Radiation forces of highly focused radially polarized hollow sinh-Gaussian beams on a Rayleigh metallic particle

Based on the vector diffraction theory, the tight focusing properties of radially polarized hollow sinh-Gaussian (HsG) beams are theoretically studied. It is found that the radially polarized HsG beams can form a longitudinally polarized sub-wavelength focal spot. Moreover, the radiation forces acting on a Rayleigh metallic particle are calculated for the case where the radially polarized HsG beams are applied. Compared with the use of conventional Gaussian beams, the high-order radially polarized HsG beams can largely enhance the radial trap stiffness and broaden the axial trap distance. The influence of the beam order m on the focusing properties and trap stiffness is investigated in detail.     

Representation and focusing properties of higher-order radially polarized Laguerre–Gaussian beams

A method based on higher-order Poincaré sphere was proposed to represent the states of polarization of higher-order radially polarized Laguerre–Gaussian (LG) vectorial beams (VBs). And the focusing properties of such LG beams of different radial orders focused by a high-NA lens were discussed. By tuning the ratio of the pupil radius to the waist of the incident beams, some cage-like or needlelike electric intensity field is generated in the focal region for several specific LG VBs with high order. Modulated by diffractive optical elements, the shape of the focal field shows novel behaviors such as splitting of cage-like modes, which provides potentially a more flexible control over micro-particles.     

Non-diffractive Vector Bessel Beams

Abstract

The non-diffractive vector Bessel beams of an arbitrary order are examined as both the solution to the vector Helmholtz wave equation and the superposition of vector components of the angular spectrum. The transverse and longitudinal intensity components of the vector Bessel beams are analysed for the radial, azimuthal, circular and linear polarizations. The radially and azimuthally polarized beams are assumed to be formed by the axicon polarizers used with the initially unpolarized or linearly polarized light. Conditions in which the linearly polarized Bessel beams can be approximated by the scalar solutions to the wave equation are also discussed.     

Propagation properties of vectorial Hermite–cosine–Gaussian beams beyond the paraxial approximation

Starting from the vectorial Rayleigh–Sommerfeld diffraction integrals, the analytical propagation expressions of vectorial nonparaxial Hermite–cosine–Gaussian (HCosG) beams in free space are derived. The on-axis intensity, far-field equation and, in particular, paraxial expressions are given and treated as special cases of our result. It is shown that for vectorial nonparaxial HCosG beams, the parameter f = 1/kw ₀, with k being the wave number and w ₀ being the waist width, determines their nonparaxiality. What is more, the decentered parameter also affects their intensity distribution and nonparaxial behavior. The calculation results indicate that the position of maximum on-axis intensity changes with the mode indices.     

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.     

Arbitrary three-dimensional polarization control based on cylindrical vector beams and binary phase coding

To obtain an arbitrary polarization in three dimensions is of significant interest for many applications. Here, we demonstrate a configuration to achieve it. After phase coding by binary phase plates, two cylindrical polarized beams are superposed and focused by a high-numerical aperture lens to obtain transversally and radially polarized components in the focus vicinity. By adjusting their intensity and phase difference, the desired three-dimensional polarization can be achieved. The proportion of the desired polarization is extremely high and the focus spot is smaller than the diffraction-limited spot size.     

Focusing of radially polarized Lorentz–Gauss beams with the power–exponent–phase vortex

Using the vector diffraction theory, the optical field of the focusing radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex is derived. The normalized intensity distributions of the focusing radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex are numerically demonstrated. The influences of the power order n and the topological charge m on the normalized intensity distribution are examined. The beam centre and the effective beam size, which are defined by the first- and the second-order moments of the intensity distribution, are the important parameters for focus. Therefore, the quantitative effects of the power order n and the topological charge m on the beam centre and the effective beam size are further investigated. This research is beneficial to the optical manipulation which is involved in the radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex.     

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.     

Focal shift in focused radially polarized ultrashort pulsed laser beams

Beginning with a beam coherence polarization (BCP) matrix, we obtain an analytical intensity expression for radially polarized ultrashort pulsed laser beams that pass through an apertureless aplanatic lens. We also investigate the intensity distribution of radially polarized beams in the vicinity of the focus. The focal shift of these beams is studied in detail. The focal shift depends strongly on Z(F) that coincides with pi times the Fresnel number.     

Propagation properties of partially coherent radially polarized beam in a turbulent atmosphere

Based on the Huygens–Fresnel principle and the unified theory of coherence and polarization of partially coherent beams, we investigate the propagation characteristics of a partially coherent radially polarized doughnut (PCRPD) beam in a turbulent atmosphere. It is found that, after propagating through a turbulent atmosphere, the doughnut beam spot is changed into a circular Gaussian beam. Moreover, the degree of coherence, the degree of polarization and the degree of cross-polarization of the beam will change on propagation, and this change is dependent upon the degree of coherence of the source and atmospheric turbulence.     

