Optical trapping with focused Airy beams

Airy beams are attractive owing to their two intriguing properties--self-bending and nondiffraction--that are particularly helpful for optical manipulation of particles. We perform theoretical and experimental investigations into the focusing property of Airy beams and provide insight into the trapping ability of tightly focused Airy beams. Experiment on optical tweezers demonstrates that the focused Airy beams can create multiple traps for two-dimensional confining particles, and the stable traps exist in the vicinity of the main intensity lobes in the focused beams. The trapping pattern can be varied with changes in the cross section of the focused beam. The focused Airy beam offers a novel way of optically manipulating microparticles.     

Airy pulsed beams

The Airy beam (AiB) has attracted a lot of attention recently because of its intriguing features; the most distinctive ones are the propagation along curved trajectories in free space and the weak diffraction. We have previously shown that the AiB is, in fact, a caustic of the rays that radiate from the tail of the Airy function aperture distribution. Here we derive a class of ultra wideband Airy pulsed beams (AiPBs), which are the extension of the AiB into the time domain. We introduce a frequency scaling of the initial aperture field that renders the ray skeleton of the field, including the caustic, frequency independent, thus ensuring that all the frequency components propagate along the same curved trajectory and that the AiPB does not disperse. The resulting AiPB preserves the intriguing features of the time-harmonic AiB discussed above. An exact closed-form solution for the AiPB is derived using the spectral theory of transients. We also derive wavefront approximations for the field in the time window around the pulse arrival, which are valid uniformly in the vicinity of the caustic. These approximations are based on the so-called uniform geometrical optics, which is extended here to the time domain.     

Nonparaxial wave analysis of three-dimensional Airy beams

The three-dimensional Airy beam (AiB) is thoroughly explored from a wave-theory point of view. We utilize the exact spectral integral for the AiB to derive local ray-based solutions that do not suffer from the limitations of the conventional parabolic equation (PE) solution and are valid far beyond the paraxial zone and for longer ranges. The ray topology near the main lobe of the AiB delineates a hyperbolic umbilic catastrophe, consisting of a cusped double-layered caustic. In the far zone this caustic is deformed and the field loses its beam shape. The field in the vicinity of this caustic is described uniformly by a hyperbolic umbilic canonical integral, which is structured explicitly on the local geometry of the caustic. In order to accommodate the finite-energy AiB, we also modify the conventional canonical integral by adding a complex loss parameter. The canonical integral is calculated using a series expansion, and the results are used to identify the validity zone of the conventional PE solution. The analysis is performed within the framework of the nondispersive AiB where the aperture field is scaled with frequency such that the ray skeleton is frequency independent. This scaling enables an extension of the theory to the ultrawideband regime and ensures that the pulsed field propagates along the curved beam trajectory without dispersion, as will be demonstrated in a subsequent publication.     

Beam wander of partially coherent Airy beams

The beam wander of a partially coherent Airy beam in a turbulent atmosphere was investigated. By using the extended Huygens–Fresnel integral, as analytical expression is derived for the second-order moment of a partially coherent Airy beam. Based on the theory proposed by Andrews, a general expression is obtained for the beam wander of a partially coherent Airy beam. With the help of the expression, various factors which impact on the beam wander are illustrated numerically. The results show that the beam wander of a partially coherent Airy beam decreases with the increase of the characteristic scale and the decrease of the coherent length or the exponent truncation factor. The value of the beam wander is a maximum when the exponent truncation factor is 0.63, no matter what the coherent lengths are. Our results provide an effective way to control the beam wander of a partially coherent Airy beam in practice.     

Vector singularities of Gaussian beams in uniaxial crystals: Optical vortex generation

The propagation of a circularly polarized singular beam through a uniaxial crystal is accompanied by the appearance of additional singularities in the polarization structure of the beam field. These vector singularities combine to form concentric ombilic lines—degenerate ombilic points of the star type, thus significantly changing the entire fine structure of the field. When the beam passes through a birefringent quarter-wave plate and a polarizer, the vector singularities transform into the usual optical vortices. Rotation of the polarizer and/or of the quarter-wave plate drives the vortices to move by preset trajectories, merge with one another, or break into elementary singularities. These processes are studied using theoretical and experimental methods.     

