A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

An overview of the recent developments in the field of cylindrical vector beams is
provided. As one class of spatially variant polarization, cylindrical vector beams
are the axially symmetric beam solution to the full vector electromagnetic wave
equation. These beams can be generated via different active and passive methods.
Techniques for manipulating these beams while maintaining the polarization symmetry
have also been developed. Their special polarization symmetry gives rise to unique
high-numerical-aperture focusing properties that find important applications in
nanoscale optical imaging and manipulation. The prospects for cylindrical vector
beams and their applications in other fields are also briefly discussed.

Cylindrical vector beams: from mathematical concepts to applications

Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

/pdf/optical-vortices-30-years-on-oam-manipulation-from-2yknluuuga.pdf

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

A higher-order Poincare sphere and Stokes parameter representation of the higher-order states of polarization of vector vortex beams that includes radial and azimuthal polarized cylindrical vector beams is presented. The higher-order Poincare sphere is constructed by naturally extending the Jones vector basis of plane wave polarization in terms of optical spin angular momentum to the total optical angular momentum that includes higher dimensional orbital angular momentum. The salient properties of this representation are illustrated by its ability to describe the higher-order modes of optical fiber waveguides, more exotic vector beams, and a higher-order Pancharatnam-Berry geometric phase.

Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light

We describe a convenient approach for generating arbitrary vector beams in a 4-f system with a spatial light modulator (SLM) and a common path interferometric arrangement. A computer-generated hologram is introduced onto SLM for performing the beam conversion. Optical realization of a variety of polarization configurations confirms the reliability and flexibility of our method.

Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement

We predict a new category of optical orbital angular momentum that is associated with the curl of polarization and a kind of vector field with radial-variant hybrid states of polarization that can carry such novel optical orbital angular momentum. We present a scheme for creating the desired vector fields. Optical trapping experiments validate that the vector fields, which have no additional phase vortex, exert torques to drive the orbital motion of the trapped isotropic microspheres.

Optical orbital angular momentum from the curl of polarization

We present an idea to generate an arbitrary space-variant vector beam with structured polarization and phase distributions. The vector beams are synthesized from the left- and right-hand polarized light, each carrying different phase distributions. Both the phase and the state of polarization of vector beams can be tailored independently and dynamically by a spatial light modulator.

Generation of vector beam with space-variant distribution of both polarization and phase.

We present an idea based on Poincare sphere and demonstrate the creation of a new type of vector fields, which have hybrid states of polarization. Such a type of hybridly polarized vector fields have completely different property from the reported scalar and vector fields. The novel vector fields are anticipated to result in new effects, phenomena, and applications.

A new type of vector fields with hybrid states of polarization

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.

Jianping Ding

Papers

Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement

Optical orbital angular momentum from the curl of polarization

Generation of vector beam with space-variant distribution of both polarization and phase.

A new type of vector fields with hybrid states of polarization

Optical trapping with focused Airy beams