A Single Noninterleaved Metasurface for High-Capacity and Flexible Mode Multiplexing of Higher-Order Poincaré Sphere Beams

Cylindrical vector vortex beams, a particular class of higher-order Poincaré sphere beams, are generalized forms of waves carrying orbital angular momentum with inhomogeneous states-of-polarization on their wavefronts. Conventional methods as well as the more recently proposed segmented/interleaved shared-aperture metasurfaces for vortex beam generation are either severely limited by bulky optical setups or by restricted channel capacity with low efficiency and mode number. Here, a noninterleaved vortex multiplexing approach is proposed, which utilizes superimposed scattered waves with opposite spin states emanating from all meta-atoms in a coherent manner, counter-intuitively enabling ultrahigh-capacity, high-efficiency, and flexible generation of massive vortex beams with structured state-of-polarization. A series of exemplary prototypes, implemented by sub-wavelength-thick metasurfaces, are demonstrated experimentally, achieving kaleidoscopic vector vortex beams. This methodology holds great promise for structured wavefront shaping, vortex generation, and high information-capacity planar photonics, which may have a profound impact on transformative technological advances in fields including spin-Hall photonics, optical holography, compressive imaging, electromagnetic communication, and so on.     

Diffractive properties of obstructed vector Laguerre-Gaussian beam under tight focusing condition

Diffractive and focusing properties of vector Laguerre-Gaussian beams with obstacle are investigated under tight focusing conditions. Using vector diffraction theory, intensity and polarization distributions near the focus at different orthogonal planes are calculated and analyzed for vector Laguerre-Gaussian beams. It is observed that the beam is able to compensate the distortion produced by obstacles when the size of the obstacle is small. The structural changes in the polarization distribution are not the same in different orthogonal planes. The polarization characteristics of the beam show a significant change when the size of the obstacle is large. A comparative study of the focusing and diffractive properties of vector Laguerre-Gaussian and vector Bessel-Gaussian beams has also been performed.     

Beam modes in graded-index media and topological phases

The change in the polarization plane of light vector beams retaining their shape (beam modes) under propagation through gradient-index media is evaluated as a topological phase acquired by cyclic and noncyclic evolutions of these beams on their projective Hilbert space (momentum sphere). The polarization changes are evaluated by means of the characteristic parameters of the light beam selected.     

Nonparaxial analyses of cylindrical vector beams with arbitrary polarization order in the far field

Abstract

Based on the vector angular spectrum representation and the method of stationary phase, the analytical expressions for the electromagnetic fields of the cylindrical vector Laguerre–Gaussian beams with arbitrary polarization order are derived in the far field. The radially, anti-vortex and linearly polarized beams can be viewed as the special cases of our general result. The analyses indicate that the beam evolution properties and nonparaxiality are closely related to the radial mode number, the polarization order number and the ratio of the waist width to the wavelength. The high polarization order cylindrical vector beams compared with the radially polarized beams are more influenced by the nonparaxiality. This research provides a convenient approach to manipulate the cylindrical vector Laguerre–Gaussian beams by choosing the special state of polarization.     

Formation of a sub-wavelength longitudinally polarized beam using a radially polarized controllable dark-hollow beam

On the basis of vector diffraction theory, the tightly focusing properties of radially polarized controllable dark-hollow (CDH) beams are examined theoretically. Calculation results demonstrate that by choosing the initial parameters of the proposed light beams suitably, a sub-wavelength (0.422λ) longitudinally polarized light beam with high beam quality (82.2%) can be formed without any filters. Meanwhile, we find that a relatively long depth of focus benefits from larger beam order. The dependence of the focal spot size on the parameters such as truncation parameter, variation constant, and beam order is also explored in detail. Moreover, an alternative method to generate the CDH beams is proposed.     

Singularities in cylindrical vector beams

Cylindrical vector beams with azimuthal and radial polarization distributions are studied for singularities. It is shown experimentally that these beams have screw dislocation as well as edge dislocation at the same time. The relation between phase and polarization of light beam is the key to understand this fact. We envisage that this has potential application in phase synthesis using polarization engineering. Further, the polarization singularities in these inhomogeneously polarized beams are examined by measuring Stokes parameters across the cross-section of these beams.     

Controllable elliptical dark-hollow beams

A new (to our knowledge) kind of light beam called the controllable elliptical dark-hollow beam (CEDHB), is introduced to describe dark-hollow beams with axially rotational asymmetry by using the tensor method. The propagation formulas of CEDHBs through paraxial aligned and misaligned nonsymmetrical optical systems are derived through vector integration. With the derived formulas, the propagation properties of CEDHBs in free-space propagation and through a misaligned thin lens are studied graphically. The CEDHBs provide a convenient model to describe and treat dark-hollow beams with axially rotational asymmetry and can be used conveniently to analyze atoms manipulated with a dark-hollow beam.     

