We investigate, in this work, the alluring properties of spiral fractional vortex beams, employing both numerical simulations and physical experiments. The spiral intensity pattern, during propagation in free space, transforms into a concentrated annular form. In addition, a novel scheme is proposed that combines a spiral phase piecewise function with a spiral transformation. This conversion of radial phase jumps to azimuthal phase jumps reveals the link between the spiral fractional vortex beam and its conventional counterpart, both of which share the same non-integer OAM mode order. We anticipate this investigation will expand the possibilities for using fractional vortex beams in optical information processing and particle handling.

A study of the Verdet constant's dispersion within magnesium fluoride (MgF2) crystals was conducted across the wavelength range from 190 nanometers to 300 nanometers. At a wavelength of 193 nanometers, the experimental findings indicated a Verdet constant of 387 radians per tesla-meter. These results were fitted according to the diamagnetic dispersion model and the classical formula of Becquerel. Employing the fitted data, one can engineer Faraday rotators for various wavelengths. These findings point to the feasibility of utilizing MgF2 as Faraday rotators, extending its application from deep-ultraviolet to vacuum-ultraviolet regions, attributed to its wide band gap.

A study of the nonlinear propagation of incoherent optical pulses, using both a normalized nonlinear Schrödinger equation and statistical analysis, demonstrates a range of operational regimes determined by the coherence time and intensity of the optical field. Evaluating the resulting intensity statistics through probability density functions reveals that, when spatial effects are absent, nonlinear propagation raises the likelihood of high intensities in a medium displaying negative dispersion, while it decreases this likelihood in a medium displaying positive dispersion. The nonlinear spatial self-focusing effect, originating from a spatial perturbation, can be minimized in the succeeding phase, influenced by the perturbation's coherence duration and its strength. Applying the Bespalov-Talanov analysis to strictly monochromatic pulses allows us to establish a benchmark for these findings.

Precisely tracking position, velocity, and acceleration, with high time resolution, is an urgent requirement for the dynamic walking, trotting, and jumping movements of highly dynamic legged robots. The ability of frequency-modulated continuous-wave (FMCW) laser ranging to provide precise measurements is evident in short-distance applications. However, the performance of FMCW light detection and ranging (LiDAR) is compromised by a low acquisition rate and nonlinearity in the laser frequency modulation over a broad bandwidth. Previous studies have not documented a sub-millisecond acquisition rate and nonlinearity correction within a wide frequency modulation bandwidth. This paper explores a synchronous nonlinearity correction algorithm applicable to a highly time-resolved FMCW LiDAR. check details The 20 kHz acquisition rate is achieved through synchronization of the laser injection current's measurement signal and modulation signal, employing a symmetrical triangular waveform. Resampling of 1000 interpolated intervals, performed during every 25-second up and down sweep, linearizes the laser frequency modulation. The measurement signal is correspondingly stretched or compressed within each 50-second interval. As per the authors' understanding, a new correlation has been established between the acquisition rate and the laser injection current's repetition frequency, which is the first such demonstration. Using this LiDAR, the trajectory of a single-legged robot's foot during its jump is meticulously recorded. A jump's upward phase demonstrates a high velocity of up to 715 m/s and an acceleration of 365 m/s². The forceful impact with the ground shows an acceleration of 302 m/s². Researchers have reported, for the first time, a foot acceleration of over 300 m/s² in a single-leg jumping robot, an achievement exceeding gravitational acceleration by more than 30 times.

Polarization holography is a highly effective tool that can be used for generating vector beams and manipulating light fields. From the diffraction characteristics of a linear polarization hologram, recorded coaxially, an approach for the generation of arbitrary vector beams is formulated. Unlike prior vector beam generation methods, this approach is unaffected by faithful reconstruction, enabling the use of arbitrary linearly polarized waves for signal detection. The polarization direction angle of the reading wave is a crucial factor in shaping the intended generalized vector beam polarization patterns. In conclusion, the flexibility of generating vector beams in this method surpasses the flexibility of previously reported methods. The experimental observations are in agreement with the anticipated theoretical outcome.

