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.     

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.     

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.     

Generation of nondiffracting quasi-circular polarization beams using an amplitude modulated phase hologram

We propose an approach to the generation of nondiffracting quasi-circularly polarized beams by a highly focusing azimuthally polarized beam using an amplitude modulated spiral phase hologram. Numerical verifications are implemented in the calculation of the electromagnetic fields and Poynting vector field near the focus based on the vector diffraction theory, and the polarization of the wavefront near the focal plane is analyzed in detail by calculating the Stokes polarization parameters. It is found that the electric field, magnetic field, and Poynting vector field can simultaneously be uniform and nondiverging over a relatively long axial range of ~7.23λ. In the transverse plane, the ellipticity and azimuthal angle of the local polarization ellipse varies from point to point. No polarization singularity and phase singularity are found at the beam center, which makes the bright spot possible.     

Focused optical beams obtained at planar structures by an imaginary shift in position

A theory for focused optical beams at planar structures is described. It is an extension of a previous theory based on summation of plane waves. The focused beam is obtained by an imaginary shift in the position vector of the plane waves. It is well suited for calculations of electromagnetic fields at planar surface plasmon resonance structures excited by a focused optical 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.     

Circular Dammann grating under high numerical aperture focusing

Circular Dammann grating (CDG) under high numerical aperture (NA) focusing is described based on Richards-Wolf vectorial diffraction theory in this paper. Several CDGs are presented under the condition of NA=0.9 with the illumination of circularly polarized plane-wave laser beams. Numerical results show that the sizes of these circular patterns with equal-intensity are in the wavelength scale, and doughnut-shaped central spots and dark rings are in the subwavelength width. To verify this kind of CDG, a binary pure-phase three-order CDG is fabricated to produce a dark center pattern surrounded by three concentric bright rings. The corresponding intensity distribution of the pattern on the focal plane of a high-NA objective (NA=0.9) is measured, and the results agree well with theoretical simulations. This kind of CDG with annular patterns of equal-intensity in the wavelength scale should be highly interesting for its potential applications in optical trapping, stimulated emission depletion (STED) microscopy, and the study of singular optics, as well as annular array illumination.     

Three-dimensional Dammann vortex array with tunable topological charge

We describe a kind of true 3D array of focused vortices with tunable topological charge, called the 3D Dammann vortex array. This 3D Dammann vortex array is arranged into the structure of a true 3D lattice in the focal region of a focusing objective, and these focused vortices are located at each node of the 3D lattice. A scheme based on a Dammann vortex grating (DVG) and a mirror is proposed to provide a choice for changing the topological charge of the 3D Dammann vortex array. For experimental demonstration, a 5×5×5 Dammann vortex array is implemented by combining a 1×7 DVG, a 1×5 Dammann zone plate, and another 5×5 Dammann grating. The topological charge of this Dammann vortex array can be tuned (from -2 to +2 with an interval of +1) by moving and rotating the mirror to select different diffraction orders of the 1×7 DVG as the incident beam. Because of these attractive properties, this 3D Dammann vortex array should be of high interest for its potential applications in various areas, such as 3D simultaneous optical manipulation, 3D parallel vortex scanning microscope, and also parallel vortex information transmission.     

Generating radial or azimuthal polarization by axial sampling of circularly polarized vortex beams

A laser beam with circular polarization can be converted into either radial or azimuthal polarization by a microfabricated spiral phase plate and a radial (or azimuthal)-type linear analyzer. The resulting polarization is axially symmetric and is able to produce tightly focused light fields beyond the diffraction limit. We describe in detail the theory behind the technique and the experimental verification of the polarization both in the far field and at the focus of a high numerical aperture lens. Vector properties of the beam under strong focusing conditions were observed by comparing the fluorescence images corresponding to the focal intensity distribution for both radial and azimuthal polarizations. The technique discussed here may easily be implemented to a wide range of optical instruments and devices that require the use of tightly focused light beams.     

Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings

Expressions describing the vortex beams that are generated by the process of Fresnel diffraction of a Gaussian beam incident out of waist on fork-shaped gratings of arbitrary integer charge p, and vortex spots in the case of Fraunhofer diffraction by these gratings, are deduced. The common general transmission function of the gratings is defined and specialized for the cases of amplitude holograms, binary amplitude gratings, and their phase versions. Optical vortex beams, or carriers of phase singularity with charges mp and -mp, are the higher negative and positive diffraction-order beams. The radial part of their wave amplitudes is described by the product of the mpth-order Gauss-doughnut function and a Kummer function, or by the first-order Gauss-doughnut function and the difference of two modified Bessel functions whose orders do not match the singularity charge value. The wave amplitude and the intensity distributions are discussed for the near and far fields in the focal plane of a convergent lens, as well as the specialization of the results when the grating charge p=0; i.e., the grating turns from forked into rectilinear. The analytical expressions for the vortex radii are also discussed.     

Axial irradiance of a focused beam

The principal maximum of axial irradiance of a focused beam with a low Fresnel number does not lie at its focal point; instead it lies at a point that is closer to the focusing pupil. It has been shown by the numerical example of a weakly truncated Gaussian beam that its value increases and its location moves closer to the pupil when spherical aberration is introduced into the beam. Such an increase has been referred to as "beyond the conventional diffraction limit." Similarly, an increase in the value and a shift in the location of the principal maximum of axial irradiance of a uniform beam toward the pupil by the introduction of some spherical aberration has been characterized as an unexpected result. We explain why and how such a result comes about and that it neither invalidates any diffraction limit nor is it unexpected. We illustrate this for uniform as well as Gaussian beams of various truncation ratios. Both focused and collimated beams aberrated by spherical aberration or astigmatism are considered.     

