Coherence Properties and Intensity Distribution of a Partially Coherent Lorentz–Gauss Beam Emerging from the Axicon

The propagation of a partially Lorentz–Gauss beam in a uniform-intensity diffractive axicon is studied according to the Huygens–Fresnel principle, the Hermite–Gaussian expansion of a Lorentz function, and using the stationary phase method. We have derived the intensity equation of a partially coherent Lorentz-Gauss beams propagating through uniform-intensity diffractive axicon, and we proved mathematically that it is the superposition of Bessel beams of various orders after emerging from axicon, using Hermite’s function series and the Bessel function integral formulas. The results show that the intensity distribution of the diffracted beam is the intensity pattern evolved from a Lorentz–Gauss shaped spot into a Gaussian-shaped spot at any position on the focal length of the axicon, and the intensity distribution of a partially Lorentz–Gauss beam generated by an axicon becomes uniform by increasing the beam width and more uniform and constant with the larger coherence width.

Stationary Phase Method in Discrete Wigner Functions and Classical Simulation of Quantum Circuits

One of the lowest-order corrections to Gaussian quantum mechanics in infinite-dimensional Hilbert spaces are Airy functions: a uniformization of the stationary phase method applied in the path integral perspective. We introduce a "periodized stationary phase method" to discrete Wigner functions of systems with odd prime dimension and show that the π8 gate is the discrete analog of the Airy function. We then establish a relationship between the stabilizer rank of states and the number of quadratic Gauss sums necessary in the periodized stationary phase method. This allows us to develop a classical strong simulation of a single qutrit marginal on t qutrit π8 gates that are followed by Clifford evolution, and show that this only requires 3t2+1 quadratic Gauss sums. This outperforms the best alternative qutrit algorithm (based on Wigner negativity and scaling as ∼30.8t for 10−2 precision) for any number of π8 gates to full precision.

The Evaluation of an Asymptotic Solution to the Sommerfeld Radiation Problem Using an Efficient Method for the Calculation of Sommerfeld Integrals in the Spectral Domain

A recently developed high-frequency asymptotic solution for the famous “Sommerfeld radiation problem” is revisited. The solution is based on an analysis performed in the spectral domain, through which a compact asymptotic formula describes the behavior of the EM field, which emanates from a vertical Hertzian radiating dipole, located above flat, lossy ground. The paper is divided into two parts. We first demonstrate an efficient technique for the accurate numerical calculation of the well-known Sommerfeld integrals. The results are compared against alternative calculation approaches and validated with the corresponding Norton figures for the surface wave. In the second part, we introduce the asymptotic solution and investigate its performance; we compare the solution with the accurate numerical evaluation for the received EM field and with a more basic asymptotic solution to the given problem, obtained via the application of the Stationary Phase Method. Simulations for various frequencies, distances, altitudes, and ground characteristics are illustrated and inferences for the applicability of the solution are made. Finally, special cases leading to analytical field expressions close as well as far from the interface are examined.

Dispersive Estimates for Full Dispersion KP Equations

We prove several dispersive estimates for the linear part of the Full Dispersion Kadomtsev–Petviashvili introduced by David Lannes to overcome some shortcomings of the classical Kadomtsev–Petviashvili equations. The proof of these estimates combines the stationary phase method with sharp asymptotics on asymmetric Bessel functions, which may be of independent interest. As a consequence, we prove that the initial value problem associated to the Full Dispersion Kadomtsev–Petviashvili is locally well-posed in $$H^s(\mathbb R^2)$$ H s ( R 2 ) , for $$s>\frac{7}{4}$$ s > 7 4 , in the capillary-gravity setting.

High Sensitive Chiral Molecule Detector Based on The Amplified Lateral Shift in Kretschmann Configuration Involving Chiral TDBCs

We investigate a high sensitive chiral molecule detector based on Goos-Hanchen shift (S) in Kretschmann configuration involving chiral TDBCs. Fresnel equations and the stationary phase method are employed to calculate S. Due to the interaction between surface plasmon polaritons and chiral TDBCs, S with chiral TDBCs are amplified at near the resonant wavelengths of chiral TDBCs. Our calculation results show that although the difference between the resonant wavelengths of left and right TDBCs is 4.5nm, the difference of S with chiral TDBCs (ΔS) can reach to 400 times as the incident wavelength in certain conditions, which can be easily observed in experiments. There is an optimal thickness of the metal film to realize the largest difference of S between Kretschmann configurations with left TDBCs and right TDBCs. We also find that the positions of the largest S for the structures with left TDBCs and right TDBCs do not overlap. Furthermore, we discuss the oscillator strength f, which is mainly determined by TDBC concentration. We find that our proposed detector is quite sensitive with f. By changing f from 0.008 to 0.014 with the step of 0.002, the change of ΔS is no less than 5 times of the incident wavelength (2.9μm). Our proposed structure is very sensitive and has potential applications in experiments.

Vector Rayleigh Diffraction of High-Power Laser Diode Beam in Optical Communication

Laser diodes (LDs) are widely used in optical wireless communication (OWC) and optical networks, and proper theoretical models are needed to precisely describe the complicated beam field of LDs. A novel mathematical model is proposed to describe the vectorial field of nonparaxial LD beams. Laser beam propagation is studied using the vector Rayleigh diffraction integrals, and the stationary phase method is used to find the asymptotic expansion of diffraction integral. The far-field distribution of the LD beam in the plane parallel and perpendicular to the junction is considered in detail, and the computed intensity distributions of the theory are compared with the corresponding measurements. This model is precise for single transverse model beam of LDs and can be applied to describe the LD beams in OWC and optical networks.

A fieldable, high-throughput, cost-efficient high performance liquid chromatography-ultraviolet absorption detection (HPLC-UV) method for the quantitation of bispyridinium quaternary aldoxime cholinesterase reactivators in blood

Mono- and bis-pyridinium quaternary aldoximes (K-oximes) have long been employed as cholinesterase reactivator components of antidotes against lethal cholinesterase-inhibiting organophosphorous chemicals. Their positive charge poses difficulties in their chromatographic analysis, resulting in the publication of different approaches for each K-oxime. A multiplexed method is presented for the rapid quantitation of 10 K-oximes in blood with its utility demonstrated in vivo. Liquid chromatography with absorbance detection was employed. Reversed-phase separation was achieved on a highly nonpolar stationary phase. Method validation was based on the respective guideline of the European Medicines Agency. Times to peak concentrations and 120-min areas under the time–concentration curves were determined in rats following intraperitoneal administration. Adequate retention and separation of K-oximes with acceptable peak shapes in short isocratic runs was achieved by adjusting ionic strength, organic content and the concentration of the ion-pairing agent of the mobile phase. Chromatographic properties were governed by optimizing the concentration of dissolved ions. Accurate adjustment of the organic content was indispensable for avoiding peak drifting and splitting. Dose-adjusted exposure to K-347 and K-868 was exceptionally low, while exposure to K-48 was the highest. The method is suitable for screening systemic exposure to various K-oximes and can be extended.