We employ a large-Fresnel-number laser system to demonstrate the three-dimensional optical coherent waves localized on Lissajous and trochoidal parametric surfaces with Lissajous and trochoidal transverse patterns in degenerate cavities. The coherent structured beams are verified to be composed of degenerate Hermite-Gaussian and Laguerre-Gaussian modes with different longitudinal indices resulted from longitudinal-transverse coupling. As well known, the Hermite- Gaussian modes can be converted into Laguerre-Gaussian modes possessing orbital angular momentum by use of a pair of cylindrical lens. Consequently, we make use of cylindrical lenses to transform the Lissajous structured beams superposed of degenerate Hermite-Gaussian modes into the intriguing trochoidal structured beam possessing optical orbital angular momentum.

This study reports a method of creating vortex array laser beams by superposing high-order laser modes on their rotated replicas. An interferometer configuration was used to convert these high-order laser modes to vortex array laser beams containing multi vortexes aligned in an almost square manner. To generate this kind vortex array laser beams, this study reports systematic approaches to the selective excitation of high-order laser modes in end-pumped solid-state lasers with laser resonators and asymmetric pumping. The resulting vortex array laser beams can be used as optical tweezers and atom traps in the form of two-dimensional arrays, or to study the transfer of angular momentum to micro particles or atoms (Bose-Einstein condensate).

We describe a diffracting beam with orbital angular momentum (OAM) but with a helical profile in both phase and amplitude components of the beam. This is different from Laguerre-Gaussian (LG) beams where only the phase component has a helical profile. Such profile in LG beams introduces a phase singularity at the centre and produces a dark region surrounded by a ring-shaped light pattern. For LG-beams, the ring radius is proportional to the degree of helicity or topological charge of the beam. The beam we describe here is initially characterized with an apodized helical phase front at the outskirts and linearly scaled towards no phase singularity at the centre of the beam. At the focal volume, we show that our beam forms an intensity distribution that can be accurately described as an "optical twister" as it propagates in the forward direction. Unlike LG beams, an optical twister can have minimal changes in radius but with a scalable OAM. Furthermore, we characterize the OAM in terms of its capacity to introduce spiral motion on particles trapped along its orbit. We also show that our "optical twister" maintains a high concentration of photons at the focus even as the topological charge is increased. Such beams can be applied to fundamental studies of light and atoms such as in quantum entanglement of the OAM, toroidal traps for cold atoms and for optical manipulation of microscopic particles.

A hybrid vector polarization beam with a donut like intensity profile is produced at the output of a spun elliptical core optical fiber by coupling an off-axis TEM₀₀ laser mode at the input. The local polarization states of the fiber output are analyzed using Stokes polarimetry. The Stokes parameters are measured using a combination of quarter wave plate and linear polarizer. A detailed polarization map of the hybrid beam's cylindrically symmetric and varying elliptical polarization state around the beam axis is also numerically discussed.

Optical and electrical conductivity properties of multi-walled carbon nanotubes (MWCNTs) and nematic liquid crystal (LC) composites are investigated. The MWCNTs with high aspect ratio L/d ≈ 300 ÷ 1000 and nematic LC 5CB (4- pentyl-4-cyanobiphenyl) are used. The composites are prepared by introduction of MWCNTs (0.0001÷0.1 % wt) into LC solvent with subsequent sonication. The increase of MWCNT concentration (between 0.0025÷0.05 % wt) results in selfaggregation of MWCNTs and formation of up to 200 micron-sized 3d aggregates with fractal boundaies. The visually observed formation of spanning MWCNT networks near the percolation threshold at ~0.025 % wt is accompanied with transition from non-conductive to conductive state and generation of optical singularities. The observed effects are explained by the strong interactions between MWCNTs and LC medium and planar orientation of 5CB molecules on the lateral surface of MWCNTs. As a result, an interfacial 5CB micro size shell with inhomogeneous structure appears around each nanotube cluster. Diffraction of laser beam on clusters fractal boundaries creates speckle field with multitude of optical vortices. The irregular birefringence of interfacial shells induces polarization singularities in propagating laser beam. Growth of the LC interfacial shell thickness in external electric field and its disappearance during transition of the nematic to isotropic liquid are measured and discussed. It is shown that the formation of 5CB interfacial shell allows fixing existence of nanostructures beyond space resolution of microscope.