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.     

Vector diffraction problem of focusing a category 1 aberrated wavefront through a multilayered lossless medium

Abstract

In optical storage and other imaging applications, a laser beam is focused through a transparent lossless medium of different refractive index. Applications include optical and magneto-optical recording. It is highly likely that, in the near future, conventional magnetic recording will transition to optically/thermally assisted magnetic recording technology. In all these applications, it is necessary to ascertain the quality of the image formed by the focusing apparatus on an imaging surface when in the neighbourhood of the focus, the focused beam of light passes through a stratified lossless medium. This paper examines the vector diffraction problem of focusing radiation through a multilayered medium. The solution is accomplished by first deriving a general solution of the focusing problem in any homogenous medium. This solution is then used to obtain the solution in the multilayered medium by applying continuity of the electric and magnetic fields at the interfaces. The technique used here allows one to calculate the field quantities in the entire image space. Furthermore, the focusing lens may have Seidel aberrations of the fourth order. The salient feature of this method is that the vector diffraction problem is solved only once - for the zeroth layer, immediately next to the exit pupil. In the remaining layers, the results are obtained by solving linear algebraic equations. The solution of the algebraic equations is obtained in closed form.     

Spatial correlation properties and correlation vortices of partially coherent vortex beams diffracted by an aperture

Taking the Gaussian–Schell model vortex beam as a typical example of partially coherent vortex beams, the spatial correlation properties and correlation vortices of partially coherent vortex beams diffracted by an aperture are studied. It is shown that the off-axis displacement and spatial coherence affects the spectral degree of coherence. The number and position of correlation vortices depend on the off-axis displacement, spatial coherence, aperture truncation and propagation distance, where the effect of aperture diffraction on the correlation vortices is stressed. The number of correlation vortices decrease as the truncation parameter increases. The correlation vortices in the diffracted field result from the vortex embedded in partially coherent beams at the source plane rather than from the aperture diffraction. The correlation vortices in the diffracted field appear even when the vortex core is stopped by the aperture.     

Phase singularities and spectral switches of focused higher-order Bessel–Gauss pulsed beams

The phase singularities and spectral switches of focused higher-order Bessel–Gauss pulsed beams are studied. Numerical calculation results are given to illustrate the dependence of phase singularities and spectral switches of focused higher-order Bessel–Gauss pulsed beams on the truncation parameter, topological charge, spatial parameter and propagation distance. It is shown that there always exists an optical vortex at the center of focused higher-order Bessel–Gauss pulsed beams and the topological charge is conserved during the propagation. The spectral switch appears in the neighborhood of the zero- or minimum-intensity position. With increasing topological charge or spatial parameter, the size of the vortex core increases and the spectral transition height decreases.     

Changes of intensity distribution of a tightly focused plane-wave pulse induced by lens dispersion

The tightly focusing properties of a linearly polarized plane-wave pulse through a high numerical aperture (NA) lens with dispersion are formulated. The effects of lens dispersion on the tightly focused intensity distribution in the focal region are studied in detail. It is found that, because of the lens dispersion, the intensity of the side lobe of the focused light spot strengthens in the transverse direction and the size of the main lobe of the focused light spot increases in the longitudinal direction as the pulse duration decreases. In addition, we compare the effects of dispersion of lens made by different types of glass on tightly focusing properties of a pulse beam. The results will be helpful to choose suitable high NA objective lens in experiment.     

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.     

微结构金属膜环带片电磁聚焦优化设计方法

微结构金属膜环带片是一类新颖的微纳光子学元件,应用于超分辨光学聚焦、纳米显微成像、精密工程测量等。阐述了微结构金属膜环带片的通用、快速矢量优化设计方法,适用于线偏振光、圆偏振光、径向偏振光等典型矢量光束,可调制产生远场超分辨聚焦光斑和超细光针场。基于三维时域有限差分法进行了微结构金属膜环带片的严格电磁理论验证,能够精确模拟光场在微结构金属膜环带沟槽内部的散射传播过程。在深紫外至可见光波段,给出了λ/10～λ/6厚金属铝膜制备微结构环带片的经验选取方法。     

3D-vortex labyrinths in the near field of solid-state microchip laser

The usage of vortex-labyrinth fields and Talbot lattices as optical dipole traps for neutral atoms is considered for the wavelength of trapping radiation in the range 0.98–2.79 µm. The square vortex lattices generated in high Fresnel number solid-state microchip lasers are studied as a possible realization. The distribution of light field is obtained via a nonstationary computational model based on Maxwell–Bloch equations for a class-B laser, discrete Fox–Lee map with relaxation of inversion and a static model based on superposition of copropagating Gaussian beams. The spatial patterns obtained numerically and observed experimentally previously are interpreted as nonlinear superposition of vortices with helicoidal phase dislocations. The distribution of light field is approximated analytically by a sum of array of vortex lines and an additional parabolic subtrap. The separable optical trapping potential is proposed with similar intensity distribution. The factorization of the macroscopic wavefunction has led to the solution of the Gross–Pitaevsky equation for an ensemble of quantum particles trapped in a vortex labyrinth formed by a spatially periodic array of Laguerre–Gaussian beams.