Complex Amplitude Research Articles

Formulation of perfect-crystal diffraction from Takagi-Taupin equations: numerical implementation in the crystalpy library.

The Takagi-Taupin equations are solved in their simplest form (zero deformation) to obtain the Bragg-diffracted and transmitted complex amplitudes. The case of plane-parallel crystal plates is discussed using a matrix model. The equations are implemented in an open-source Python library crystalpy adapted for numerical applications such as crystal reflectivity calculations and ray tracing.

Vector modulation of fully-polarized phase conjugate light field through scattering media

Vector modulation of the light field through scattering media holds significant scientific and application value in areas such as optical imaging, optical communications, nonlinear optics, and biomedicine. Digital optical phase conjugation (DOPC), grounded in the time reversal principle, has been extensively investigated for wavefront shaping in scattering media. Nonetheless, reports on vector modulation of phase conjugate beams via DOPC remain scarce. In this study, we propose a vector DOPC to recover and modulate the polarization state of the phase conjugate beams based on vector decomposition and superimposition of light field. First, pre-set two orthogonal polarization basis probe beams to pass through a multimode fiber and use digital holography to record the phase distribution of their orthogonal polarization components in the speckle field. Then, perform polarization-preserving phase conjugation and vector superposition of both components simultaneously. By altering the phase difference and amplitude ratio between the two, vector modulation of the synthesized phase conjugate beam can be achieved. Theoretical analysis aligns well with experimental results, demonstrating a positive impact on understanding the physical properties of scattering media and expanding the applications of the DOPC technique.

Broadband and parallel multiple-order optical spatial differentiation enabled by Bessel vortex modulated metalens

Optical analog image processing technology is expected to provide an effective solution for high-throughput and real-time data processing with low power consumption. In various operations, optical spatial differential operations are essential in edge extraction, data compression, and feature classification. Unfortunately, existing methods can only perform low-order or selectively perform a particular high-order differential operation. Here, we propose and experimentally demonstrate a Bessel vortex modulated metalens composed of a single complex amplitude metasurface, which can perform multiple-order radial differential operations over a wide band by presetting the order of the corresponding Bessel vortex. This architecture further enables angle multiplexing to create multiple information channels that synchronously perform multi-order spatial differential operations, indicating the superiority of the proposed devices in parallel processing. Our approach may find various applications in artificial intelligence, machine vision, autonomous driving, and advanced biomedical imaging.

Metasurface-Based Diffractive Optical Networks With Dual-Channel Complex Amplitude Modulation

Metasurface-Based Diffractive Optical Networks With Dual-Channel Complex Amplitude Modulation

Deep learning and genetic algorithm driven accelerated design for frequency-multiplexed complex-amplitude coding meta-hologram

Frequency-multiplexed metasurfaces represent a significant innovation in breaking the functional limitations of traditional metasurfaces, showing immense potential in multi-channel communication. However, existing frequency-multiplexed metasurfaces primarily focus on pure phase and linear polarization modulation, neglecting the modulation for complex amplitude and circularly polarized waves. Additionally, crosstalk suppression between dual-frequency channels often requires meticulous tuning of the meta-atom structure. Therefore, manually designing a set of meta-atoms that satisfies both complex amplitude modulation and low crosstalk at dual frequencies is extremely challenging and time-consuming. Here, we utilize the method of deep learning and genetic algorithm to design a kind of meta-atom capable of bi-spectral 2-bit amplitude and arbitrary phase modulation, which greatly reduces the design difficulty and achieves excellent low-crosstalk performance. This method can be easily generalized to the design of other complex meta-atoms to improve the design efficiency. Furthermore, we propose a frequency-multiplexed complex-amplitude coding meta-hologram for modulating left-handed circularly polarized (LCP) waves. When illuminated with LCP light, it can reconstruct two distinct holographic images at two different frequencies in the near field with high quality. The independent modulation capability of the metasurface for multiple degrees of freedom of frequency, amplitude and phase gives it broad application prospects in multi-channel communication, data storage and perfect holography.

Spatially distributed low-cross talk vector beams.

