Generation of high-uniformity and high-resolution Bessel beam arrays through all-dielectric metasurfaces

Bessel beam arrays are progressively attracting attention in recent years due to their remarkable non-diffracting nature and parallel manipulation capabilities in diverse applications. However, the poor phase discretization of conventional approaches such as spatial light modulators leads to low numerical aperture (NA) beam arrays due to the limitation imposed by the Nyquist sampling theorem and poor uniformity of the beam intensity. The key contribution of this study is to experimentally demonstrate the generation of high-uniformity and high-resolution Bessel beam arrays by utilizing all-dielectric metasurfaces. This is attained by optimizing the design of the supercell of a Dammann grating, particularly decreasing each supercell of the grating to a proper size. We demonstrate a 4 × 4 array of Bessel beams with a subwavelength transverse dimension (570 nm, ∼0.9λ) and a large NA of 0.4 for each beam in the array, while maintaining a relatively high uniformity intensity (52.40%) for the array. Additionally, the Bessel beam arrays are generated in a broadband range through the proposed all-dielectric metasurfaces. Our results are of great significance and particularly useful for applications of metasurface-based Bessel beam arrays in multidisciplinary fields such as laser fabrication, biomedical imaging, data storage, and multi-particle trapping.

A PSF Approach to Far Field Discretization for Conformal Sources

In this paper we introduce a sampling scheme based on the application of an inverse source problem approach to the far field radiated by a conformal current source. The regularized solution of the problem requires the computation of the Singular Value Decomposition (SVD) of the relevant linear operator, leading to introduce the Point Spread Function in the observation domain, which can be related to the capability of the source to radiate a focusing beam. Then, the application of the Kramer generalized sampling theorem allows introducing a non-uniform discretization of the angular observation domain, tailored to each source geometry. The nearly optimal property of the scheme is compared with the best approximation achievable under a regularized inversion of the pertinent SVD. Numerical results for different two-dimensional curve sources show the effectiveness of the approach with respect to standard sampling approaches with uniform spacing, since it allows to reduce the number of sampling points of the far field.

A PSF Approach to Far Field Discretization for Conformal Sources

In this paper we introduce a sampling scheme based on the application of an inverse source problem approach to the far field radiated by a conformal current source. The regularized solution of the problem requires the computation of the Singular Value Decomposition (SVD) of the relevant linear operator, leading to introduce the Point Spread Function in the observation domain, which can be related to the capability of the source to radiate a focusing beam. Then, the application of the Kramer generalized sampling theorem allows introducing a non-uniform discretization of the angular observation domain, tailored to each source geometry. The nearly optimal property of the scheme is compared with the best approximation achievable under a regularized inversion of the pertinent SVD. Numerical results for different two-dimensional curve sources show the effectiveness of the approach with respect to standard sampling approaches with uniform spacing, since it allows to reduce the number of sampling points of the far field.

量子力学、香农采样定理与数理统计学的数学联系

对于原子的基本结构，目前物理学认为电子围绕原子核运动，其不同轨道之间通常是分离的。对波函数、坍塌的解释有不同的观点。从信号处理的角度看：不妨假设电子围绕原子核做连续的复杂运动；利用奈奎斯特-香农采样定理（Nyquist-Shannon sampling theorem），可以把高速运动的微观粒子的连续行为的长期观察结果，采样成不连续的概率方式，即量子力学。“标准”的量子力学建立时（1926年前后），数学里的概率论和数理统计学还没有发展成熟。数学工具的不足，是引起波函数与坍塌解释不同看法的数学原因。

BPSK Modulation-Based Local Oscillator-Free IQ Demodulation for Millimeter Wave Imaging

The precision of local oscillator (LO) signal in in-phase and quadrature (IQ) demodulation strongly affects the imaging performance of millimeter wave (mmWave) radars. Therefore, to eliminate the requirement for high-precision LO, a simple yet effective digital IQ demodulation method has been proposed with the aid of a specified sampling scheme in order to eliminate the demand for LO. Based on the bandpass sampling theorem, the characteristic of the intermediate frequency signal of mmWave imaging indicates that the LO is unrequired if the sampling rate is twice of the frequency of the carrier of the intermediate signal. In this way, the in-phase signal would be directly and accurately obtained by performing the Binary-Phase-Shift-Keying (BPSK) modulation on the samples, based on which the IQ demodulation would be completed by using the Hilbert transform. The proposed method does not employ LO and thus simplifies the demodulation process and is suitable for implementation in a Field-Programmable Gate Array (FPGA) with fewer hardware resources. To verify the method, a three-dimensional mmWave radar imaging is carried out at the 30-34 GHz bandwidth, where the sampling and digital IQ demodulation are realized by an ADC (AD9250) and FPGA (XC7K325T), respectively. The results show a simplified transceiver with lower requirements and the prospect of the proposed method being applied in radar imaging and other related fields.

Essentials of Geophysical Data Processing

A concise introduction to geophysical data processing - many of the techniques associated with the general field of time series analysis - for advanced students, researchers, and professionals. The textbook begins with calculus before transitioning to discrete time series via the sampling theorem, aliasing, use of complex sinusoids, development of the discrete Fourier transform from the Fourier series, and an overview of linear digital filter types and descriptions. Aimed at senior undergraduate and graduate students in geophysics, environmental science, and engineering with no previous background in linear algebra, probability, or statistics, this textbook draws scenarios and datasets from across the world of geophysics, and shows how data processing techniques can be applied to real-world problems using detailed examples, illustrations, and exercises (using MATLAB or similar computing environment). Online supplementary resources include datasets for students, and a solutions manual and all the figures from the book as PowerPoints for course instructors.

Block Sparse Bayesian Recovery with Correlated LSM Prior

Compressed sensing can recover sparse signals using a much smaller number of samples than the traditional Nyquist sampling theorem. Block sparse signals (BSS) with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. Utilizing the sparse structure can improve the recovery performance. In this paper, we consider recovering arbitrary BSS with a sparse Bayesian learning framework by inducing correlated Laplacian scale mixture (LSM) prior, which can model the dependence of adjacent elements of the block sparse signal, and then a block sparse Bayesian learning algorithm is proposed via variational Bayesian inference. Moreover, we present a fast version of the proposed recovery algorithm, which does not involve the computation of matrix inversion and has robust recovery performance in the low SNR case. The experimental results with simulated data and ISAR imaging show that the proposed algorithms can efficiently reconstruct BSS and have good antinoise ability in noisy environments.