Complex Amplitude Research Articles

Detection of ceramic stress intensity factor based on digital holography

This study investigates the application of digital holography in investigating fracture problems of the ceramic material magnesium oxide under three-point bending fracture experiments. A digital holographic optical path system was constructed for this purpose. Three-point bending experiments were performed on magnesium oxide samples using the system, with holograms of the specimens recorded both before and after the application of loads. By utilizing the angular spectrum diffraction reconstruction algorithm, we obtained the complex amplitude of the object wave under varying load conditions and computed the phase changes of the object wave corresponding to different loads. Subsequently, we derived interference fringes from these phase changes, enabling the measurement of the stress intensity factor of magnesium oxide through holographic interferometry and plane stress theory. A comparison of the experimental measurements with theoretical values demonstrates that digital holographic technology is a viable method for measuring the stress intensity factor of ceramic magnesium oxide.

Unpaired learning for digital holographic reconstruction and generation.

Traditional numerical reconstruction methods in digital holography (DH) are faced with problems such as inaccurate and time-consuming unwrapping or the need to capture multiple holograms with different diffraction distances. In recent years, deep learning, believed to be a new and effective optimization tool, has been widely used in digital holography. However, most supervised deep learning methods require large-scale paired data, and their preparation is time-consuming and laborious. Here, we propose what we believe to be a new deep learning approach that can use less unpaired data to train neural networks, thereby reducing the need for labeled data. By using CycleGAN, the calculation process of the loss function does not need paired data, and the network can learn the mapping knowledge between two domains, instead of the data and its corresponding label. As such, the proposed method can reconstruct complex amplitudes for holographic reconstruction. And more importantly, the trained network learns the knowledge of the imaging system, leading to the capability to generate experimentally synthetic holograms at the same time. To the best of our knowledge, this is the first demonstration of such high-quality physics-based experimental hologram simulator in DH. The reconstructed complex amplitudes have higher image quality, while the generated holograms can represent realistic system status and reconstruct the input complex amplitudes.

Phase-gradient force-based optical array sorter

Microparticle sorting is crucial for applications in biomedicine, environmental monitoring, and biochip technology. However, traditional optical sorting methods often rely on external equipment, such as microfluidic devices. In this Letter, we proposed a phase-gradient force-based optical array sorting (POAS) scheme, which achieves the accurate transporting and sorting of the particles by regulating the phase-gradient force based on the physical characteristics of the particles. The method combines the function of particle transporting and sorting, eliminating the need for external auxiliary equipment. Based on the POAS scheme, we used the complex amplitude beam shaping algorithms to design a 1 × 2 array sorting beam with the controllable phase-gradient forces. The array sorting beam was used to experimentally sort two kinds of particles with different sizes, and the particles are first transported and then precisely sorted at the designated sorting nodes. All the parameters of the sorting beam were adjustable, which greatly enhances the flexibility and scalability of the optical sorting technology. This study provides an alternative scheme for the high-throughput particle sorting, which can be easily integrated into the optical sorting chips for applications in medical detection and drug delivery.

Temporal multiplexing complex amplitude computer-generated holography for 3D display with natural depth perception

Temporal multiplexing complex amplitude computer-generated holography for 3D display with natural depth perception

Zipper Pattern: An Investigation into Psychotic Criminal Detection Using EEG Signals.

Background: Electroencephalography (EEG) signal-based machine learning models are among the most cost-effective methods for information retrieval. In this context, we aimed to investigate the cortical activities of psychotic criminal subjects by deploying an explainable feature engineering (XFE) model using an EEG psychotic criminal dataset. Methods: In this study, a new EEG psychotic criminal dataset was curated, containing EEG signals from psychotic criminal and control groups. To extract meaningful findings from this dataset, we presented a new channel-based feature extraction function named Zipper Pattern (ZPat). The proposed ZPat extracts features by analyzing the relationships between channels. In the feature selection phase of the proposed XFE model, an iterative neighborhood component analysis (INCA) feature selector was used to choose the most distinctive features. In the classification phase, we employed an ensemble and iterative distance-based classifier to achieve high classification performance. Therefore, a t-algorithm-based k-nearest neighbors (tkNN) classifier was used to obtain classification results. The Directed Lobish (DLob) symbolic language was used to derive interpretable results from the identities of the selected feature vectors in the final phase of the proposed ZPat-based XFE model. Results: To obtain the classification results from the ZPat-based XFE model, leave-one-record-out (LORO) and 10-fold cross-validation (CV) methods were used. The proposed ZPat-based model achieved over 95% classification accuracy on the curated EEG psychotic criminal dataset. Moreover, a cortical connectome diagram related to psychotic criminal detection was created using a DLob-based explainable artificial intelligence (XAI) method. Conclusions: In this regard, the proposed ZPat-based XFE model achieved both high classification performance and interpretability. Thus, the model contributes to feature engineering, psychiatry, neuroscience, and forensic sciences. Moreover, the presented ZPat-based XFE model is one of the pioneering XAI models for investigating psychotic criminal/criminal individuals.