A spatially distributed low-cross talk vector beam refers to a vector beam that exhibits different intensities, phases, and polarization states along the propagation direction. This type of vector beam features low-cross talk between beams on different planes and finds extensive applications in optical communications and related fields. However, current technologies face challenges such as intensity interference at different imaging planes and difficulties in the precise control of phases and polarization states, which affect beam quality. In this study, we investigated the beam propagation process and employed a global optimization strategy to precisely control the intensity and phase distribution of the beam fields. This approach ensures that the beam forms the desired complex amplitude distribution in the target region while effectively suppressing cross talk in non-target regions. We utilized the method to generate two beams with complementary intensities and phases. Subsequently, through an interference optical path, we separated these two beams and converted them into orthogonal polarization states. Finally, by superimposing these two beams, we obtained a spatially varying low-cross talk vector beam. We experimentally validated the beam's different optical characteristics and low-cross talk properties on three planes. Our work opens up new prospects, to the best of our knowledge, for holographic technology with capabilities for ultra-fine depth control and polarization multiplexing.

Ringdown amplitudes of nonspinning eccentric binaries

Closed-form expressions for the ringdown complex amplitudes of nonspinning unequal-mass binaries in arbitrarily eccentric orbits are presented. They are built upon 237 numerical simulations contained within the RIT catalog, through the parameterisation introduced in [Phys. Rev. Lett. 132 (2024) 101401]. Global fits for the complex amplitudes, associated to linear quasinormal mode frequencies of the dominant ringdown modes, are obtained in a factorised form immediately applicable to any existing quasi-circular model. Similarly to merger amplitudes, ringdown ones increase by more than 50% compared to the circular case for high impact parameters (medium eccentricities), while strongly suppressed in the low impact parameter (highly eccentric) limit. Such reduction can be explained by a transition between an “orbital-type” and an “infall-type” dynamics. The amplitudes (phases) fits accuracy lies around a few percent (deciradians) for the majority of the dataset, comparable to the accuracy of current state-of-the-art quasi-circular ringdown models, and well within current statistical errors of current LIGO-Virgo-Kagra ringdown observations. These expressions constitute another building block towards the construction of complete general relativistic inspiral-merger-ringdown semi-analytical templates, and allow to extend numerically-informed spectroscopic analyses beyond the circular limit. Such generalisations are key to achieve accurate inference of compact binaries astrophysical properties, and tame astrophysical systematics within observational investigations of strong-field general relativistic dynamics.

Neural encoding for spatial release from informational masking and its correlation with behavioral metrics.

The central auditory system encompasses two primary functions: identification and localization. Spatial release from masking (SRM) highlights speech recognition in competing noise and improves the listening experience when a spatial cue is introduced between noise and target speech. This assessment focuses on the integrity of auditory function and holds clinical significance. However, infants or pre-lingual subjects sometimes provide less reliable results. This study investigates the value of cortical auditory evoked potentials (CAEPs) onset and acoustic change complex (ACC) as an objective measurement of SRM. Thirty normal-hearing young adults (11 males) were recruited. We found the spatial separation of signals and noise (±90° symmetrically) resulted in a signal-to-noise ratio (SNR) improvement of 9.00 ± 1.71 dB behaviorally. It significantly enhanced cortical processing at all SNR levels, shortened CAEP latencies, and increased amplitudes, resulting in a greater number of measurable peaks for ACC. SRM showed mild to moderate correlations with the differences between two conditions in CAEP measures. The regression model combining N1'-P2' amplitude at 5 dB SNR (R2 = 0.26), P1 amplitude at 0 dB SNR (R2 = 0.14), and P1 latency at -5 dB SNR (R2 = 0.15), explained 45.3% of the variance in SRM. Our study demonstrates that introducing spatial cues can improve speech perception and enhance central auditory processing in normal-hearing young adults. CAEPs may contribute to predictions about SRM and hold potential for practical application.NEW & NOTEWORTHY The neural encoding of spatial release from masking (SRM) can be observed in normal-hearing young adults. Spatial separation between target and masker improves speech perception in noise and enhances central auditory processing. The behavioral results showed mild-to-moderate correlations with electrophysiological measures, with acoustic change complex (ACC) amplitude being a better indicator than onset components. Cortical auditory evoked potentials (CAEPs) may contribute to predictions about spatial release from masking, especially when behavioral tests are less reliable.

