Backward Propagation Research Articles

STCO: Enhancing Training Efficiency via Structured Sparse Tensor Compilation Optimization

Network sparsification serves as an effective technique to accelerate Deep Neural Network (DNN) inference. However, existing sparsification techniques often rely on structured sparsity, which yields limited benefits. This is primarily due to the significant memory and computational overhead introduced by numerous sparse storage formats during address generation and gradient updates. Additionally, many of these solutions are tailored solely for the inference phase, neglecting the crucial training phase. In this paper, we introduce STCO, a novel Sparse Tensor Compilation Optimization technique that significantly enhances training efficiency through structured sparse tensor compilation. Central to STCO is the Tensorization-aware Index Entity (TIE) format, which effectively represents structured sparse tensors by eliminating redundant indices and minimizing storage overhead. The TIE format plays a pivotal role in the Address-carry flow (AC flow) pass, which optimizes the data layout at the computational graph level. This pass leverages the TIE format to enhance the efficiency of tensor representations, enabling more compact and efficient sparse tensor storage. Meanwhile, a shape inference pass utilizes the AC flow to derive optimized tensor shapes, further refining the performance of sparse tensor operations. Moreover, the Address-Carry TIE Flow dynamically tracks nonzero addresses, extending the benefits of sparse optimization to both forward and backward propagation. This seamless integration into the training pipeline enables a smooth transition to sparse tensor compilation without significant modifications to existing codebases. To further boost training performance, we implement an operator-level AC flow optimization pass tailored for structured sparse tensors. This pass generates efficient addresses, ensuring minimal computational overhead during sparse tensor operations. The flexibility of STCO allows it to be efficiently integrated into various frameworks or compilers, providing a robust solution for enhancing training efficiency with structured sparse tensors. Experiments demonstrated that STCO achieved impressive speedups of 3.64 ×, 5.43 ×, 4.89 ×, and 3.91 × when compared to state-of-the-art sparse formats on VGG16, ResNet-18, MobileNetV1, and MobileNetV2, respectively. These findings underscore the efficiency and superiority of our proposed approach in leveraging unstructured sparsity for Deep Neural Network inference acceleration.

A novel autonomous exploration algorithm via LiDAR/IMU SLAM and hierarchical subsystem for mobile robot in unknown indoor environments

Abstract Autonomous exploration in unknown environments is an essential capability for mobile robots. The complexity of autonomous exploration, however, means that existing algorithms struggle to balance efficiency and comprehensiveness, causing low mapping accuracy and redundant path planning. To perform accurate and efficient exploration tasks, we have proposed a novel autonomous exploration algorithm via LiDAR/IMU (Inertial Measurement Unit) Simultaneous Localization and Mapping (SLAM) and hierarchical subsystem for mobile robot in unknown environments. Firstly, to enhance mapping accuracy for mobile robot exploration, LiDAR/IMU SLAM is improved with the assistance of backward propagation and iterated Kalman filter, and Bidirectional Rapidly–Exploring Random Trees* (BI–RRT*) is applied for efficient frontier point detection. Secondly, we optimize local path planning by leveraging information theory through perceptual quality evaluation, which is then integrated with global path planning utilizing an enhanced Travelling Salesman Problem solver and a sparse grid map to amplify exploration efficiency. Thirdly, an enhanced hierarchical autonomous exploration method for mobile robots is proposed, which incorporates local path planning for seamless navigation around highly promising exploration spots, coupled with global path planning to effectively interconnect various sub–regions. Finally, simulations and field tests have demonstrated that the proposed method explores an unknown indoor environment with a 30.8% reduction in exploration time and a 29.9% reduction in exploration path in comparison with Dynamic Stage Viewpoint Planner. The map constructed in this paper has more accurate details and exploration paths have been shortened to ensure effective exploration.

XGrad: Boosting Gradient-Based Optimizers With Weight Prediction.