We report here the characteristics of dark hollow beams (DHBs) generated using negative micro-axicons fabricated via selective chemical etching process in the tip of optical fibers. The DHB output from the etched fibers were further manipulated to generate single and multiple period optical bottle beams, 0^th- and 1^st- order Bessel beams and astigmatic Bessel beams and beams with helical wavefront. Selective excitation of the guided modes in single and multimode optical fibers with V-numbers ranging from 2.405 - 5.69 are etched to different negative cone dimensions and are used to generate in a controllable way DHBs and related optical beams. Negative cones are etched in the fiber tips via selective chemical etching process wherein the different etch rates of the fiber core and cladding dopants and dopant concentration results in different cone angles and cone depths. Input laser beam guided through the optical fiber diffracts and refracts at the tip generating beams with one or many bright rings surrounding the dark central spot. By positioning the DHB in the front focal plane of a bi-convex lens we generate Bessel beams whose characteristics are compared with that generated using positive cone etched in the fiber tip and bulk axicon. Under certain excitation conditions we also observe helical wavefront DHBs with phase dislocation embedded in the beam.

Light distributions of Bessel-Gauss and Laguerre-Gauss type carry an orbital angular momentum and thus can be regarded as particular types of optical vortex beams. Optical vortices in highly intense femtosecond laser pulses are expected to lead to a variety of specific applications like momentum selective spectroscopy, nonlinear laser-material interaction or quantum information processing. Here we report on experiments with a Ti:sapphire laser oscillator at wavelengths around 800 nm. To compare the pulsed and cw case, the system was driven with and without mode-locking. At the minimum pulse duration of about 10 fs, a FWHM spectral bandwidth of 120 nm was available. By applying diffractive spiral phase elements, beams with topological charges of m = 1 and m = 2 were formed. The specific propagation behavior was studied by detecting spatially resolved intensity and spectral maps. In addition to the helical beam generation with fixed phase patterns, adaptive approaches based on liquid-crystal microdisplays are considered.

The term 'optical binding' conveniently encapsulates a variety of phenomena whereby light can exert a modifying influence on inter-particle forces. The mutual attraction that the 'binding' description suggests is not universal; both attractive and repulsive forces, as well as torques can be generated, according to the particle morphology and optical geometry. Generally, such forces and torques propel particles towards local sites of potential energy minimum, forming the stable structures that have been observed in numerous experimental studies. The underlying mechanisms by means of which such effects are produced have admitted various theoretical interpretations. The most widely invoked explanations include collective scattering, dynamically induced dipole coupling, optically-dressed Casimir-Polder interactions, and virtual photon coupling. By appeal to the framework that led to the first predictions of the effect, based on quantum electrodynamics, it can be demonstrated that many of these apparently distinct representations reflects a different facet of the same fundamental mechanism, leading in each case to the same equations of motion. Further analysis, based on the same framework, also reveals the potential operation of another mechanism, associated with dipolar response to local dc fields that result from optical rectification. This secondary mechanism can engender shifts in the positions of the potential energy minima for optical binding. The effects of multi-particle interactions can be addressed in a theoretical representation that is especially well suited for modeling applications, including the generation of potential energy landscapes.

Mechanical equilibrium at zero temperature does not necessarily imply thermodynamic equilibrium at finite temperature for a particle confined by a static, but non-conservative force field. Instead, the diffusing particle can enter into a steady state characterized by toroidal circulation in the probability flux, which we call a Brownian vortex. The circulatory bias in the particle's thermally-driven trajectory is not simply a deterministic response to the solenoidal component of the force, but rather reflects an interplay between advection and diffusion in which thermal fluctuations extract work from the non-conservative force field. As an example of this previously unrecognized class of stochastic machines, we consider a colloidal sphere diffusing in a conventional optical tweezer. We demonstrate both theoretically and experimentally that non-conservative optical forces bias the particle's fluctuations into toroidal vortexes whose circulation can reverse direction with temperature or laser power.

