Diffraction grating parameter retrieval using non-paraxial structured beams in coherent Fourier scatterometry

In recent years, a lot of works have been published that use parameter retrieval using Orbital Angular Momentum (OAM) beams. Most make use of the OAM of different Laguerre-Gauss modes. However, those specific optical beams are paraxial beams and this limits the regime in which they can be used. In this paper, we report on the first results on retrieving the geometric parameters of a diffraction grating by analysing the corresponding complex-valued (i.e., amplitude and phase) Helmholtz Natural Modes (HNM) spectra containing both the azimuthal (i.e., n) and radial (i.e., m) indices. HNMs are a set of orthogonal, non-paraxial beams with finite energy carrying OAM. We use the coherent Fourier scatterometry (CFS) setup to calculate the field scattered from the diffraction grating. The amplitude and phase contributions of each HNM are then obtained by numerically calculating the overlap integral of the scattered field with the different modes. We show results on the sensitivity of the HNMs to several grating parameters.

Boundedness and Compactness of Hankel Operators on Large Fock Space

We introduce the BMO spaces and use them to characterize complex-valued functions f such that the big Hankel operators H f and H f ¯ are both bounded or compact from a weighted large Fock space F p ϕ into a weighted Lebesgue space L p ϕ when 1 ≤ p < ∞ .

An Approach of Integral Equations in Complex-Valued b -Metric Space Using Commuting Self-Maps

This paper is aimed at establishing some unique common fixed point theorems in complex-valued b -metric space under the rational type contraction conditions for three self-mappings in which the one self-map is continuous. A continuous self-map is commutable with the other two self-mappings. Our results are verified by some suitable examples. Ultimately, our results have been utilized to prove the existing solution to the two Urysohn integral type equations. This application illustrates how complex-valued b -metric space can be used in other types of integral operators.

Inverse scattering for three-dimensional quasi-linear biharmonic operator

We consider an inverse scattering problem of recovering the unknown coefficients of a quasi-linearly perturbed biharmonic operator in the three-dimensional case. These unknown complex-valued coefficients are assumed to satisfy some regularity conditions on their nonlinearity, but they can be discontinuous or singular in their space variable. We prove Saito’s formula and uniqueness theorem of recovering some essential information about the unknown coefficients from the knowledge of the high frequency scattering amplitude.

A Complex-Valued Encoding Multichain Seeker Optimization Algorithm for Engineering Problems

This article comes up with a complex-valued encoding multichain seeker optimization algorithm (CMSOA) for the engineering optimization problems. The complex-valued encoding strategy and the multichain strategy are leaded in the seeker optimization algorithm (SOA). These strategies enhance the individuals’ diversity, enhance the local search, avert falling into the local optimum, and are the influential global optimization strategies. This article chooses fifteen benchmark functions, four proportional integral derivative (PID) control parameter models, and six constrained engineering problems to test. According to the experimental results, the CMSOA can be used in the benchmark functions, in the PID control parameter optimization, and in the optimization of constrained engineering problems. Compared to the particle swarm optimization (PSO), simulated annealing based on genetic algorithm (SA_GA), gravitational search algorithm (GSA), sine cosine algorithm (SCA), multiverse optimizer (MVO), and seeker optimization algorithm (SOA), the optimization ability and robustness of the CMSOA are better than those of others algorithms.

Enhanced Millimeter-Wave 3-D Imaging via Complex-Valued Fully Convolutional Neural Network

To solve the problems of high computational complexity and unstable image quality inherent in the compressive sensing (CS) method, we propose a complex-valued fully convolutional neural network (CVFCNN)-based method for near-field enhanced millimeter-wave (MMW) three-dimensional (3-D) imaging. A generalized form of the complex parametric rectified linear unit (CPReLU) activation function with independent and learnable parameters is presented to improve the performance of CVFCNN. The CVFCNN structure is designed, and the formulas of the complex-valued back-propagation algorithm are derived in detail, in response to the lack of a machine learning library for a complex-valued neural network (CVNN). Compared with a real-valued fully convolutional neural network (RVFCNN), the proposed CVFCNN offers better performance while needing fewer parameters. In addition, it outperforms the CVFCNN that was used in radar imaging with different activation functions. Numerical simulations and experiments are provided to verify the efficacy of the proposed network, in comparison with state-of-the-art networks and the CS method for enhanced MMW imaging.