In a seven-core fiber (SCF), we demonstrated a two-dimensional vector displacement (bending) sensor with high angular resolution, utilizing the Vernier effect induced by two cascaded Fabry-Perot interferometers (FPIs). Plane-shaped refractive index modulations, serving as reflection mirrors, are produced by femtosecond laser direct writing and slit-beam shaping within the SCF, which consequently forms the FPI. check details For vector displacement measurement, three sets of cascaded FPIs are built in the center core and two non-diagonal edge cores of the SCF structure. The proposed sensor showcases high sensitivity to displacement, with a noteworthy dependence on the direction of the measured movement. Measurements of wavelength shifts enable the calculation of the fiber displacement's magnitude and direction. Furthermore, the source's variations along with the temperature's cross-reactivity can be countered by observing the central core's bending-insensitive FPI.

Utilizing existing lighting fixtures, visible light positioning (VLP) technology delivers highly accurate positioning data, making it a promising component of intelligent transportation systems (ITS). Despite theoretical advantages, the effectiveness of visible light positioning in real-world situations is constrained by signal interruptions caused by the irregular placement of light-emitting diodes (LEDs) and the substantial time needed for the positioning algorithm. Experimental results are provided in this paper for a proposed single LED VLP (SL-VLP) and inertial fusion positioning technique, which uses a particle filter (PF). The resilience of VLPs is bolstered in sparse LED light configurations. In concert with this, the time invested and the exactness of positioning under different rates of system failure and speeds are analyzed. By employing the suggested vehicle positioning technique, the experimental outcomes show mean positioning errors of 0.009 meters at 0% SL-VLP outage rate, 0.011 meters at 5.5% outage rate, 0.015 meters at 11% outage rate, and 0.018 meters at 22% outage rate.

A precise estimate of the topological transition within the symmetrically arranged Al2O3/Ag/Al2O3 multilayer is achieved by multiplying characteristic film matrices, rather than employing an effective medium approximation for the anisotropic medium. The relationship between iso-frequency curves, wavelength, and metal filling fraction is investigated in a multilayer structure composed of a type I hyperbolic metamaterial, a type II hyperbolic metamaterial, a dielectric-like medium, and a metal-like medium. The estimated negative refraction of the wave vector in a type II hyperbolic metamaterial is verified through near-field simulation.

A numerical approach, utilizing the Maxwell-paradigmatic-Kerr equations, is employed to study the harmonic radiation produced when a vortex laser field interacts with an epsilon-near-zero (ENZ) material. A laser field of substantial duration permits the generation of harmonics up to the seventh order at a laser intensity of 10^9 watts per square centimeter. Besides, the intensities of high-order vortex harmonics are greater at the ENZ frequency, directly attributable to the enhancement of the ENZ field. Quite interestingly, for a laser field with a short pulse length, the apparent frequency redshift happens beyond the amplification of high-order vortex harmonic radiation. A fluctuating field enhancement factor near the ENZ frequency and the substantial modification in the laser waveform propagating through the ENZ material are responsible. Due to a linear relationship between the topological number of harmonic radiation and its harmonic order, high-order vortex harmonics exhibiting redshift retain the precise harmonic orders dictated by each harmonic's transverse electric field pattern.

Fabricating ultra-precision optics necessitates the utilization of subaperture polishing as a key technique. Despite this, the multifaceted origins of errors in the polishing procedure result in considerable fabrication deviations, characterized by unpredictable, chaotic variations, making precise prediction through physical models challenging. check details The initial results of this study indicated the statistical predictability of chaotic errors, leading to the creation of a statistical chaotic-error perception (SCP) model. The polishing results demonstrated a roughly linear dependence on the random characteristics of the chaotic errors, which were quantified by their expected value and variance. Building upon the Preston equation, a more sophisticated convolution fabrication formula was created, enabling the quantitative prediction of the evolution of form error during each polishing cycle for various tools. This premise supports the development of a self-modifying decision model which addresses the effects of chaotic error. It employs the proposed mid- and low-spatial-frequency error criteria to enable the automated selection of tool and processing parameters. Appropriate tool influence function (TIF) selection and subsequent modification can reliably produce an ultra-precision surface possessing equivalent accuracy, even with tools exhibiting low levels of determinism. Observed through the experiment, the average prediction error for each convergence cycle was found to decrease by 614%.