Vectorial Hermite-Laguerre-Gaussian beams beyond the paraxial approximation

Starting from the vectorial Rayleigh-Sommerfeld integrals, the free-space propagation expressions for vectorial Hermit-Lagucrre-Gaussian （HLG） beams beyond the paraxial approximation are derived. The far-field expressions and the scalar paraxial results are given as special cases of our general expressions. The intensity distributions of vectorial nonparaxial HLG beams are studied and illustrated with numerical examples.

A Semi-Vectorial Hybrid Morphological Segmentation of Multicomponent Images Based on Multithreshold Analysis of Multidimensional Compact Histogram

In this work, we propose an original approach of semi-vectorial hybrid morphological segmentation for multicomponent images or multidimensional data by analyzing compact multidimensional histograms based on different orders. Its principle consists first of segment marginally each component of the multicomponent image into different numbers of classes fixed at K. The segmentation of each component of the image uses a scalar segmentation strategy by histogram analysis;we mainly count the methods by searching for peaks or modes of the histogram and those based on a multi-thresholding of the histogram. It is the latter that we have used in this paper, it relies particularly on the multi-thresholding method of OTSU. Then, in the case where i) each component of the image admits exactly K classes, K vector thresholds are constructed by an optimal pairing of which each component of the vector thresholds are those resulting from the marginal segmentations. In addition, the multidimensional compact histogram of the multicomponent image is computed and the attribute tuples or ‘colors’ of the histogram are ordered relative to the threshold vectors to produce (K + 1) intervals in the partial order giving rise to a segmentation of the multidimensional histogram into K classes. The remaining colors of the histogram are assigned to the closest class relative to their center of gravity. ii) In the contrary case, a vectorial spatial matching between the classes of the scalar components of the image is produced to obtain an over-segmentation, then an interclass fusion is performed to obtain a maximum of K classes. Indeed, the relevance of our segmentation method has been highlighted in relation to other methods, such as K-means, using unsupervised and supervised quantitative segmentation evaluation criteria. So the robustness of our method relatively to noise has been tested.

Nonparaxial propagation of a vectorial apertured off-axis Lorentz beam

Based on the vectorial Ftayleigh-Sommerfeld integral formula and the complex Gaussian expansion of the hardedge aperture function, an analytical propagation expression for a nonparaxial vectorial off-axis Lorentz beam passing through a rectangular aperture is derived. The unapertured case, the far field expression and the scalar paraxial result are also presented as special cases of the general formulae, respectively. Some numerical examples are also given to show the propagation characteristics of a nonparaxial vectorial off-axis Lorentz beam through a rectangular aperture. It is indicated that the f parameter, the off-axis displacement and the truncation parameter all play an important role in determining nonparaxial propagation behaviour.

VECTORIAL EKELAND VARIATIONAL PRINCIPLE AND CYCLICALLY ANTIMONOTONE EQUILIBRIUM PROBLEMS

In this article, we extend the cyclic antimonotonicity from scalar bifunctions to vector bifunctions. We find out a cyclically antimonotone vector bifunction can be regarded as a family of cyclically antimonotone scalar bifunctions. Using a pre-order principle(see Qiu, 2014), we prove a new version of Ekeland variational principle(briefly, denoted by EVP), which is quite different from the previous ones, for the objective function consists of a family of scalar functions. From the new version, we deduce several vectorial EVPs for cyclically antimonotone equilibrium problems, which extend and improve the previous results. By developing the original method proposed by Castellani and Giuli, we deduce a number of existence results(no matter scalar-valued case,or vector-valued case), when the feasible set is a sequentially compact topological space or a countably compact topological space. Finally, we propose a general coercivity condition. Combining the general coercivity condition and the obtained existence results with compactness conditions, we obtain several existence results for equilibrium problems in noncompact settings.