We subject micrometer-sized, optically trapped colloidal particles in a non-polar liquid to a sinusoidally varying electric field, and measure their resulting movement. From this movement, we calculate the electrophoretic mobility and charge of the particle in the liquid. The use of high frequencies of the electric field (well above the corner frequency of the optical tweezers) allows us to estimate the electrical charge of colloidal particles with an accuracy of the order of the electron charge in a time interval of only 10 ms. This technique can be used to provide valuable information about the dynamics of the poorly understood processes that lead to the charge on colloidal particles in non-polar liquids.

In the past decade, experiments involving the manipulation and observation of nanostructures with light using optical tweezers methodology have developed from proof-of-principle experiments to an established quantitative technique in fields ranging from (bio)physics to cell biology. With optical tweezers, microscopically small objects can be held and manipulated. At the same time, the forces exerted on the trapped objects can be accurately measured. With the Prism-Award winning NanoTracker a platform for performing experiments using specimen from single molecules to whole cells is available. With two time-continuous traps, it allows the controlled trapping and accurate tracking of nanoparticles, suspended either in a microfluidic multichannel flow chamber or even in a temperaturecontrolled open Petri dish. With its 3D detection system, particle displacements in the trap can be recorded with nanometer precision. Moreover, dynamic forces acting on the particle can be measured with better than picoNewton resolution on a microsecond time-scale. Here, we discuss design features of and measurements done with the NanoTracker platform. In particular, we show how one of the hallmarks of single-molecule biophysics, the overstretching transition of DNA, can be studied in a versatile manner and used for protein-DNA interaction mechanics. Moreover, on the lower side of the force range the other benchmark single-molecule biophysics, kinesin's 8-nm steps and stall forces, are shown to be measurable. With the NanoTracker, optical tweezers finally transcend from the labs of self-building scientists who helped the technique mature, to a turn-key system able to serve a much wider community of researchers in the life sciences.

If the state of polarization of a monochromatic light beam is changed in a cyclical manner, the beam acquires-in addition to the usual dynamic phase-a geometric phase. This so-called Pancharatnam-Berry phase, equals half the solid angle of the contour traced out on the Poincar´e sphere. We show that such a geometric interpretation also exists for the Pancharatnam connection, the criterion according to which two beams with different polarization states are said to be in phase. This interpretation offers a new and intuitive method to calculate the geometric phase that accompanies non-cyclic polarization changes. We also present a novel setup that allows the observation of the geometric phase for such changes. The phase can depend in a linear or in a nonlinear fashion on the orientation of the optical elements, and sometimes the dependence is singular. Experimental results that confirm these three types of behavior are presented. The observed singular behavior may be applied in the design of optical switches.

We study the geometric origin of generalized Gouy phases in paraxial optical modes of arbitrary order. We focus on the specific case of cyclic beam transformations of non-astigmatic vortex beams, thereby, generalizing the well-known geometric phase shift for first-order beams with orbital angular momentum to modes of arbitrary order. Our method involves two pairs of bosonic ladder operators, which, analogous to the algebraic description of the quantum-mechanical harmonic oscillator in two dimensions, connect transverse modes of different order. Rather than studying the geometry of the infinite-dimensional space of higher-order modes, we focus on the space underlying the ladder operators. We identify overall phases of the ladder operators, thereby obtaining the phases of all higher-order modes, and show that the variation of these phases under optical elements and transformations has a geometric interpretation in terms of the other parameters involved.