A complex neural network model by Hilbert Transform

The phase information of the optical wave plays a vital role in processing wave-related signals. In deep learning fields, complex-valued neural networks are put forward on the concept of complex amplitudes for full utilization of phase information. To build a complex-valued neural network, the common way is to exploit Fourier Transform of the observed signal to extract amplitude and phase information. However, this will lead to spectrum waste for a real-valued signal by introducing negative frequencies that have no physical meaning. To this end, we attempt to use Hilbert Transform as an alternative to yield a single sideband spectrum and avoid negative frequencies from interacting with positive ones. On the other hand, Fourier transform is a global analysis thus it tells nothing about the time domain. As our key insight, we further explore the usage of instantaneous frequency calculated by Hilbert Transform and propose a new method of constructing complex input from a time–frequency angle. Simple pixel-wise classification experiments are carried out on two hyperspectral datasets and MNIST dataset. Experimental results have demonstrated that Hilbert Transform with instantaneous frequency performs better by a large margin than Fourier Transform owing to the additional time information.

HLSM-MIPV Algorithm of unbalance vibration suppression of dual-rotor in contra-rotating propfan

The inner and outer rotors of the contra-rotating propfan dual-rotor system, utilizing dual intershaft bearings, exhibit anisotropic support characteristics, whereas the vibration of the dual-rotor system is cross-coupled. This combination makes the identification of unbalanced responses and the efficiency of dynamic balancing challenging. To address this issue, this paper proposes a method for the dynamic balancing of the contra-rotating dual-rotor based on Harmonic Least Squares Method and Modified Initial Phase Vector (HLSM-MIPV). Firstly, a test bench for the contra-rotating dual-rotor system is constructed using two Micro-Electro-Mechanical Systems (MEMS) sensors. Secondly, unbalanced vibration vectors of the dual-rotor are identified using Harmonic Least Squares Method (HLSM). Thirdly, the Harmonic Component Method with the Modified Initial Phase Vector (MIPV-HCM) is introduced to balance the force and couple unbalance under anisotropic stiffness conditions. Finally, dynamic balancing tests on the test bench demonstrate that the MIPV-HCM method achieves an additional vibration reduction of 4 %–17 % compared to the traditional HCM.

Reordering of point-vortex lattices under anisotropic diffraction: far-field analysis

Abstract A study of the far-field complex amplitude obtained from initially ordered arrays of N × M point-vortices with equal unitary topological charge embedded in carrier beams with different geometry is presented. This can be understood as the final stationary configuration after the dynamical evolution of the vortices upon propagation, and our aim is to investigate the impact of a geometric anisotropy on the diffraction process by using an elliptic Gaussian beam as a carrier and a rectangular vortex lattice. For comparison, illumination by a circular Gaussian beam and a plane wave diffracted by a rectangular aperture are also analyzed. We show that vortices tend to cluster in some regions under high eccentricity of the carrier and there can be an entire redistribution of the vortices depending on the size of the initial array with respect to the size of the carrier, which inherits some geometric characteristics of the latter.

Collective oscillations in a three-dimensional spin model with non-reciprocal interactions

Abstract We study the onset of collective oscillations at low temperature in a three-dimensional spin model with non-reciprocal short-range interactions. Performing numerical simulations of the model, the presence of a continuous phase transition to global oscillations is confirmed by a finite-size scaling analysis, yielding values of the exponents β and ν compatible with both the three-dimensional XY and Ising equilibrium universality classes. By systematically varying the interaction range, we show that collective oscillations in this spin model actually result from two successive phase transitions: a mean-field phase transition over finite-size neighborhoods, which leads to the emergence of local noisy oscillators, and a synchronization transition of local noisy oscillators, which generates coherent macroscopic oscillations. Using a Fokker–Planck equation under a local mean-field approximation, we derive from the spin dynamics coupled Langevin equations for the complex amplitudes describing noisy oscillations on a mesoscopic scale. The phase diagram of these coupled equations is qualitatively obtained from a fully-connected (mean-field) approximation. This analytical approach allows us to clearly disentangle the onset of local and global oscillations, and to identify the two main control parameters, expressed as combinations of the microscopic parameters of the spin dynamics, that control the phase diagram of the model.