Spatial pattern analysis of forest trees based on the vectorial mark

Analysis of spatial patterns to describe the spatial correlation between a tree location and marks(i.e.,structural variables),can reveal stand history,population dynamics,competition and symbiosis.However,most studies of spatial patterns have concentrated on tree location and tree sizes rather than on crown asymmetry especially with direct analysis among marks characterizing facilitation and competition among of trees,and thus cannot reveal the cause of the distributions of tree locations and quantitative marks.To explore the spatial correlation among quantitative and vectorial marks and their implication on population dynamics,we extracted vertical and horizontal marks(tree height and crown projection area)characterizing tree size,and a vectorial mark(crown displacement vector characterizing the crown asymmetry)using an airborne laser scanning point cloud obtained from two forest stands in Oxfordshire,UK.Quantitatively and vectorially marked spatial patterns were developed,with corresponding null models established for a significance test.We analyzed eight types of univariate and bivariate spatial patterns,after first proposing four types.The accuracy of the pattern analysis based on an algorithm-segmented point cloud was compared with that of a truly segmented point cloud.The algorithm-segmented point cloud managed to detect 70–86%of patterns correctly.The eight types of spatial patterns analyzed the spatial distribution of trees,the spatial correlation between tree size and facilitated or competitive interactions of sycamore and other species.These four types of univariate patterns jointly showed that,at smaller scales,the trees tend to be clustered,and taller,with larger crowns due to the detected facilitations among trees in the study area.The four types of bivariate patterns found that at smaller scales there are taller trees and more facilitation among sycamore and other species,while crown size is mostly homogeneous across scales.These results indicate that interspecific facilitation and competition mainly affect tree height in the study area.This work further confirms the connection of tree size with individual facilitation and competition,revealing the potential spatial structure that previously was hard to detect.

Generation of diffraction-free vectorial elliptic hollow beams with space-varying inhomogeneous polarizations

Diffraction-free vectorial elliptic hollow beams(vEHBs)are generated by an optical system composed of a short elliptic hollow fiber(EHF)and an axicon.Each beam has a closed elliptic annular intensity profile and space-varying polarization states in its diffraction-free distance of more than 1 m.The generated beams have a counter-clockwise or clockwise periodically-rotated inhomogeneous polarization.And the spin angular momentum(SAM)of the vEHBs is 1ħor-1ħwhich is consistent with the type of dual-mode in the EHF and the periodic polarization rotations of the vEHBs.The vEHBs have potential applications in optically trapping and micromanipulating the micro-or nano-particles,quantum information transmission,and Bose-Einstein condensates,etc.

Far-field divergence of a vectorial plane wave diffracted by a circular aperture from the vectorial structure

Based on the vectorial structure of an electromagnetic wave, the analytical and concise expressions for the TE and TM terms of a veetorial plane wave diffracted by a circular aperture are derived in the far-field. The expressions of the energy flux distributions of the TE term, the TM term and the diffracted plane wave are also presented. The ratios of the power of the TE and TM terms to that of the diffracted plane wave are examined in the far-field. In addition, the far-field divergence angles of the TE term, the TM term and the diffracted plane wave, which are related to the energy flux distribution, are investigated. The different energy flux distributions of the TE and TM terms result in the discrepancy of their divergence angles. The influences of the linearly polarized angle and the radius of the circular aperture on the far-field divergence angles of the TE term, the TM term and the diffracted plane wave are discussed in detail. This research may promote the recognition of the optical propagation through a circular aperture.

Full-vectorial analysis of optical waveguides by the finite difference method based on polynomial interpolation

Based on the polynomial interpolation, a new finite difference （FD） method in solving the full-vectorial guidedmodes for step-index optical waveguides is proposed. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are considered in the absence of the limitations of scalar and semivectorial approximation, and the present PD scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for buried rectangular waveguides and optical rib waveguides are presented. The hybrid nature of the vectorial modes is demonstrated and the singular behaviours of the minor field components in the corners are observed. Moreover, solutions are in good agreement with those published early, which tests the validity of the present approach.

Vectorial Bed load Equations and River Width Dynamic Adjustment Modeling

Based on the analysis of forces acting on non-cohesive sediment particle under non-equilibrium con- dition,a vectorial equation of coarse particle movement on arbitrarily riverbed and the mathematical model used to simulate river width adjust are developed,some flume experiments for the time evolution of straight river channel are done.