In this paper, we propose a general deep learning training framework XGrad which introduces weight prediction into the popular gradient-based optimizers to boost their convergence and generalization when training the deep neural network (DNN) models. In particular, ahead of each mini-batch training, the future weights are predicted according to the update rule of the used optimizer and are then applied to both the forward pass and backward propagation. In this way, during the whole training period, the optimizer always utilizes the gradients w.r.t. the future weights to update the DNN parameters, making the gradient-based optimizer achieve better convergence and generalization compared to the original optimizer without weight prediction. XGrad is rather straightforward to implement yet pretty effective in boosting the convergence of gradient-based optimizers and the accuracy of DNN models. Empirical results concerning five popular optimizers including SGD with momentum, Adam, AdamW, AdaBelief, and AdaM3 demonstrate the effectiveness of our proposal. The experimental results validate that XGrad can attain higher model accuracy than the baseline optimizers when training the DNN models.

RAM-YOLOv8: A multi-fault detection method for photovoltaic module

ABSTRACT Given the constraints in fault type identification, localization precision, and detection efficiency inherent in current photovoltaic fault detection methodologies, this paper introduces an innovative detection approach integrating RAM-YOLOv8 with the Swin Transformer. To mitigate the limitations in model extraction capabilities during the detection process and circumvent the vanishing gradient issue encountered during backward information propagation, this study introduces a residual aggregation module as a substitute for the original C2F module, thereby augmenting feature extraction efficiency. Furthermore, within the feature fusion network, the Swin attention mechanism fusion module is designed by integrating the Swin Transformer’s architectural concept to minimize the loss of weak defect information and suppress irrelevant background interference. The model achieves a detection accuracy of 88.5% on the dataset, representing a 7% improvement over the original YOLOv8 algorithm, with a detection rate of 83.33 FPS on an RTX2080 GPU. This method offers a robust and efficient fault detection solution for PV systems, rendering it a practical approach for enhancing system performance and reducing maintenance costs.

Thermographic assessment of mastitis progression in sahiwal cattle: Insights into the patterns in the natural course of infection

Mastitis is a global concern in the dairy sector, demanding innovative solutions for effective management for quality lifetime milk production. In this study, infrared thermography (IRT) as a non-invasive technology was integrated into routine farm activities for continuous health monitoring of animals. For 30 days, we systematically monitored the udder health status in 40 Sahiwal cows (160 quarters), employing IRT along with the California Mastitis Test (CMT). We also assessed somatic cell count (SCC), microbial identification, and milk quality parameters of representative samples. The thermal imaging data was analyzed, considering both backward propagation from the 0th day to the −10th day and forward propagation from the 0th day to the +10th day. Our findings revealed that on the 0th day, the mean temperatures of the udder surface skin temperature (USST) and teat skin surface temperature (TSST) exhibited differences (p < 0.05) between the quarters affected by sub-clinical mastitis (SCM) and clinical mastitis (CM) in comparison to the healthy quarters, with the highest degree of difference observed. The observed temperature differences between CM and SCM quarters compared to healthy ranged from 1.8 to 3.62 °C and 0.98 to 3.23 °C for USST, and from 1.68 to 3.16 °C and 0.56 to 2.32 °C for TSST, respectively. Furthermore, our observations indicated that both udder and teat quarters responded differently to mastitis. A temperature rise of 1.37 °C in SCM quarters and 1.75 °C in CM quarters was observed between the −10th and -8th day relative to day 0, with the increase being more pronounced in the morning hours. Also, a notable temperature surge occurred during the -2nd and -1st days relative to the 0th day. The log10SCC values and milk quality parameters significantly differed (p < 0.05) between mastitis-affected and healthy samples. In addition, Staphylococcus spp. was identified as the predominant mastitis-causing pathogen in the bacteriological identification conducted in this study. Therefore, IRT efficiently assesses the initiation point of udder infection in Sahiwal cows, aiding in effective udder health management.