Fourier ptychographic microscopy with multi-height illumination based on energy threshold pre-search

Fourier ptychographic microscopy (FPM) technology combines the concepts of synthetic aperture imaging, ptychography, and phase retrieval to address the contradiction between the large field of view and high resolution in traditional microscopy and can achieve high-resolution amplitude and phase images with a large field of view. However, for most samples, the primary information is concentrated in the low-frequency region, and traditional single-height FPM may suffer from insufficient sampling, leading to low reconstruction accuracy. In addition, the reconstruction process typically requires a large number of low-resolution images, which also significantly reduces the reconstruction efficiency. To overcome these issues, this paper proposes a form of FPM with multi-height illumination based on an energy threshold pre-search. This method simply involves moving the LED array to three planes for multi-height sample illumination on the traditional FPM hardware, thus improving the sampling conditions and enhancing the reconstruction accuracy. The low-resolution images acquired in this way are then screened using an energy threshold method to select images with higher energy, and a phase retrieval method is employed to reconstruct high-resolution complex amplitude images. The results of simulations and experiments demonstrate that compared to traditional methods, our approach not only improves the reconstruction accuracy but also reduces the number of low-resolution images by at least approximately 60%, thereby significantly enhancing the reconstruction efficiency.

How labels shape visuocortical processing in infants.

The current study examined the extent to which labels shape visuocortical processing during the first year of life during a brief (~6-min) associative learning task. Images of computer-generated artificial objects were paired with either individual-level (e.g., Jimmy, Boris) or category-level labels (e.g., Hitchel) while event-related potentials were recorded in response to the onset of the visual stimulus in 6- (n=41), 9- (n=27), and 12-month-old (n=28) infants. Analyses examined experience-dependent visuocortical changes within and across trials, label conditions, and ages. Overall, results demonstrate that infants deploy greater visuocortical resources during the first half of associative learning trials and to stimuli paired with category-level relative to individual-level labels. Waveform morphologies also differed between stimuli paired with individual- and category-level labels and across the age groups, with more complex deflections and amplitude differences between label type at 9- and 12-month-olds, but not 6-month-old infants. The present results highlight the importance of associative learning during infancy and suggest that category- versus individual-level labels differentially direct infant attention and visuocortical processing.

Generation of arbitrary vector orbital angular momentum beams on higher-order Poincaré spheres based on an all-dielectric metasurface with complex amplitude modulation

Vector orbital angular momentum (OAM) beams, described by higher-order Poincaré (HOP) sphere, are generalized forms of waves carrying OAM with an inhomogeneous polarization of wavefronts. We construct all-dielectric metasurfaces with adjustable amplitude, polarization, and phase to generate arbitrary vector OAM beams. The metasurface is composed of two pairs of silicon nanopillars arranged alternately. Using the interference effect of the four meta-atoms related to the circular polarization, combined with the propagation and geometric phases, two OAM beams with controlled amplitude, phase, and equal topological charge but opposite signs can be obtained under the incidence of orthogonally circularly polarized lights. For the x linearly polarized light, arbitrary vector OAM beams on the HOP sphere are generated via the superposition of the above OAM beams. Additionally, the evolution process of the beam on the longitude and latitude of the Poincaré sphere is revealed by changing the amplitude and phase of the two OAM beams. This work provides a simple, effective, and flexible method for realizing vector OAM beams while having potential implications for the generation and manipulation of vectorial light fields at the micro-nano scale.

Analysis of oceanic suspended particulate matter in the western North Pacific using the complex amplitude sensor

Oceanic suspended particulate matter (SPM) plays important roles in the coupling of climate and biogeochemical cycles via ocean–atmosphere interactions. However, methods for quantifying the properties of SPM in seawater have not yet been well established. Here we present the application of the recently developed complex amplitude sensor (CAS) for analyzing the complex forward-scattering amplitude of individual SPM (0.2–5.0 µm in diameter) obtained at depths of 0–100 m during a research cruise in the western North Pacific. The measured distribution of the complex amplitude indicated that the CAS-derived SPM data could be roughly classified into five major types. Comparison with reference sample’s complex amplitude data and scanning electron microscopy analysis suggested that these types could be attributed mainly to diatom fragments, carbonaceous materials (likely organic matter), mineral dusts, iron oxides, or black carbon. Depth profiles revealed that relatively high concentrations of SPM, presumably dominated by diatom fragments and carbonaceous materials with peak diameters of 0.7–1.0 µm, were typically associated with elevated turbidities and chlorophyll a concentrations. Based on this case study, we discuss the practical advantages and limitations of using the CAS to measure size-resolved concentrations of SPM in seawater and to characterize its composition.