Speckle‐Free 3D Holography in the Wigner Domain

AbstractComputer‐generated hologram (CGH) provides an approach to modulate the 3D coherent wavefront and has been widely used in many optical applications. Over the past few decades, extensive efforts have been made to design optimization models for high‐quality reconstruction. However, the reconstruction quality is still limited due to the mismatch of the bandwidth between the reconstructed field of interest and the reconstructed complex amplitude field in 3D space. Here, an ideal numerical light field mapping physical model from the hologram plane to the 3D image plane for speckle‐free 3D holography in the Wigner domain is established. With the aid of the Wigner distribution function (WDF), which allows the analysis of a light field from not only the space domain but also the spatial frequency domain, the bandwidth properties of the reconstructed field in 3D space are analyzed, which provides a guideline for the sampling of the reconstructed field to efficiently describe the speckles and artifacts. Accordingly, a comprehensive CGH optimization method in the Wigner domain is proposed to constrain the reconstructed intensity fluctuations without errors and omissions for high‐quality reconstruction. As such, this method enables speckle‐free and artifact‐free reconstruction with a twice improvement in peak signal‐to‐noise ratio (PSNR) and a five times improvement in structural similarity index measure (SSIM) compared to conventional phase‐only holograms. The optical experimental results show that this method paves the road for the future implementation of speckle‐free color 3D holography harnessing the advanced integrated photonic devices, and also offers an efficient and practical route for various optical applications, such as 3D display, optical encryption, beam shaping, optical computing and so on.

RF photonic interference mitigation system using silicon nitride ring resonator network.

We experimentally demonstrate what we believe to be a novel RF interference mitigation technique using a network of low-loss silicon nitride ring resonators. The rings are used for complex (phase and amplitude) line-by-line shaping of higher-order sidebands from an electro-optic modulator to discriminate large and small RF signal input, thereby achieving strong (30 dB) mitigation of a large signal and virtually no mitigation for small signals.

High-quality and efficient phase-only hologram generation method based on complex amplitude constrained Gerchberg-Saxton algorithm

High-quality and efficient phase-only hologram generation method based on complex amplitude constrained Gerchberg-Saxton algorithm

Spintronic effects and devices in nonlinear optics

In this perspective article, we discuss the analogy between spin transport in magnetization texture and the nonlinear process of sum frequency generation, where the signal and idler complex amplitudes represent the two-dimensional spinor, while the nonlinear coupling represents the material magnetization. This analogy unveils new nonlinear optical effects in both spatial and temporal domains, including the analog of the famous Stern–Gerlach effect, the topological Hall effect in magnetic skyrmion structures, and the transverse localization of spin currents in a disordered magnetic spin-glass phase. Moreover, it enables us to realize new all-optical devices that manipulate superposition states of the signal and idler. Examples include a pump-controlled spin valve, which can either reflect or transmit the signal-idler waves when they are in-phase, and a spin waveguide that guides only in-phase signal-idler waves.

Guided and Space Waves Multiplexed Metasurface for Advanced Electromagnetic Functionalities in Microwave Region.