Research on improved underwater cable image processing technique based on CNN-GAN

In this study, we propose a CNN-GAN-based real-time processing technique for filtering images of underwater cables used in power systems. This addresses the excessive interference impurities that are frequently observed in images captured by remotely operated vehicles (ROVs). The process begins with the input of the original image into the convolutional neural network (CNN). Subsequently, the training outcomes, which serve as input parameters for the generative adversarial network (GAN), facilitate the filtering process. The system also calculates both the structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR), performing model updates via backward propagation. This technique utilizes deep learning technologies to achieve rapid, real-time filtering of underwater cable images. The experimental results reveal that the loss function of the CNN reaches 0.16 with an accuracy of 97.5%, while the loss function of the adversarial GAN network approaches 0.05. Compared with traditional methods such as DDN, JORDOR, RESCAN, and PRENet, the proposed CNN-GAN algorithm exhibits superior performance, as evidenced by the higher PSNR and SSIM values. Specifically, for clear water images, the PSNR reaches 29.86 dB and the SSIM is 0.9045. For severely polluted images, the PSNR is 28.67 dB and the SSIM is 0.8965, while for unevenly illuminated images, the PSNR and SSIM values are 24.37 dB and 0.88, respectively. These enhancements significantly benefit the monitoring and maintenance of power systems.

High-Sensitivity Janus Sensor Enabled by Multilayered Metastructure Based on the Photonic Spin Hall Effect and Its Potential Applications in Bio-Sensing.

The refractive index (RI) of biological tissues is a fundamental material parameter that characterizes how light interacts with tissues, making accurate measurement of RI crucial for biomedical diagnostics and environmental monitoring. A Janus sensor (JBS) is designed in this paper, and the photonic spin Hall effect (PSHE) is used to detect subtle changes in RI in biological tissues. The asymmetric arrangement of the dielectric layers breaks spatial parity symmetry, resulting in significantly different PSHE displacements during the forward and backward propagation of electromagnetic waves, thereby realizing the Janus effect. The designed JBS can detect the RI range of 1.3~1.55 RIU when electromagnetic waves are incident along the +z-axis, with a sensitivity of 96.29°/refractive index unit (RIU). In the reverse direction, blood glucose concentrations are identified by the JBS, achieving a sensitivity of 18.30°/RIU. Detecting different RI range from forward and backward scales not only overcomes the limitation that single-scale sensors can only detect a single RI range, but also provides new insights and applications for optical biological detection through high-sensitivity, label-free and non-contact detection.

Layered heterogeneous structures integrated device for multiplication, division arithmetic unit and multiple-physical sensing

A layered heterogeneous structure (LHS), consisting of silver, liquid crystal, and nonlinear dielectric layers, is proposed to realize functions of computing and sensing. By leveraging the optical Tamm state, the intrinsic absorption principle of liquid crystal, and nonlinear effects, the design of an integrated device capable of passive multiplication and division operations, along with high-performance multi-physical quantity sensing functionalities, is achieved. The given LHS exhibits Janus properties, with different physical functions manifested depending on the direction of electromagnetic wave (EW) propagation. During forward propagation of EWs, the LHS displays high and sharp absorptivity peaks at 774.8 and 1517.6 nm. The relationship between the two peaks approximates a frequency multiplication factor of 1.960, enabling signal multiplication. Furthermore, the two absorptivity peaks at different wavelengths facilitate the sensing of serum creatinine solution concentration and external pressure, with sensitivity (S), quality factors (Q), and figure of merit (FOM) of 266.76 μmol L−1/nm and 213.33 GPa/nm, as well as 248.76 and 348.22, 84.1 L (μmol)−1 and 49.06 GPa−1, respectively. During backward propagation of EWs, absorptivity peaks with distinct resolutions are observed at 1423 and 2809 nm, with a multiple relationship between them of 1.974, enabling frequency doubling for signal division. Additionally, the absorptivity curve facilitates temperature sensing over a wide range from 257 to 347 K. Owing to the unique temperature S of liquid crystal, different sensitivities and resolutions are observed at 257 to 297 K and 307 to 347 K, with S of 1.015 and 0.686 K/nm, and corresponding Q and FOM of 21.57 and 12.576, 0.076 K−1 and 0.003 04 K−1, respectively.