Bessel–Bessel–Gaussian vortex laser beams

Abstract We obtain and investigate Bessel–Bessel–Gaussian vortex beams (BBG beams) with the complex amplitude being equal to a product of the Gaussian function with two Bessel functions, whose arguments are expressed as complicated radicals including the cylindrical coordinates and a free parameter that defines the shape of the intensity distribution. If this parameter is small, the intensity has the shape of an inhomogeneous ring. For larger values of this parameter, the intensity has the shape of two arcs or ‘crescents’, oriented by their concave sides to each other. The complex amplitude of such beams is derived in explicit form for an arbitrary distance from the waist. We demonstrate that the BBG beams rotate upon propagation anomalously fast: at a distance much shorter than the Rayleigh length, the intensity distribution is already rotated by almost 45°, whereas typically, the rotation angle of vortex Gaussian beams is equal to the Gouy phase. It is also shown that the parameter of the BBG beam allows controlling its topological charge (TC): when the parameter value is positive and increases, the beam TC also increases stepwise by an even number. Besides, we study two other similar vortex BBG beams: either with four local intensity maxima, lying on the Cartesian coordinates axes, or with one intensity maximum with a crescent shape, whose center is on the horizontal axis. The derived three new families of asymmetric vortex laser beams, whose complex amplitude is described by explicit analytical expressions at an arbitrary distance from the waist, extend the variety of laser beams that can be used for manipulating and rotating microparticles, free space data transmission, and in quantum informatics.

Automated phase-visibility modulating interferometry

This paper presents the Phase-Visibility Modulating Interferometry (PVMI) method automated by a microcontroller and three servomotors, under inhomogeneous out-of-phase amplitude modulation (OPAM) in the On-Off Modulation (OOM) mode. PVMI is implemented in a triple-aperture common-path interferometer (TACPI), based on a 4f optical imaging system. The high mechanical stability of the TACPI and the properties of the PVMI technique make the present method immune to noise, robust, fast, and convenient for measuring complex amplitude with high resolution and accuracy. PVMI does not preprocess and post-process the experimental irradiances and does not need a phase step shifter or a carrier frequency. Therefore, a calibration is unnecessary, there are no detuning errors, and no bandwidth reduction. The great advantage of automated PVMI is explained and demonstrated experimentally for three translucent objects. The focal length estimation of a lens with a percentual deviation of 0.14 to validate the automated PVMI, and the evaluation of two arbitrary translucent objects with high resolution and accuracy.

ЗАСТОСУВАННЯ ФАЗНИХ СТРУМОВИХ КОНТУРІВ ДЛЯ МОДЕЛЮВАННЯ ГАРМОНІЙНОГО МАГНІТНОГО ПОЛЯ МАГНІТОЕЛЕКТРИЧНОГО ГЕНЕРАТОРА

The model of electromagnetic field of a magnetoelectric generator with a smooth cylindrical rotor and surface-mounted permanent magnets is investigated. Permanent magnets are interpreted using complex amplitudes of a system of current loops with harmonic currents. The aim of the study is to develop a mathematical model for calculating the harmonic magnetic field of a magnetoelectric generator with permanent magnets by replacing the permanent magnets with phase current loops with complex current amplitudes and to investigate its adequacy. Three variations of model representation of permanent magnets placed on the surface of the magnetic core are utilized. Depending on the model representation of permanent magnets, two dynamic generator models and two harmonic models have been developed. For each model, equations of the electromagnetic field are written. An example of a three-phase scheme of current loops of the rotor for modeling the electromagnetic field of the magnetoelectric generator with complex amplitudes of currents is presented. Comparison of the magnetic field induction, current, voltage, and electromagnetic torque is performed with three variations of magnet width relative to the pole pitch. References 14, figures 5, table 1.

High-security holographic display with content and copyright protection based on complex amplitude modulation

The computer-generated hologram provides an approach to modulate the coherent wavefront and has been widely applied in holographic displays. In the actual application, holograms need to be transmitted through the network, which results in the illegal acquisition and malicious manipulation of holographic images. Therefore, it is necessary to develop a practical method to protect the content and copyright of holographic images. In this paper, we develop a high-security holographic display method based on complex amplitude modulation. In our proposed method, the complex hologram of a holographic image is decomposed into two phase-only holograms, one of which is designed as the ciphertext, and the other is regarded as the key. As a result, the holographic image can be reconstructed only when the ciphertext and the key are paired, which boosts the security of the holographic image. Meanwhile, the copyright of the holographic image is protected via a watermark that is embedded in the ciphertext in the form of a hologram. Due to the simultaneous use of encryption and watermark technology, our proposed method could transmit holographic images at a high security level, and has great potential to be applied in holographic displays in the future.