Tight focusing properties of hybridly polarized vector beams

We theoretically investigate the tight focusing properties of hybridly polarized vector beams. Some numerical results are obtained to illustrate the intensity, phase, and polarization of tightly focused hybridly polarized vector beams. It is shown that the shape of the focal pattern may change from an elliptical beam to a ring focus with increasing radial index. The phase distribution around the tightly focused ring is shown to be the helical phase profile, indicating that the radial-variant spin angular momentum of hybridly polarized vector beams can be converted into the radial-variant orbital angular momentum.     

Some closed-form solutions in random vibration of Bernoulli-Euler beams

The only closed-form solutions for random vibration of beams are that due to Houdijk, for the tip mean-square displacement of a cantilever beam under space- and time-wise ideal white noise, and that due to Eringen for a simply-supported beam under identical excitation. In both instances, beams possessing transverse damping were treated. In the present study closed-form solutions are found for uniform, simply supported beams subjected to a stationary excitation that is white both in space and time. The beams possess either structural, Voigt or rotary damping mechanisms. Expressions are obtained for the space-time correlation functions of displacement, velocity and stress. Previously derived interesting conclusions by Crandall and Yildiz on divergence of the mean-square stress for a beam with Voigt damping, and its convergence for the beam with combined transverse and rotary damping, are confirmed. Moreover, the closed form solution is obtained for the probabilistic characteristics of a beam under a number of separate or combined dampings.     

Triple-beam lens transducers for three-dimensional ultrasonic fluidflow estimation

This paper reports on estimating the 3-D flow velocity vector of blood with ultrasound triple-beam lens transducers. The design, construction, and characterization of experimental lens transducers is described along with the theory of 3-D flow velocity estimation. A triple beam lens transducer consists of three piezoelectric elements mounted on the top surface of a lens. The lens acts to direct and focus the ultrasound from the elements such that three parallel, closely spaced ultrasound beams are generated. Blood cell scatterers are tracked as they move along the beams and from beam to beam using RF correlation techniques. Lenses from fused quartz and aluminum have been designed and fabricated, and the characteristics of the lenses along with lens design considerations and tradeoffs are discussed. The three-dimensional flow velocity vector of fluid in a blood flow phantom has been experimentally measured with an aluminum lens, indicating that the accurate estimation of the 3-D blood flow velocity vector is possible     

Experimental studies of new ductile coupling beams and multi-storey shear walls

The span-depth ratios of coupling beams to interconnect shear walls are generally small, so that brittle shear failure may occur and lead to reduced ductility. In order to improve the ductility of coupling beams for earthquake loading, a new type of ductile coupling beam is proposed in this paper. Along the middle depth of this beam, a slit through the entire thickness (a narrow hole) near each end and two lateral keyways along the remaining middle part of the span are made. The reductions of the stiffness under service load and the ultimate carrying capacity of the beam due to the weakening mentioned above are small and the ductility is greatly increased. Tests of 4-storey walls interconnected by coupling beams in three different constructions (monolithic beams, beams with a through-slit and new-type beams) indicated that shear walls with the new coupling beams possess the best aseismic behaviours under cyclic loading. The proposed new coupling beam has been used in a high-rise building.     

Polarization pattern of vector vortex beams generated by q-plates with different topological charges

We describe the polarization topology of the vector beams emerging from a patterned birefringent liquid crystal plate with a topological charge q at its center (q-plate). The polarization topological structures for different q-plates and different input polarization states have been studied experimentally by measuring the Stokes parameters point-by-point in the beam transverse plane. Furthermore, we used a tuned q=1/2-plate to generate cylindrical vector beams with radial or azimuthal polarizations, with the possibility of switching dynamically between these two cases by simply changing the linear polarization of the input beam.     

Structural damage identification using transfer matrix with lumped crack properties

A novel damage detection scheme is developed for detecting multiple cracks in beams, based on a transfer matrix (TM) approach. Lumped Crack TM of a beam element with multiple cracks is derived based on lumped crack properties. A cracked beam element is assumed as two intact beam elements connected with a hinge or torsional spring. The crack is modelled as an element of zero length and mass, but with elastic properties. Lumped crack approach is simpler for multiple cracks than the possible alternative methods. The state vector at a node includes displacements, forces and moments at that node; when it is multiplied with TM the state vector at the adjacent node can be obtained. The crack identification strategy used here, involves measuring the initial state vector at a node, in the zone of interest. The displacements at the adjacent nodes are measured and these are predicted using TM. Using an optimization algorithm the unknown crack parameters in the TM are solved by minimizing the deviation between measured and predicted displacements. The method is verified using several numerical models as well as experiments with cracked beams. The TM is shown to be suitable for local identification and also fast and accurate compare to other methods.     