Simple interferometric technique for generation of a radially polarized light beam

We present a theoretical and experimental investigation of an interferometric technique for converting a linearly polarized Gaussian beam into a radially polarized doughnut beam. The experimental setup accomplishes the coherent summation of two orthogonally polarized TEM01 and TEM10 beams that are obtained from the transformation of a TEM00 beam by use of a simple binary diffractive optical element. We have shown that the degree of radial polarization is maximum at a given distance from the interferometer output port that depends on the diameter of the incident beam at the interferometer input port.     

Focusing of radially and azimuthally polarized beams through a uniaxial crystal

We calculated and measured the difference between focal positions of radially and azimuthally polarized beams after passing through a uniaxial crystal. Calculations were carried out on the basis of the ray optics and the vector diffraction theory. The results of the calculations were in good agreement with those of the experiment. In addition, we discussed the polarization selection in a hemispherical laser cavity that was used for the generation of a radially polarized beam by use of the birefringence of a c-cut Nd:YVO4 laser crystal [Opt. Lett. 31, 2151 (2006)]. The stability range of the laser cavity length for the generation of a radially polarized beam was also in good agreement with the differences mentioned above.     

Reflection and non-specular effects of 2D gaussian beams in interfaces between isotropic and uniaxial anisotropic media

Abstract

In the present paper bidimensional Gaussian linearly polarized beams, which are incident on an interface between an isotropic medium and a non-absorbing non-magnetic uniaxial crystal are considered. The relation between the reflection coefficients and the non-specular effects are studied. The expressions for the first order effects in the case of a beam linearly polarized in a plane perpendicular to the one containing the crystal optical axis and the normal to the interface are analytically determined. Two highly symmetric geometries are analysed and the results are compared to those obtained with isotropic interfaces.     

Polarization separation of light in holographic grating reflection in conical mounting

Abstract

We experimentally investigate the interaction of linearly polarized light with a holographic grating in a conical mounting. Due to the periodic structure, the polarization properties of the reflected zeroth-order beam are highly sensitive to the conical angle. When a focused Gaussian beam with linear polarization impinges on an air–grating interface at an exceptional conical angle, a spatial splitting of the reflected beam is observed behind a polarizer. We find that it can be interpreted using the anisotropy of the polarization distribution in holographic grating reflection.     

Creation of subwavelength light needle,equidistant multi-focus,and uniform light tunnel

A versatile method is presented for the creation of ultra-long subwavelength light needles with high-purity longitudinal polarization, uniform light tunnels of variable length and with narrow dark channel, or coaxially equidistant multi-focus with prescribed number and spacing. This is achieved by modulating the radially or azimuthally polarized vector beams using the same kind of amplitude apodization filter under a high numerical aperture aplanatic lens system. These peculiar focusing patterns may suit a variety of potential applications, such as optical trapping, particle acceleration, atom optical experiments, and near-field scanning optical microscopy.     

Generation of radially polarized beams with an image-rotating resonator

We show how a passive image-rotating optical resonator can be used to convert a linearly polarised, lowest-order Gaussian beam into a radially polarized beam. The image and polarization rotation of the cavity removes the frequency degeneracy of the modes, making it possible to select the radially polarized mode by cavity tuning. With the addition of gain, the same cavity should operate as a radially polarized laser when injection seeded at the proper wavelength.     

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.     

The M 2 factor of hermite-cosh-gaussian beams

Abstract

Based on the second-order moments method, the closed-form expression for the M ²-factor of Hermite-cosh-Gaussian beams is derived, which depends on the beam order n and decentred parameter a. The result shows a more general characteristic, because cosh-Gaussian, Hermite-Gaussian and fundamental Gaussian beams can be regarded as the special cases of Hermite-cosh-Gaussian beams.     

Atom guiding along high order Laguerre–Gaussian light beams formed by spatial light modulation

A spatial light modulator (SLM) has been used to create high quality Laguerre–Gaussian (LG) light beams, which have been used to study the guiding of cold rubidium atoms. The SLM allows real-time variation of the hollow guiding beam and permits direct comparison of the guided atom fluxes for different LG modes with minimal adjustment of the other optical components. It is demonstrated that, by increasing the azimuthal index l of the Laguerre–Gaussian beam, the radiation pressure pushing the trapped atoms may be reduced while maintaining the same guided flux. This is the first comparative study of hollow beam atom guiding, and further demonstrates the versatility of the SLM for studies in atom optics.     

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.