Eganmcmillan7178

It is worth highlighting that, for the first time to the best of our knowledge, vertical profiles of atmospheric parameters and $C_n^2$ were measured at Lhasa, south of the Tibetan Plateau, using balloon-borne radiosondes. Based on the measurements, two new statistical models (Lhasa HMN and Lhasa Dewan) for estimating turbulence strength are proposed. Attention has been paid to evaluate the reliability of the two models to reconstruct vertical profiles of $C_n^2$ from a statistical perspective. The statistical analyses presenting the Lhasa HMN model are accompanied with lower bias, root mean square error (RMSE), and bias-corrected RMSE ($\sigma$) than those of the Lhasa Dewan model, which implies the Lhasa HMN model can better reveal the nature of turbulence characteristics of Lhasa influenced by unique local weather conditions. In addition, the comparison between the Lhasa HMN model and measurements in calculating integrated astroclimatic parameters is carried out, and the result suggests that the performance of the Lhasa HMN model is reliable and satisfactory. The new reliable $C_n^2$ model offers new insight into the characteristics of optical turbulence at Lhasa and provides support for pursuing astronomical site selection in the Tibetan Plateau.Unlike the Mueller matrix, where parameters are not directly accessible for physical interpretation, the state-generating matrix recently introduced [J. Opt. Soc. Am. A34, 80 (2017)JOAOD60740-323210.1364/JOSAA.34.000080] provides a powerful mathematical tool for formulating all properties of nondepolarizing systems. Extending this notion to the case of depolarizing differential Mueller matrices is the issue we address in this paper. We show that the formulation of the problem using complex random vectors makes it possible to directly introduce the formalism of a state-generating matrix in the case of differential depolarizing matrices. Examples of physical interpretations that can be obtained are presented specifically for a homogeneous medium. Illustrations are given when the complex vector degenerates into a complex scalar and when a Gaussian random processes hypothesis is made.We performed Mueller matrix Monte Carlo simulations of the propagation of optical radiation in diffusely scattering media for collimated incidence and report the results as a function of thickness and the angle subtended by the detector. For sufficiently small thickness, a fraction of the radiation does not undergo any scattering events and is emitted at zero angle. Thus, for a very small detector angle, the measured signal will indicate mostly the attenuation of the coherent contribution, while for larger angles, the diffuse scattering radiation will contribute significantly more. The degree to which the radiation is depolarized thus depends on the angle subtended by the detector. A three-stream model-where the coherent radiation, the forward diffusely scattered radiation, and the backward scattered radiation are propagated according to the differential Mueller matrix formalism-is introduced and describes the results from the Monte Carlo simulations and the results of measurements well. This scatter-based model for depolarization in diffusely scattering media is an alternative to that based upon elementary fluctuation theory applied to a single propagation stream. Results for average photon path length, determined from the Monte Carlo simulations, suggest that applying fluctuation theory to photon path length may unify the two approaches.We determine the interval of the inhomogeneity parameter of a Jones matrix to get physically realizable optical systems satisfying the passivity condition. It is found that the inhomogeneity parameter depends on the inner product of the eigenvectors of the Jones matrix, but its maximum value depends exclusively on its eigenvalues.Using the Richards-Wolf diffraction integral theory and the tightly focused ultrashort pulse vector model, the focusing phenomena at the focal plane of subcycle and few-cycle radially polarized ultrashort pulses are studied. The dynamic focusing is revealed at the focal plane. Mizoribine cell line First, the subcycle or few-cycle ultrashort pulses shrink towards the focus. Then the ultrashort pulses diverge from the focus. So, the convergence and divergence moving halo at the focal plane can be observed. When approaching the focus, the amplitude of the pulse becomes larger. The phenomena can be understood from the Huygens-Fresnel principle and are important for applications of the focused ultrashort pulses.We developed a new alterative technique of the digital sorting of Laguerre-Gaussian beams (LG) by radial numbers resorting to algebra of the high-order intensity moments. The term "digital mode sorting" involves sorting the main mode characteristics (in the form of a mode spectrum) by the computer cells. If necessary, the spatial mode spectrum can be reproduced, for example, by means of a spatial light modulator. In the experiment, we investigated both a single LG mode and a composition of LG modes with the same topological charge but different radial numbers subjected to perturbations via a hard-edged circular aperture. The LG beams sorting was accomplished by monitoring the amplitude spectrum of the triggered secondary LG modes then recovering the sorted modes and the perturbed beam as a whole. We have revealed degenerate states of the perturbed LG beam composition when the one kth mode in the amplitude spectrum can be related to a set of LG modes with the same radial numbers. In order to decrypt and to sort beams in such a degenerate state, it is necessary to know several keys, the number of which is equal to the number of LG modes in the initial wave composition. We were also able to analyze and to sort such degenerate mode states. For monitoring the measure of uncertainty arising in the perturbed beam, we measured informational entropy (Shannon entropy).Linear canonical transforms (LCTs) are important in several areas of signal processing; in particular, they were extended to complex-valued parameters to describe optical systems. A special case of these complex LCTs is the Bargmann transform. Recently, Pei and Huang [J. Opt. Soc. Am. A34, 18 (2017)JOAOD60740-323210.1364/JOSAA.34.000018] presented a normalization of the Bargmann transform so that it becomes possible to delimit it near infinity. In this paper, we follow the Pei-Huang algorithm to introduce the discrete normalized Bargmann transform by the relationship between Bargmann and gyrator transforms in the SU(2) finite harmonic oscillator model, and we compare it with the discrete Bargmann transform based on coherent states of the SU(2) oscillator model. This transformation is invertible and unitary. We show that, as in the continuous analog, the discrete normalized Bargmann transform converts the Hermite-Kravchuk functions into Laguerre-Kravchuk functions. In addition, we demonstrate that the discrete su(1,1) repulsive oscillator functions self-reproduce under this discrete transform with little error.