Complex-valued soft-log threshold reweighting for sparsity of complex-valued convolutional neural networks

Complex-valued convolutional neural networks (CVCNNs) have been demonstrated effectiveness in classifying complex signals and synthetic aperture radar (SAR) images. However, due to the introduction of complex-valued parameters, CVCNNs tend to become redundant with heavy floating-point operations. Model sparsity is emerged as an efficient method of removing the redundancy without much loss of performance. Currently, there are few studies on the sparsity problem of CVCNNs. Therefore, a complex-valued soft-log threshold reweighting (CV-SLTR) algorithm is proposed for the design of sparse CVCNN to reduce the number of weight parameters and simplify the structure of CVCNN. On one hand, considering the difference between complex and real numbers, we redefine and derive the complex-valued log-sum threshold method. On the other hand, by considering the distinctive characteristics of complex-valued convolutional (CConv) layers and complex-valued fully connected (CFC) layers of CVCNNs, the complex-valued soft and log-sum threshold methods are respectively developed to prune the weights of different layers during the forward propagation, and the sparsity thresholds are optimized during the backward propagation by inducing a sparsity budget. Furthermore, different optimizers can be integrated with CV-SLTR. When stochastic gradient descent (SGD) is used, the convergence of CV-SLTR is proved if Lipschitzian continuity is satisfied. Experiments on the RadioML 2016.10A and S1SLC-CVDL datasets show that the proposed algorithm is efficient for the sparsity of CVCNNs. It is worth noting that the proposed algorithm has fast sparsity speed while maintaining high classification accuracy. These demonstrate the feasibility and potential of the CV-SLTR algorithm.

PhotoSolver: A bidirectional photonic solver for systems of linear equations

Solving systems of linear equations is one of the most fundamental challenges in computing, with ubiquitous applications in science and engineering. Solving large-scale linear equations is particularly challenging, requiring tremendous computing expenses. However, conventional solvers in electronic digital computers face inevitable physical bottlenecks that hinder further advancements in electronic chips. Unlike the electronic architectures, optical computing harnesses the inherent advantages of lights, such as ultimately high speed, negligible energy consumption, and high parallelism, making optical architectures attractive sources for ultra-high speed analog computing. Especially, recent advances in integrated photonic circuits bring exciting new possibilities for high performance computing based on photonic chips. In this work, we propose a bidirectional PhotoSolver using the propagation of optical signals in different directions on a single integrated photonic chip to perform multiple operations in solving systems of linear equations, scalable to solve large-scale systems. Specifically, we propose an in situ approach to iteratively update solutions by performing the forward and backward propagations within a single photonic chip. Furthermore, we propose a partitioning approach to solve large-scale systems using arrays of photonic chips. Numerical experiments demonstrate these capabilities with representative systems of linear equations. By utilizing lights propagating in integrated photonic chips, our PhotoSolvers provide a promising computing architecture to solve large systems of linear equations, with potentials in wide computational applications.

Magneto-optical chiral metasurfaces for achieving polarization-independent nonreciprocal transmission.

Nonreciprocal transmission, resulting from the breaking of Lorentz reciprocity, plays a pivotal role in nonreciprocal communication systems by enabling asymmetric forward and backward propagations. Metasurfaces endowed with nonreciprocity represent a compact and facile platform for manipulating electromagnetic waves in an unprecedented manner. However, most passive metasurfaces that achieve nonreciprocal transmissions are polarization dependent. While incorporation of active elements or nonlinear materials can achieve polarization-independent nonreciprocal metasurfaces, the complicated configurations limit their practical applications. To address this issue, we propose and demonstrate a passive and linear metasurface that combines magneto-optical and chiral effects, enabling polarization-independent isolation. The designed metasurface achieves a transmittance of up to 80%, with a high contrast between forward and backward propagations. Our work introduces a novel mechanism for nonreciprocal transmission and lays the foundation for the development of compact, polarization-insensitive nonreciprocal devices.