It is shown that for an incoherent superposition of the orthogonally polarized laser beams the polarization singularities of a new type arise at the transversal cross-section of a paraxial combined beam instead of common singularities, such as amplitude zeroes (optical vortices) inherent in scalar fields, and polarization singularities such as C points and L lines inherent in completely coherent vector fields. There are U contours along which the degree of polarization equals zero and the state of polarization is undetermined (singular), and isolated P points where the degree of polarization equals unity and the state of polarization is determined by the non-vanishing component of the combined beam. Optical vortices of the orthogonally polarized component lie under P points. P points differ essentially from C points of singular optics of coherent fields by the absence of topological charge and certain morphology of heighborhood (S, M, L). Crossing U line is accompanied by step-like change of the state of polarization onto orthogonal one (sign principle). U and P singularities are represented at a whole Stokes space, namely at and inside of the Poincare sphere. Correlation among completely coherent and completely incoherent vector singularities is considered for the first time. First experimental examples of reconstruction of the combined beam's vector skeleton formed by U and P singularities as the extrema of the complex degree of polarization are given.

The propagation of a hybrid vector polarization beam is experimentally investigated in an uniaxial birefringent quartz crystal. The hybrid beam can be expressed as a superposition of two orthogonal linearly polarized Laguerre-Gaussian modes of opposite topological charge. When propagating through the crystal, the beam decomposes into the two orthogonal components traveling along the ordinary and extraordinary rays. Investigation of the beams phase and polarization structure after propagation through the crystal shows a fork fringe pattern arising from interference between the orthogonally polarized components of opposite topological charge.

We report here the demonstration of rotational Doppler Effect (RDE) and measurement of rotational frequency shifts (RFS) in single-charge helical-phased cylindrical vector beams directly generated using a two-mode optical fiber. The vector-vortex beam with a shifted vortex core, generated by propagating the Gaussian laser beam as an offset-skew ray selectively excites both the fundamental and first low-order waveguide modes simultaneously in the two-mode optical fiber. Rotation frequency of the output beam around a shifted axis of the beam is measured as a function the analyzer rotation for changing handedness of the input circular polarization to demonstrate RDE in the directly excited cylindrical vector-vortex beams. Even small variations in the input launch conditions were found to dramatically alter the stability of the vortex beams and hence the demonstration of RDE.

It is shown the space-time dynamics of optical singularities is fully described by singularities trajectories in space-time domain, or evolution of transverse coordinates(x, y) in some fixed plane z₀. The dynamics of generic developing speckle fields was realized experimentally by laser induced scattering in LiNbO₃:Fe photorefractive crystal. The space-time trajectories of singularities can be divided topologically on two classes with essentially different scenario and duration. Some of them (direct topological reactions) consist from nucleation of singularities pair at some (x, y, z₀, t) point, their movement and annihilation. They possess form of closed loops with relatively short time of existence. Another much more probable class of trajectories are chain topological reactions. Each of them consists from sequence of links, i.e. of singularities nucleation in various points (x_i y_i, t_i) and following annihilation of both singularities in other space-time points with alien singularities of opposite topological indices. Their topology and properties are established. Chain topological reactions can stop on the borders of a developing speckle field or go to infinity. Examples of measured both types of topological reactions for optical vortices (polarization C points) in scalar (elliptically polarized) natural developing speckle fields are presented.

We report a violation of the CHSH inequality for ghost-images. This is achieved by using two spatially separated phase modulators within the context of a two-photon parametric down-conversion experiment. We obtain edge enhanced images as a direct consequence of the quantum correlations in the orbital angular momentum (OAM) of the down-converted photon pairs. For phase objects, with differently orientated edges, we show a violation of the CHSH Bell-type inequality for an OAM subspace, thereby unambiguously revealing the quantum nature of our ghost-imaging arrangement.

We present a study of the imaging of the interference of spatial-helical modes of single photons. This work includes a mathematical treatment that accounts for the direction of propagation and spatial mode degrees of freedom in the situation where light travels through an interferometer that prepares the light in distinct spatial modes and makes them interfere. We present results of the interference at the single photon level of the spatialhelical modes with topological charge 1 and 0. The results are consistent with the expectation that each photon carries the entire spatial mode information.

Optically bound arrays of microparticles in counter-propagating laser traps are typically constrained to the beam axis. Here we discuss the mechanisms underlying the formation of these chains, and report on binding where the particles are displaced from the beam axis. We also describe circulatory motion of the bound arrays around the beam axis. We show both experimental results and a Mie scattering simulation, and discuss the physical basis for the effects.