Non-diffracting Airy beams in planar optical waveguides: a convenient method for visualization

In this paper we present an analysis of non-diffracting Airy beam solutions in planar waveguides. It is proposed that observing fluorescence from dye-doped polymers that can be coated on such planar waveguides can provide a simple and convenient technique for visualization and measurement of the propagation trajectories of such beams as well as studies on other characteristics of such non-diffracting beams.     

论爱里斑中的光流分布

低温辐射计对测量光束的质量要求很高。一般采用空间滤波器使爱里斑以外的次级亮环全部挡掉。本文较深入地研究了爱里斑中的光流分布，从而理论指导实践，使激光束更加纯净。     

Dispersion effects on the interaction of Airy beams and dark solitons

We simulate and analyse an Airy pulse coupled with a dark soliton in a single-mode fibre by solving the non-linear Schrödinger equation (NLSE). Simulations show that the group velocity parameter β₂₂ has a huge impact on the interaction between the Airy pulse and the dark soliton. At some values of β₂₂, a bright soliton arises from the Airy pulse. The intensity of the bright soliton reaches a maximum when β₂₂ takes a certain value. Meanwhile, the transmission distance and the primary energy of the Airy pulse are affected by the different values of β₂₂. However, when the Airy pulse propagates in a linear medium, varying the value of β₂₂ has only a slight impact on the interaction, and no bright soliton detaches from the Airy pulse. In brief, the dispersion effect has a large impact on the interaction of Airy pulses and dark solitons in a non-linear medium; however, dispersion has a lesser impact on interactions in a linear medium.     

A finite element convergence study for accelerating flow problems

The convergence properties of several non-linear solution procedures were examined with respect to the accelerated flow of a fluid in a converging channel (the Hamel problem), using two different finite element computer programs with different elemental construction. The Reynolds number varied from that for creeping flow to 1088 without exceeding the radius of convergence. Special attention was given to the successive substitution and Newton–Raphson solution algorithms, with a significant advantage in rate of convergence noted for the latter.     

Generation of high quality Airy beams with blazed micro-optical cubic phase plates

We design and fabricate a hybrid refractive-diffractive cubic phase plate (CPP) with a combined conventional blazed grating for generating high quality Airy beams. The grating enables elimination of direct incident illumination in the reconstructed beam. The CPP is fabricated in a negative photoresist on a substrate by laser direct writing lithography with precise exposure control of gray scales. Experimentally measured intensity distribution of the Airy beam is found in good agreement with the theoretical predictions. Furthermore, self-healing and nondiffraction properties of the Airy beam are verified experimentally. The proposed method gives rise to a simple, reliable, and low-cost micro-optical element solution for the generation of high quality Airy beams.     

Direct generation of Bessel beams

Two implementations are identified to create a Bessel beam directly, i.e. without the spatial filtering of an initially Gaussian beam. The first implementation is based on a resonator configuration whose lowest-loss transverse mode is a Bessel beam. Numerical simulation to corroborate the geometrical optical arguments is presented. The second implementation is based on the theorem that the angular-plane wave spectrum of a Bessel beam is composed of a cone of wave vectors. This cone is also generated through a phase-matching condition in a four-wave mixing process. This leads to the conclusion that anti-Stokes radiation generated in a nonlinear material will leave the substrate under the form of a Bessel beam.     

复合材料空间薄壁梁的有限元分析模型

在剪切梁理论的基础上, 采用9 节点平面单元模拟梁任意截面形状; 采用27 节点体单元, 模拟截面出平面外的二次翘曲位移, 从而建立了空间复合材料任意截面薄壁梁考虑二次翘曲的有限元分析模型。根据本文中导出的复合材料有限元模型编制了相应的分析计算程序。算例表明: 本文中建立的复合材料薄壁梁模型正确, 可以用于考虑多种耦合影响因素作用下复杂结构空间薄壁复合材料梁的有限元分析计算。      

Single-photon generation by electron beams

We propose a drastically new method for generating single photons in a deterministic way by interaction of electron beams with optical waveguides. We find a single swift electron to produce a guided photon with large probability. The change in energy and propagation direction of the electron reveals the creation of a photon, with the photon energy directly read from the energy-loss spectrum or the beam displacement. Our study demonstrates the viability of deterministically creating single guided photons using electron beams with better than picosecond time uncertainty, thus opening a new avenue for making room temperature, heralded frequency-tunable sources affordable for scientific and commercial developments.     