Nowadays, metasurfaces have attracted considerable attention due to their promising and advanced control of electromagnetic (EM) waves. However, it is still challenging to shape guided waves into desired free-space mode, while simultaneously manipulating spatial incident waves using a single metasurface. Herein, a class of metasurfaces capable of multiplexing guided and space waves is proposed to achieve advanced EM functionalities in microwave regions, which can find great application potentials in radar systems, wireless communications, and wireless power transfer (WPT). The proposed metasurface, composed of specially designed meta-atoms with polarization-dependent radiation and reflection properties, provides the capability to fully manipulate complex amplitude of guided waves and reflection phase of space incident wave independently and simultaneously, thus enabling arbitrary radiation and reflection functionalities without encountering crosstalk issues. As examples of potential applications, three advanced EM functionalities operating in both far-field and near-field regions are presented: low-sidelobe microwave antenna with reduced radar cross section (RCS), multifunctional WPT, and feed multiplexed holograms, respectively. The far-field characteristics of the low sidelobe level antennas showing radiated beams at ±30° together with RCS reduction under arbitrarily polarized incidences are validated by both simulations and measurements. A good agreement between experiments and simulations is also observed for the near-field intensity distribution of the hologram, which further validates the feasibility of near-field shaping. The findings significantly expand the capabilities of metasurfaces in manipulating EM waves and stimulate advanced multifunctional metadevices facing more challenging and diversified application demands.

Deep learning enhanced quantum holography with undetected photons

Holography is an essential technique of generating three-dimensional images. Recently, quantum holography with undetected photons (QHUP) has emerged as a groundbreaking method capable of capturing complex amplitude images. Despite its potential, the practical application of QHUP has been limited by susceptibility to phase disturbances, low interference visibility, and limited spatial resolution. Deep learning, recognized for its ability in processing complex data, holds significant promise in addressing these challenges. In this report, we present an ample advancement in QHUP achieved by harnessing the power of deep learning to extract images from single-shot holograms, resulting in vastly reduced noise and distortion, alongside a notable enhancement in spatial resolution. The proposed and demonstrated deep learning QHUP (DL-QHUP) methodology offers a transformative solution by delivering high-speed imaging, improved spatial resolution, and superior noise resilience, making it suitable for diverse applications across an array of research fields stretching from biomedical imaging to remote sensing. DL-QHUP signifies a crucial leap forward in the realm of holography, demonstrating its immense potential to revolutionize imaging capabilities and pave the way for advancements in various scientific disciplines. The integration of DL-QHUP promises to unlock new possibilities in imaging applications, transcending existing limitations and offering unparalleled performance in challenging environments.

Mesoscale field theory for quasicrystals

We present a mesoscale field theory unifying the modeling of growth, elasticity, and dislocations in quasicrystals. The theory is based on the amplitudes entering their density-wave representation. We introduce a free energy functional for complex amplitudes and assume nonconserved dissipative dynamics to describe their evolution. Elasticity, including phononic and phasonic deformations, along with defect nucleation and motion, emerges self-consistently by prescribing only the symmetry of quasicrystals. Predictions on the formation of semicoherent interfaces and dislocation kinematics are given. Published by the American Physical Society 2024

Approximate analytical description of the structured laser beam in the far zone.

In the last few years, new ways of structuring light have emerged, with the potential to be used in a wide variety of applications, including materials processing, micro-particle manipulation and charged particle acceleration. One of these techniques is the structured laser beam (SLB). The important advantages of this beam are the simple generation principle using spherical aberration and the potentially infinite propagation range. This makes the SLB a good candidate for use in alignment over long distances or in free space optical communication. However, understanding the distribution of the optical field in such a beam is not trivial and a full analytical description of the SLB is still missing. This paper proposes an approximate analytical scalar description of the SLB complex amplitude, which characterizes the optical field in the far zone with sufficient accuracy for applications such as alignment or optical communication. The proposed approach has been successfully validated through simulations and experimental measurements.

Single-exposure beam quality analysis via lens-free coherent amplitude modulation imaging.

A single-exposure method for complex amplitude reconstruction in beam quality analysis is proposed, utilizing lens-free coherent amplitude modulation imaging (LF-CAMI). This approach leverages a partially saturated diffraction pattern to reconstruct the complex amplitude of a measured laser beam. The corresponding intensity images near the beam waist along the axial direction are determined directly via the Fresnel diffraction formula. Spatial beam parameters, including the beam quality factor M2, are then calculated following the ISO 11146-1 standard. The feasibility of the proposed method is validated through theoretical analysis and experiments, targeting both static and dynamic laser beams. Experimental results demonstrate that this method yields results consistent with those obtained using commercial beam quality analysis instruments while reducing the total measurement time by approximately 80%. The proposed method is compact, cost-effective, and immune to aberrations and offers a fast and accurate measurement process, making it particularly suitable for beam quality analysis in various laser systems, especially pulsed laser systems.