A NEW DERIVATION OF THE VECTORIAL EQUATION OF MOTION FOR A TEST PARTICLE IN THE SCHWARZCHILD FIELD

A new derivation of the vectorial equation of motion for a test particle in the Schwarzchild field is given which greatly simplifies the procedure given by C. A. Murray[1]

A Simulation Model for Sexual and Vectorial Transmission of Zika Virus(ZIKV)

Nowadays the Zika virus (ZIKV) has been one of the most studied vector-borne diseases due to the considerable outbreaks that have generated around the world as well as due to the new transmission mechanisms and health complications originated. According to statistics of the INS-Colombia for July 2016, 68% of the population infected by ZIKV (confirmed cases) are pregnant women. Furthermore, the Quindío department belongs to the states with more than 50% of the total infected persons being pregnant women. Taking into account those characteristics, a theoretical model is proposed and analyzed to describe the population dynamics considering the sexual and vectorial transmission of ZIKV, with special emphasis in the consequences of the non-vectorial transmission in the population. The obtained results with simulations through the beta parameter indicate that the probability of sexual transmission between susceptible women and infected men points out the importance of campaigns to inculcate prevention measures for the safe sexual relationships between ZIKV infected population.

A General Vectorial Ekeland's Variational Principle with a P-distance

In this paper, by using p-distances on uniform spaces, we establish a general vectorial Ekeland variational principle （in short EVP）, where the objective function is defined on a uniform space and taking values in a pre-ordered real linear space and the perturbation involves a p-distance and a monotone function of the objective function. Since p-distances are very extensive, such a form of the perturbation in deed contains many different forms of perturbations appeared in the previous versions of EVP. Besides, we only require the objective function has a very weak property, as a substitute for lower semi-continuity, and only require the domain space （which is a uniform space） has a very weak type of completeness, i.e., completeness with respect to a certain p-distance. Such very weak type of completeness even includes local completeness when the uniform space is a locally convex topological vector space. From the general vectorial EVP, we deduce a general vectorial Caristi＇s fixed point theorem and a general vectorial Takahashi＇s nonconvex minimization theorem. Moreover, we show that the above three theorems are equivalent to each other. We see that the above general vectorial EVP includes many particular versions of EVP, which extend and complement the related known results.

Full vectorial feature of second-harmonic generation with full Poincaré beams

We demonstrate the full vectorial feature of second-harmonic generation(SHG), i.e., from infrared full Poincaré beams to visible full Poincaré beams, based on two cascading type I phase-matching beta barium borate crystals of orthogonal optical axes. We visualize the structured features of the vectorial SHG wave by using Stokes polarimetry and show the interesting doubling effect of the polarization topological index, i.e., a low-order full Poincaré beam is converted to a high-order one. However, the polarization singularities of both C points and L lines are found to keep invariant during the SHG process. Our scheme could offer a deeper understanding on the interaction of vectorial light fields with media and can be generalized to other nonlinear optical effects.

Revealing complex optical phenomena through vectorial metrics

Advances in vectorial polarization-resolved imaging are bringing new capabilities to applications ranging from fundamental physics through to clinical diagnosis.Imaging polarimetry requires determination of the Mueller matrix(MM)at every point,providing a complete description of an object’s vectorial properties.Despite forming a comprehensive representation,the MM does not usually provide easily interpretable information about the object’s internal structure.Certain simpler vectorial metrics are derived from subsets of the MM elements.These metrics permit extraction of signatures that provide direct indicators of hidden optical properties of complex systems,while featuring an intriguing asymmetry about what information can or cannot be inferred via these metrics.We harness such characteristics to reveal the spin Hall effect of light,infer microscopic structure within laser-written photonic waveguides,and conduct rapid pathological diagnosis through analysis of healthy and cancerous tissue.This provides new insight for the broader usage of such asymmetric inferred vectorial information.

A non-local vectorial total variational model for multichannel SAR image speckle suppression

Abstract This paper aims at the multichannel synthetic aperture radar （SAR） image speckle reduc- tion. This paper proposes a novel energy minimized regularization model for multichannel image denoising, which is an extension of the non-local total variational model for gray-scale image. It contains two terms, namely the vectorial data fidelity term and the non-local vectorial total variation term. The latter is constructed by high-dimensional non-local gradient that contains the structure information of the multichannel image. The existence and the uniqueness of the solution of the model are proved. A fixed point iterative algorithm is designed to acquire the solution of this model. The convergence property of this algorithm is proved as well. This model is applied to the multipolarimetric and multi-temporal RAI）ARSAT-2 images despeckling. The result shows that this model performs better than the original vectorial total variational model on texture preserving.