Hybrid finite element for analysis of functionally graded beams

A hybrid finite element model is presented, where stiffness and mass distributions over a beam with functionally graded material (FGM) are accurately modeled for both elastic and inelastic material responses. Von Mises and Drucker-Prager plasticity models are implemented for metallic and ceramic parts of FGM, respectively. Three-dimensional stress-strain relations are solved by a general closest point projection algorithm, and then condensed to the dimensions of the beam element. Numerical examples and verification studies on a proposed element demonstrate accuracy and robustness under inelastic material response as well as capturing fundamental, higher, and mix modes of vibration frequencies and shapes.     

A simple finite element for beams on elastic foundations

A simple "routine" beam on elastic foundation finite element using a polynomial displacement function has been developed which yields acceptably accurate deflection, shear and bending moment values for prismatic or non-prismatic beams of elastic material resting on foundations with varying or nonlinear subgrade reactions. Limited extension of the formulation to an "exact" finite element using the exact displacement function of a beam on elastic foundation has also been carried out. The subgrade is represented by a non-homogeneous solid medium to include nonlinear parameters if required. The iterative solution is extended to cases where the beam may uplift because the foundation is a no tension material. The model is also suitable for calculating the elastic deflections, membrane. and bending stress resultants for axisymmetrically loaded variable thickness shells of revolution. A computer program called FEBEF [finite element: beam on elastic foundation] incorporating the routine finite element has been prepared for the solution of beams on elastic foundations and axi symmetrically loaded shells of revolution.     

A C0 finite element formulation for thin-walled beams

Timoshenko's and Vlasov's beam theories are combined to produce a C⁰ finite element formulation for arbitrary cross section thin-walled beams. Section properties are generated using a curvilinear co-ordinate system to describe the cross section dimensions. The element includes both shear and warping deformations caused by the bending moments and the bimoment. A Gauss quadrature order is employed which exactly integrates the bending and warping stiffness matrices and provides a reduced integration order for the shear stiffness matrices. Numerical results are presented for a channel section cantilever beam. The influence of shear deformation is investigated and the calculated results are shown to be in excellent agreement with the classical solutions.     

Extended focus diffractive optical element for Gaussian laser beams

The depth of focus of the Gaussian beam is extended by introducing a wavefront phase correction with properly designed diffractive optical elements. Results of the computer simulations show that, compared with other methods, the presented method demonstrates a reduced focal spot size and low sidelobes in a focal domain, within a considerable range of defocusing distances. Experimental results for the visible range diffractive optical element with a focus of 40 mm and a depth of focus that extends to 1 mm agree with the theory.     

Using mosaic crystals for the generation of intense X-ray beams

The parametric X-ray (PXR) yield due to 500-MeV electrons in a 2-mm-thick diamond crystal with a mosaicity angle of ～0.2 mrad has been studied. It is shown that the mosaic crystal structure leads to a significant (about fourfold) increase in the PXR yield doe to the contribution of diffracted bremsstrahlung radiation. Advantages of using mosaic crystals for the generation of intense X-ray beams are discussed.     

Optical heterodyne detection of random electromagnetic beams

Abstract

In this paper we present a general analysis for the optical heterodyne detection of random electromagnetic beams. To describe the ensemble of quasimonochromatic beams which are partially polarized and partially coherent, we use a recently developed matrix treatment. We derive an expression for the signal-to-noise ratio (SNR) in terms of the beam coherence polarization matrices of the beams on the detector surface. Numerical examples are given for the SNR variation in the case of partially polarized Gaussian Schell model beams and the optimum detection is discussed in terms of beam parameters of the local oscillator.