BiFSMNv2: Pushing Binary Neural Networks for Keyword Spotting to Real-Network Performance.

Deep neural networks, such as the deep-FSMN, have been widely studied for keyword spotting (KWS) applications while suffering expensive computation and storage. Therefore, network compression technologies such as binarization are studied to deploy KWS models on edge. In this article, we present a strong yet efficient binary neural network for KWS, namely, BiFSMNv2, pushing it to the real-network accuracy performance. First, we present a dual-scale thinnable 1-bit-architecture (DTA) to recover the representation capability of the binarized computation units by dual-scale activation binarization and liberate the speedup potential from an overall architecture perspective. Second, we also construct a frequency-independent distillation (FID) scheme for KWS binarization-aware training, which distills the high- and low-frequency components independently to mitigate the information mismatch between full-precision and binarized representations. Moreover, we propose the learning propagation binarizer (LPB), a general and efficient binarizer that enables the forward and backward propagation of binary KWS networks to be continuously improved through learning. We implement and deploy BiFSMNv2 on ARMv8 real-world hardware with a novel fast bitwise computation kernel (FBCK), which is proposed to fully use registers and increase instruction throughput. Comprehensive experiments show our BiFSMNv2 outperforms the existing binary networks for KWS by convincing margins across different datasets and achieves comparable accuracy with the full-precision networks (only a tiny 1.51% drop on Speech Commands V1-12). We highlight that benefiting from the compact architecture and optimized hardware kernel, BiFSMNv2 can achieve an impressive 25.1× speedup and 20.2× storage-saving on edge hardware.

Time-reversed information flow through a wormhole in scalar–tensor gravity

This Letter aims to advance unexplored properties of a new class of Closed Timelike Curves recently discovered in scalar–tensor gravity, reported in Nguyen and Lobo (2023) [31] and Nguyen and Azreg-Aïnou (2023) [30]. Therein, it was shown that when the Weak Energy Condition is violated, the topology of spacetime in scalar–tensor gravity is altered and directly enables the formation of two-way traversable wormholes. Furthermore, each of these wormholes acts a gateway between two time-mirrored worlds, where the two asymptotically flat sheets in the Kruskal–Szekeres diagram are glued antipodally along three directions—time t and the polar and azimuth angles (θ,φ) of the 2-sphere—to form a wormhole throat. This contrasts with the standard embedding diagram which typically glues the sheets only along the θ and φ directions. Crucially, due to the ‘gluing’ along the t direction, the wormhole becomes a portal connecting the two spacetime sheets with opposite physical time flows, enabling the emergence of closed timelike loops which straddle the throat. In this Letter, we shall point out that this portal mathematically permits the possibility of backward propagation of information against time. This feature is ubiquitous for wormholes in scalar–tensor theories. In addition, we formulate the Feynman sum for transition amplitudes of microscopic particles in the proximity of a wormhole throat in which we account for timelike paths that experience time reversal.

Safe dynamic sparse training of modified RBF networks for joint feature selection and classification

Developing an efficient embedded feature selection method for both binary and multiclass classification problems is a fundamental topic to be further studied. In this paper, the conventional radial basis function (RBF) network is modified for joint feature selection and classification. By utilizing the anisotropic Gaussian basis function, an individual weight parameter is assigned to each feature for feature weighting. The L1-regularized loss function is designed by combining the softmax cross entropy loss with L1 regularization terms imposing on feature and output weights. A specialized active-set limited-memory projected Quasi-Newton (SAL-PQN) algorithm is proposed to minimize the L1-regularized loss function, which can optimize all the adjustable parameters and zero out the redundant feature and output weights simultaneously. Furthermore, a safe dynamic pruning strategy is integrated into the SAL-PQN algorithm for dynamic sparse training of the modified RBF network, which continuously excludes the dynamically zeroed-out feature weights from the training process. It is theoretically assured of yielding the same gradient updates as SAL-PQN, thus the relevant computation of the zeroed-out feature weights in the forward and backward propagations can be safely eliminated. The experimental results demonstrate the effectiveness and efficiency of the proposed methods for joint feature selection and classification, and illustrate the practical utility of the inherent feature weighting capability.

