Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2503.23195

Accurate paraxial Maxwell beams

Tomasz Radozycki
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this work, the paraxial version of Maxwell equations is derived with the use of two Riemann-Silberstein vectors. Exact solutions of these equations are then obtained representing the paraxial electromagnetic fields. These fields satisfy the full Maxwell equations up to the order of $(λ/w_0)^2$. The solutions contain some additional terms, which turn out to be relevant for polarization, especially in the case of beams endowed with orbital angular momentum.

Explore related subjects

physics.optics

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Tomasz Radozycki. 2025-03-29. Accurate paraxial Maxwell beams. https://arxiv.org/abs/2503.23195

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Exoplanet Detection Using Adaptive Quantum-Optimal Measurement

Detecting terrestrial exoplanets in the habitable zones of nearby stars remains a critical challenge. Such planets can be \(10^8\) to \(10^{10}\) times fainter than their host stars and lie at diffraction-limited angular separations, where starlight strongly obscures the companion signal. Here we present an adaptive quantum measurement method for estimating the number, positions, and brightnesses of mutually incoherent point sources in the sub-Rayleigh, ultra-high-contrast regime, operating at contrasts down to \(10^{-8}\) -- five orders of magnitude beyond previous quantum imaging approaches to exoplanet detection. The method adopts a spatial-mode basis that is updated to maximize the quantum Fisher information per detected photon. Estimation is performed by maximum likelihood in log-brightness coordinates, and the source count is determined by Bayesian-information-criterion (BIC) model selection directly from photon-count statistics, without a tunable detection threshold. For point sources within sub-Rayleigh separations and with brightness ratios spanning eight orders of magnitude, the method reconstructs complete scenes with a mean success rate of \(72.5\%\). Furthermore, it is robust to misalignment, maintaining a \(71.3\%\) success rate under offsets of up to six pixels. These results demonstrate that terrestrial exoplanets can be detected below the Rayleigh limit, a regime previously inaccessible to direct imaging.

physics.optics↗
arXiv2026

Research and simulation of analytical polarization control enabled by optical computing on an integrated photonics chip

Dynamic polarization controllers are key devices with broad applications in many fields. However, most on-chip polarization controllers still rely on traditional blind-search methods, whereas analytical optical-computing approaches remain insufficiently explored, particularly with respect to calibration and endless polarization control. With the accurate relative phase of Mach-Zehnder interferometer (MZI) being fully controllable on an integrated photonics chip, we present an analytical polarization control (APC) method using four phase shifters and optical computing, eliminating the need for the traditional inefficient blind-search procedure. The basic structures and operations of APC are clarified. The proposed calibration method and endless control method enable continuous APC while compensating for phase differences within the MZI structures. We simulate the influence of the endless control unit on polarization control and quantify the effect of the fourth phase difference on the output extinction ratio. With the fourth phase shifter, the phase difference encountered during Stokes vector measurement can be effectively compensated, and rotations around all three axes on the Poincaré sphere can be realized. These results establish a practical APC architecture based on optical computing for photonics chips. The proposed APC methods, combined with a FPGA-based hardware acceleration, will enable high speed on-chip polarization controllers.

physics.optics↗
arXiv2026

Optical Mode Sorting with a Programmable Diffractive Neural Network

Programmable diffractive optical processors are particularly attractive for spatial light manipulation because their optical transformations can be dynamically reconfigured and adapted without modifying the physical hardware. However, their practical performance is often limited by the gap between simulation and experiment caused by optical aberrations, alignment errors, and nonideal phase responses. In this paper, we introduce a hybrid optimization framework that combines high-dimensional numerical design with low-dimensional hardware-in-the-loop calibration, enabling programmable diffractive optical networks to compensate experimentally for mismatch without retraining their underlying optical transformations. We demonstrate a programmable optical diffractive neural network (ODNN) designed by back-propagation to spatially sort six linearly polarized modes supported by a multimode fiber. The experimental distortions are represented using a truncated Zernike basis with only 19 correction coefficients per layer. These coefficients are optimized directly on the physical system using stochastic parallel gradient descent, avoiding re-optimization of the full pixelated phase masks. Experimentally, the proposed calibration yields an SNR improvement of approximately 3.26 dB, and a decrease in amplitude error of 0.04. This separation of high-dimensional optical-function design from low-dimensional physical calibration provides a scalable route towards adaptive and reconfigurable spatial-mode processors for optical router on spatial modes and wavelengths, programmable photonic computer systems and quantum information processing.

physics.optics↗