Nonlinear transformation of complex amplitudes via quantum singular value transformation

Due to the linearity of quantum operations, it is not straightforward to implement nonlinear transformations on a quantum computer, making some practical tasks like a neural network hard to achieve. In this paper, we define a task called and provide an algorithm to achieve this task. Specifically, we construct a block encoding of complex amplitudes from a state preparation unitary. This allows us to transform the complex amplitudes by using quantum singular value transformation. We evaluate the required overhead in terms of input dimension and precision, which reveals that the algorithm depends on the roughly square root of input dimension and achieves an exponential speedup on precision compared with previous work. We also discuss its possible applications to quantum machine learning, where complex amplitudes encoding classical or quantum data are processed by the proposed method. In this paper, we provide a promising way to introduce the highly complex nonlinearity of the quantum states, which is essentially missing in quantum mechanics. Published by the American Physical Society 2024

Rationally independent free fermions with local hopping

Rationally independent free fermions are those where sums of single-particle energies multiplied by arbitrary rational coefficients vanish only if the coefficients are all zero. This property guaranties that they have no degeneracies in the many-body spectrum and gives them relaxation properties more similar to those of generic systems. Using classic results from number theory we provide minimal examples of rationally independent free fermion models for every system size in one dimension. This is accomplished by considering a free fermion model with a chemical potential, and hopping terms corresponding to all the divisors of the number of sites, each one with an incommensurate complex amplitude. We then move on to discuss the many-body spectral statistics for these models. Indeed, because of their nondegenerate spectrum, these systems are potentially compatible with Poissonian spectral statistics, as opposed to most noninteracting systems. We show that local probes—like the ratio of consecutive level spacings—look very similar to what is expected for the Poisson statistics. We however demonstrate that free fermion models can never have Poisson statistics with an analysis of the moments of the spectral form factor. Published by the American Physical Society 2024

Miniaturized on-chip optical differentiator based on 2F-structured metasurfaces.

Analog optical computing based on Fourier optics has attracted ever-growing attention, offering unprecedented low power consumption and high parallelism computation at the speed of light. Typically, classical optical 4F systems have been widely employed as one of the most common approaches for analog optical computing. However, most existing schemes replicate the original architecture relying on two Fourier transforms and one spatial-frequency filtering, resulting in bulky size and complex structure. Here, we propose a novel, to the best of our knowledge, on-chip 2F structure that achieves ultra-miniaturized optical analog computing. Taking advantage of the exceptional design flexibility of metasurfaces, we reduce the optical path length through a combination of phase compensation and complex amplitude modulation, thereby significantly simplifying the system structure without sacrificing accuracy compared to the traditional 4F system. As a proof-of-concept demonstration, we design and fabricate an on-chip optical differentiator on a silicon-on-insulator platform, achieving 84.01% and 79.81% differentiation accuracy in simulation and experiment, respectively.

Pure Point Diffraction and Almost Periodicity

AbstractThis article deals with pure point diffraction and its connection to various notions of almost periodicity. We explain why the Fibonacci chain does not fit into the classical concept of Bohr almost periodicity and how it fits into the classes of mean, Besicovitch and Weyl almost periodic point sets. We report on recent results which characterize pure point diffraction as mean almost periodicity of the underlying structure, and discuss how the complex amplitudes fit into this picture.

Heterogeneous-Gradient Supercell Metasurfaces for Independent Complex Amplitude Control over Multiple Diffraction Channels.

The ability to achieve independent complex amplitude control across multiple channels can significantly increase the information capacity of photonic devices. Diffraction inherently holds numerous channels, which are good candidates for dense light manipulation in angular space. However, no convenient method is currently available for attaining this. Here, a flexible interference approach utilizing silicon-based transmission-type heterogeneous-gradient supercell metasurfaces is proposed. By simply designing the phases of the meta-atoms' radiations within a supercell, the complex amplitude of each diffraction channel can be individually and analytically controlled. Crucially, the complex amplitudes of multiple diffraction channels can be simultaneously controlled in a non-interleaved manner, where the number of channels is determined by the number of effective adjusting degrees of freedom (DoF). As a proof-of-concept validation, several meta-devices are experimentally demonstrated in the terahertz regime, which can generate multiple vortex beams, focal points, and splitting beams in different desired diffraction angles. This advancement heralds a new pathway for the development of multifunctional photonic devices with enhanced channel capacity, offering significant potential for both research and practical applications in photonics.

Aharonov-Anandan phase and topological vector potentials underlying an Akhmediev breather

Aharonov-Anandan phase and topological vector potentials underlying an Akhmediev breather