Design and optimization of staggered fin structure of heat exchanger based on Machine learning

A multi-scale coupling method based on the unit heat transfer model is proposed to simulate the flow heat transfer performance of a heat exchanger, in view of the complex structure of the heat transfer unit model inside the staggered tooth type heat exchanger and the characteristics of coolant flow. The numerical simulation results are compared with experimental results, and the errors of the simulation results under different working conditions are small, indicating that the modelling method is reliable. On this basis, the heat transfer unit model parameters of staggered fins were established by three-dimensional numerical simulations. The heat transfer performance of the heat exchanger under different structures was compared using a comprehensive evaluation factor, i.e., j/f. The results and experimental data show that the best flow heat transfer performance is achieved with a liquid-side fin length of 7.2 mm, an oil-side fin length of 4.8 mm, a liquid-side fin height of 3.1 mm and an oil-side fin height of 3.1 mm, an inlet flow velocity of 0.2 m/s and a flow angle of 90°. Later, an agent model was established using backward propagation (BP) artificial neural network (ANN) to predict the flow heat transfer performance of the heat transfer unit model, and it was concluded that the f-factor, j-factor and j/f predicted by the ANN model matched well with the simulated values, and the predicted trends of different indicators were the same as the real law, which proved that the error between the predicted and actual values was small, and the above structural parameters were the best architectural parameters, which eventually improved the heat transfer performance by 17 %.

Sustainability and adaptation dynamics in Global Food Security: A Bayesian Belief Network approach

This study investigates the dependencies between the Global Food Security Index (GFSI) and indicators related to sustainability and adaptation using Bayesian Belief Network (BBN) models. Methodologically, the study utilizes the forward and backward propagation capabilities of BBNs in GeNIe software to identify critical indicators. It also examines the predictive power of these indicators by analyzing their mutual value of information in Hugin software. Data utilized in the analysis include GFSI data for 2022 and associated sustainability and adaptation indicators. Key findings reveal the critical importance of proactive risk management strategies, sustainable agricultural practices, and effective governance mechanisms in shaping food security outcomes. Disparities between high- and low-performing countries in GFSI outcomes underscore the need for tailored interventions to address systemic vulnerabilities. High-performing countries in the food security environment exhibit a very high probability of 93% of achieving high performance in the national agricultural adaptation policy. Conversely, low-performing countries exhibit a very high probability of 91% of achieving low performance in the agricultural water risk – quality indicator. The study contributes theoretically by uncovering the complex interactions within food systems and practically by offering insights for policymakers and practitioners to develop targeted interventions. The implications of the findings emphasize the importance of integrated approaches and evidence-based policymaking to address food security challenges effectively.

Hybrid optical-electronic compensation of fiber nonlinearity for long-haul coherent optical transmission

Abstract From the concepts of the dispersion-folded digital backward propagation (DBP) and optical phase conjugation (OPC), a hybrid optical-electronic nonlinearity-compensation scheme is proposed to enhance the system performance of the dispersion-managed transmission. The computational complexity of the proposed scheme, compared with that of the conventional DBP method, is reduced significantly while the performance penalty is negligible. The compensation efficiency of the proposed scheme has been validated in a 5 (and 9)-channel PM-16QAM system at 256 Gbit/s.

