large-range measurement is presented. The proposed technique is based on the birefringence effect and phase detection of polarization interferometry with a polarization camera. The phase difference variation between the s- and p-polarized light induced by a rolling birefringent crystal can be obtained by a polarization camera. The roll angle displacement of the birefringent crystal can be determined from the detected phase difference variation. Several experiments were performed to evaluate the feasibility and performance of the proposed technique. The experimental results demonstrate that the resolution of the system can reach 0.003° with a 10° measurement range. The nonlinear and periodic errors of the system are also analyzed.

Using ASE sources in remote beamforming system with Space-Division-Multiplex fiber

Weakly-coupled Space-Division-Multiplex (SDM) fiber is a promising candidate transmission medium for the remote true-time-delay (TTD) beamforming system. However, the signal-to-crosstalk beating interference (SCBI) can result in severe phase difference (or time delay) variation between TTD channels, which deteriorates the beam direction stability. Here, we develop a model to illustrate the phase variation problem when employing the coherent light source. To obtain a stable beam direction, we propose using an ASE source instead of a coherent source as the optical carrier. When utilizing the ASE source, the signal-to-noise ratio (SNR) of the remote RF signals is also thoroughly derived. It indicates that the RF signal with high SNR can be achieved via increasing the ASE source bandwidth and pre-compensating the fiber link dispersion. We carry out a proof-of-concept experiment of the remote beamforming system with the ASE source at the end. The variation of the phase difference between different channels is less than 3°. The SNR of the RF signal is over 110 dB with a 1 Hz bandwidth. These results pave the way for exploring the SDM fiber in the remote beamforming system.

Seismic radiation from wind turbines: observations and analytical modeling of frequency-dependent amplitude decays

Abstract. In this study, we determine spectral characteristics and amplitude decays of wind turbine induced seismic signals in the far field of a wind farm (WF) close to Uettingen, Germany. Average power spectral densities (PSDs) are calculated from 10 min time segments extracted from (up to) 6 months of continuous recordings at 19 seismic stations, positioned along an 8 km profile starting from the WF. We identify seven distinct PSD peaks in the frequency range between 1 and 8 Hz that can be observed to at least 4 km distance; lower-frequency peaks are detectable up to the end of the profile. At distances between 300 m and 4 km the PSD amplitude decay can be described by a power law with exponent b. The measured b values exhibit a linear frequency dependence and range from b=0.39 at 1.14 Hz to b=3.93 at 7.6 Hz. In a second step, the seismic radiation and amplitude decays are modeled using an analytical approach that approximates the surface wave field. Since we observe temporally varying phase differences between seismograms recorded directly at the base of the individual wind turbines (WTs), source signal phase information is included in the modeling approach. We show that phase differences between source signals have significant effects on the seismic radiation pattern and amplitude decays. Therefore, we develop a phase shift elimination method to handle the challenge of choosing representative source characteristics as an input for the modeling. To optimize the fitting of modeled and observed amplitude decay curves, we perform a grid search to constrain the two model parameters, i.e., the seismic shear wave velocity and quality factor. The comparison of modeled and observed amplitude decays for the seven prominent frequencies shows very good agreement and allows the constraint of shear velocities and quality factors for a two-layer model of the subsurface. The approach is generalized to predict amplitude decays and radiation patterns for WFs of arbitrary geometry.