Vector wave analysis for nonnormal incident rays in epimicroscopic refractive index profile measurements

We have investigated the effects of nonnormal incident rays in calculating the refractive index profile of a dielectric sample using the reflectance measurement data obtained with a scanning confocal epimicroscope and also by solving three-dimensional vector wave equations for linearly polarized light. The numerically calculated reflection data of tightly focused Gaussian beams with different numerical apertures (NAs) on planar surfaces with various refractive indices confirm that the reflectance increases with an increase in the NA of a focusing objective lens. This is due to the nonnormal incident ray components of a Gaussian beam. We have found that the refractive index obtained with the assumption of a normal incident beam is far from the real value when the NA of a focusing lens becomes larger than 0.5, and thus the variation in the reflectance for different angular components in a Gaussian beam must be taken into consideration while using a larger NA lens. Errors in practical refractive index calculation for an optical fiber based on a normal incident beam in reflectance measurements can be as large as 1% in comparison to real values calculated by our three-dimensional vector wave equations.     

基于铁木辛柯梁理论的工字梁剪切变形计算方法研究

飞机机翼通常采用工字梁作为支撑结构,然而由于工字梁的几何参数改变,理论计算会受到影响,梁理论的选择会直接影响计算结果。目前,现有的工字梁挠度计算主要基于欧拉-伯努利梁理论,未充分考虑梁弯曲时存在的剪切变形。因此,本文提出了一种基于铁木辛柯梁理论的考虑剪切作用的工字梁计算方法,用于针对受集中力影响的工字梁进行计算。通过表征剪切变形对梁变形的影响,获得了剪切变形对梁的作用规律,并解释了剪切变形在梁中的变形机制。研究表明,当工字悬臂梁靠近固定端一定范围内以及梁的跨高比小于5时,计算时应考虑剪切变形的影响。该计算方法得出的内力计算理论结果与仿真及电测法结果基本一致,可以应用于实际工程计算中。     

Conversion of the high-mode solitons in strongly nonlocal nonlinear media

The conversion of high-mode solitons propagating in Strongly Nonlocal Nonlinear Media (SNNM) in three coordinate systems, namely, the elliptic coordinate system, the rectangular coordinate system and the cylindrical coordinate system, based on the Snyder–Mitchell Model that describes the paraxial beam propagating in SNNM, is discussed. Through constituting the trial solution with modulating the Gaussian beam by Ince polynomials, the closed-solution of Gaussian beams in elliptic coordinate is accessed. The Ince–Gaussian (IG) beams constitute the exact and continuous transition modes between Hermite–Gaussian beams and Laguerre–Gaussian (LG) beams, which is controlled by the elliptic parameter. The conditions of conversion in the three types of solitons are given in relation to the Gouy phase invariability in stable propagation. The profiles of the IG breather at a different propagating distance are numerically obtained, and the conversions of a few IG solitons are illustrated. The difference between the IG soliton and the corresponding LG soliton is remarkable from the Poynting vector and phase plots at their profiles along the propagating axis.     

Calculating the pressure force of the non-paraxial cylindrical Gaussian beam exerted upon a homogeneous circular-shaped cylinder

Forces exerted upon a dielectric cylinder of infinite length and arbitrary, or circular, cross-section by the non-paraxial cylindrical Gaussian beam are considered. The projections of the vector of the light force pressure exerted upon a dielectric cylinder of arbitrary and circular cross-section are expressed analytically. In particular, the pressure force is expressed through the coefficients of decomposition of the non-paraxial Gaussian beam into the cylindrical functions. Using numerical examples, a possibility to optically trap a circular-shaped cylinder in two oppositely directed Gaussian beams or a single non-paraxial Gaussian beam is demonstrated.     

Sharper focal spot formed by higher-order radially polarized laser beams

The intensity distributions near the focal point for radially polarized laser beams including higher-order transverse modes are calculated based on vector diffraction theory. For higher-order radially polarized mode beams as well as a fundamental mode (R-TEM01*) beam, the strong longitudinal component forms a sharper spot at the focal point under a high-NA focusing condition. In particular, double-ring-shaped radially polarized mode (R-TEM11*) beams can effectively reduce the focal spot size because of destructive interference between the inner and the outer rings with pi phase shift. Compared with an R-TEM01* beam focusing in a limit of NA=1, the full width at half-maximum values of the focal spot for an R-TEM11* beam are decreased by 13.6% for the longitudinal component and 25.8% for the total intensity.     

Laser beam propagation in atmospheric turbulence

The optical effects of atmospheric turbulence on the propagation of low power laser beams are reviewed in this paper. The optical effects are produced by the temperature fluctuations which result in fluctuations of the refractive index of air. The commonly-used models of index-of-refraction fluctuations are presented. Laser beams experience fluctuations of beam size, beam position, and intensity distribution within the beam due to refractive turbulence. Some of the observed effects are qualitatively explained by treating the turbulent atmosphere as a collection of moving gaseous lenses of various sizes. Analytical results and experimental verifications of the variance, covariance and probability distribution of intensity fluctuations in weak turbulence are presented. For stronger turbulence, a saturation of the optical scintillations is observed. The saturation of scintillations involves a progressive break-up of the beam into multiple patches; the beam loses some of its lateral coherence. Heterodyne systems operating in a turbulent atmosphere experience a loss of heterodyne signal due to the destruction of coherence.