Creation of radially polarized optical fields with multiple controllable parameters using a vectorial optical field generator

A vectorial optical field generator(VOF-Gen) based on two reflective phase-only liquid crystal spatial light modulators enables the creation of an arbitrary optical complex field. In this work, the capabilities of the VOF-Gen in terms of manipulating the spatial distributions of phase, amplitude, and polarization are experimentally demonstrated by generating a radially polarized optical field consisted of five annular rings, the focusing properties of which are also numerically studied with vectorial diffraction theory. By carefully adjusting the relative amplitude and phase between the adjacent rings, an optical needle field with purely longitudinal polarization can be produced in the focal region of a high numerical aperture lens. The versatile method presented in this work can be easily extended to the generation of a vectorial optical field with any desired complex distributions.

Vectorial Variational Principle with Variable Set-Valued Perturbation

We give a general vectorial Ekeland＇s variational principle, where the objective function is defined on an F-type topological space and taking values in a pre-ordered real linear space. Being quite different from the previous versions of vectorial Ekeland＇s variational principle, the perturbation in our version is no longer only dependent on a fixed positive vector or a fixed family of positive vectors. It contains a family of set-valued functions taking values in the positive cone and a family of subadditive functions of topology generating quasi-metrics. Hence, the direction of the perturbation in the new version is a family of variable subsets which are dependent on the objective function values. The general version includes and improves a number of known versions of vectorial Ekeland＇s variational principle. From the general Ekeland＇s principle, we deduce the corresponding versions of Caristi-Kirk＇s fixed point theorem and Takahashi＇s nonconvex minimization theorem. Finally, we prove that all the three theorems are equivalent to each other.

Ultrafast multi-target control of tightly focused light fields

The control of ultrafast optical field is of great interest in developing ultrafast optics as well as the investigation on vari-ous light-matter interactions with ultrashort pulses.However,conventional spatial encoding approaches have only lim-ited steerable targets usually neglecting the temporal effect,thus hindering their broad applications.Here we present a new concept for realizing ultrafast modulation of multi-target focal fields based on the facile combination of time-depend-ent vectorial diffraction theory with fast Fourier transform.This is achieved by focusing femtosecond pulsed light carrying vectorial-vortex by a single objective lens under tight focusing condition.It is uncovered that the ultrafast temporal de-gree of freedom within a configurable temporal duration(~400 fs)plays a pivotal role in determining the rich and exotic features of the focused optical field at one time,namely,bright-dark alternation,periodic rotation,and longitudinal/trans-verse polarization conversion.The underlying control mechanisms have been unveiled.Besides being of academic in-terest in diverse ultrafast spectral regimes,these peculiar behaviors of the space-time evolutionary beams may underpin prolific ultrafast-related applications such as multifunctional integrated optical chip,high-efficiency laser trapping,micro-structure rotation,super-resolution optical microscopy,precise optical measurement,and liveness tracking.

Tight focusing of femtosecond elliptically polarised vortex light pulses

This paper studies the tight focusing properties of femtosecond elliptically polarised vortex light pulses. Based on Richards-Wolf vectorial diffraction integral, the expressions for the electric field, the velocity of the femtosecond light pulse and the total angular momentum of focused pluses are derived. The numerical calculations are also given to illustrate the intensity distribution, phase contour, the group velocity variation and the total angular momentum near the focus. It finds that near the focus the femtosecond elliptically polarised vortex light pulse can travel at various group speeds, that is, slower or faster than light speed in vacuum, depending on the numerical aperture of the focusing objective system. Moreover, it also studies the influence of the numerical aperture of the focusing objective and the time duration of the elliptically polarised vortex light pulse on the total angular momentum distribution in the focused field.

A 3-Node Co-Rotational Triangular Finite Element for Non-Smooth,Folded and Multi-Shell Laminated Composite Structures

Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.