Optical binding is a phenomenon that is exhibited by micro-and nano-particle systems, suitably irradiated with offresonance laser light. Recent quantum electrodynamical studies on optically induced inter-particle potential energy surfaces have revealed unexpected features of considerable intricacy. When several particles are present, multi-particle binding effects can commonly result in the formation of a variety of geometrical assemblies. The exploitation of these features presents a host of opportunities for the optical fabrication of nanoscale structures, based on the fine control of attractive and repulsive forces, and the torques that operate on particle pairs. This paper reports the results of a preliminary analysis of the structures formed by optically driven self-assembly, and the three-dimensional symmetry of energetically favored forms. In systems where permanent dipole moments are present, optical binding may also be influenced by a static interaction mechanism. The possible influence of such effects on assembly formation is also explored, and consideration is given to the possible departures from such symmetry which might then be anticipated.

Lately, several groups successfully used ultrashort laser pulses to selectively permeabilize the membrane of living cells to achieve transport of foreign molecules, like DNA, into the cells. For this, the high field intensities of tightly focused laser pulses are used to induce multiphoton absorption and the creation of a small scale optical breakdown at the membrane of the target cell. Afterwards, DNA or other foreign molecules are able to diffuse into the cell and achieve, for example, transfection of living cells. However, the cell throughput of this method is low, as, due to tight focusing. We present a technique to achieve fs-laser transfection in living cells at higher throughput by implementing optical traps into microfluidic chips. For this, a trapping laser beam, is coupled into a microscope setup and combined with a Ti:Sa fslaser beam to achieve simultaneous trapping and optical perforation.

The high-refractive index contrast (▵n ~0.65 as compared to silicon oxide) of Tantalum pentoxide (Ta₂O₅) waveguide allows strong confinement of light in waveguides of sub-micron thickness (200 nm). This enhances the intensity in the evanescent field, which we have employed for efficient propelling of micro-particles. The feasibility of opto-fluidics sorting of different sized micro-particles based on their varying optical propulsion velocity is suggested. Optical propulsion of fixed red blood cells (RBC) with velocity higher than previously obtained is also reported. The optical propulsion velocities of RBC in isotonic solution (0.25 M sucrose) and water have been compared.

Optical Airy beams have gained significant attention due to their parabolic trajectory, accelerating and nondiffractive behavior. The phase velocity of the Airy solution to the paraxial wave equation is described showing a unique behavior. The velocity is shown to vary spatially and in magnitude as the beam propagates through vacuum along its curved trajectory.

Non-diffracting laser modes and interfering non-diffracting beams have been extensively studied. Interfering nondiffracting beams generate novel laser modes. In this paper we accumulate various interfering conditions for nondiffracting beams and discuss the properties of the resultant beam. Contrasting intensity profiles and topological charge distribution are obtained on varying interfering conditions. Collinear propagation of non-diffracting laser beams is also reported.

Phase-extraction from fringe patterns is an inevitable procedure in many applications, such as interferometry, Moiré analysis, and profilometry using structured light illumination. Errors to phase-extraction always occur when the signal-to- noise ratio is weak. In this paper, we use the empirical mode decomposition (EMD) with a generalized analysis model to reduce the white noise from a fringe pattern. It is found that phases can be extracted with high accuracy once noise-reduction is performed with this model.

Optical vortex (Laguerre-Gauss) modes can be created by introducing a π/2 phase shift between orthogonal components of Hermite-Gauss (HG) modes. The well-known astigmatic mode converter design described by M.W. Beijersbergen et al. [Optics Communications 96 pgs. 123 132, 1993] achieves this condition by manipulating the differing Gouy phases along orthogonal axes between a matched pair of cylinder lenses. Apparently not well known is that quite useful mode conversions can easily be achieved with a single cylinder lens. We explain the operating principle of such a single lens mode converter, and describe and illustrate how to match the input HG mode to the required Rayleigh range z_Η = f_cyl with one additional spherical lens. Setting up and optimizing such a simplified mode converter is an excellent exercise for undergraduate students, and the resulting optical vortex beams can be used for a variety of instructional experiments.