Exploring temporal dependencies among country-level logistics performance indicators

PurposeThe Logistics Performance Index (LPI), published by the World Bank, is a key measure of national-level logistics performance. It comprises six indicators: customs, infrastructure, international shipments, service quality, timeliness, and tracking and tracing. The objective of this study is to explore temporal dependencies among the six LPI indicators while operationalizing the World Bank’s LPI framework in terms of mapping the input indicators (customs, infrastructure, and service quality) to the outcome indicators (international shipments representing cost, timeliness, and tracking and tracing representing reliability).Design/methodology/approachA Bayesian Belief Network (BBN)-based methodology was adopted to effectively map temporal dependencies among variables in a probabilistic network setting. Using forward and backward propagation features of BBN inferencing, critical variables were also identified. A BBN model was developed using the World Bank’s LPI datasets for 2010, 2012, 2014, 2016, 2018, and 2023, covering the six LPI indicators for 118 countries.FindingsThe prediction accuracy of the model is 88.1%. Strong dependencies are found across the six LPI indicators over time. The forward propagation analysis of the model reveals that “logistics competence and quality” is the most critical input indicator that can influence all three outcome indicators over time. The backward propagation analysis indicates that “customs” is the most critical indicator for improving the performance on the “international shipments” indicator, whereas “logistics competence and quality” can significantly improve the performance on the “timeliness” and “tracking and tracing” indicators. The sensitivity analysis of the model reveals that “logistics competence and quality” and “infrastructure” are the key indicators that can influence the results across the three outcome indicators. These findings provide useful insights to researchers regarding the importance of exploring the temporal modeling of dependencies among the LPI indicators. Moreover, policymakers can use these findings to help their countries target specific input indicators to improve country-level logistics performance.Originality/valueThis paper contributes to the literature on logistics management by exploring the temporal dependencies among the six LPI indicators for 118 countries over the last 14 years. Moreover, this paper proposes and operationalizes a data-driven BBN modeling approach in this unique context.

Cone beam neutron interferometry: From modeling to applications

Phase-grating moiré interferometers (PGMIs) have emerged as promising candidates for the next generation of neutron interferometry, enabling the use of a polychromatic beam and manifesting interference patterns that can be directly imaged by existing neutron cameras. However, the modeling of the various PGMI configurations is limited to cumbersome numerical calculations and backward propagation models which often do not enable one to explore the setup parameters. Here we generalize the Fresnel scaling theorem to introduce a k-space model for PGMI setups illuminated by a cone beam, thus enabling an intuitive forward propagation model for a wide range of parameters and experimental setups. The interference manifested by a PGMI is shown to be a special case of the Talbot effect, and the optimal fringe visibility is shown to occur at the moiré location of the Talbot distances. We derive analytical expressions for the contrast and the propagating intensity profiles in various conditions and provide the first analysis of the PGMI dark-field imaging signal when considering sample characterization. The model's predictions are compared to experimental measurements and good agreement is found between them. Last, we propose and experimentally verify a method to recover contrast at typically inaccessible PGMI autocorrelation lengths. The presented work provides a toolbox for analyzing and understanding existing PGMI setups and their future applications, for example extensions to two-dimensional PGMIs and characterization of samples with nontrivial structures. Published by the American Physical Society 2024

Non-reciprocal optical bistability of sandwiched structure containing magnetic Weyl semimetals

We investigate non-reciprocal optical bistability (OB) of sandwiched structure comprising of two magnetic Weyl semimetal (WSM) layers and a nonlinear layer. The resonant tunneling mode in the sandwiched structure with a nonlinear layer creates favorable conditions for the emergence of OB. Besides, the inherent non-reciprocal nature of WSM enables non-reciprocal transmission of OB in the absence of an external magnetic field. By employing the transfer matrix method, we simulate the OB curves for forward and backward propagations, as well as analyze the non-reciprocity of OB. Furthermore, the impacts of various parameters on non-reciprocal OB are comprehensively discussed. The results demonstrate that the non-reciprocal OB curve and the width of the isolation of the non-reciprocal OB can be tuned by adjusting the thickness and the axial vector of the WSM, the temperature as well as the incident angle. This work would provide crucial insights for the design of high-performance non-reciprocal devices.