Flat-top Focus Research Articles

Formation of subwavelength tunable flat-top focus with double foci characteristic by tightly focused cylindrical vector beams

We report a numerical investigation on the generation of a subwavelength flat-top focus by tuning the polarization angle of the incident beam under tight focusing conditions. Our approach uses a binary phase mask containing two regions of opposite phases, with a variable diameter of the inner region. Properly tuning the diameter of the inner region of the mask, the flat-top profile of variable sizes (above and below the subwavelength region) is generated in a controlled manner with the various incident polarization angles of the beam and with the different numerical aperture (NA) value of the lens. Our study reveals that a particular cut-off value of polarization angle, above which the subwavelength flat-top is generated, corresponds to a specific NA that increases with the increase in the NA value. In addition, the emergence of the dual foci structure is observed in the longitudinal direction with increasing NA of the lens. The flat-top's polarization degrees-of-freedom and dual foci properties open up promising routes for potential applications in fluorescence polarization microscopy and multiplane particle trapping.

The Error Analysis of the Complex Modulation for Flattop Focusing Beam Shaping

In order to obtain a focusing flattop beam with high uniformity, complex modulation is used to modulate the optical pupil function, and the beam shaping algorithm is designed with a single phase-only spatial light modulator (SLM). Actually, the wavefront aberrations introduced by each element reduce the uniformity of the shaped beam. In particular, the wavefront aberrations in different positions have different effects on this complex modulation algorithm. However, there is a lack of the corresponding error data and robustness analysis. Here, the error and robustness of the complex modulation algorithm are analyzed when different types of aberrations (defocus, astigmatism, and coma) exist in different positions of the shaping optical system, and the mixed area magnification-free (MRAF) algorithm is used as a reference for comparison. The results show that coma has the greatest effect on the beam shaping quality. It is also proved that the impact on the beam quality when there are aberrations in the laser and beam expansion system is greater than those in the SLM and the focusing lens for the complex modulation algorithm, which is different from the MRAF case.

Centimeter-scale low-damage micromachining on single-crystal 4H–SiC substrates using a femtosecond laser with square-shaped Flat-Top focus spots

Femtosecond (fs) lasers have been proved to be reliable tools for high-precision and high-quality micromachining of ceramic materials. Nevertheless, fs laser processing using a single-mode beam with a Gaussian intensity distribution is difficult to obtain large-area flat and uniform processed surfaces. In this study, we utilize a customized diffractive optical element (DOE) to redistribute the laser pulse energy from Gaussian to square-shaped Flat-Top profile to realize centimeter-scale low-damage micromachining on single-crystal 4H–SiC substrates. We systematically investigated the effects of processing parameters on the changes in surface morphology and composition, and an optimal processing strategy was provided. Mechanisms of the formation of surface nanoparticles and the removal of surface micro-burrs were discussed. We also examined the distribution of subsurface defects caused by fs laser processing by removing a thin surface layer with a certain depth through chemical mechanical polishing (CMP). Our results show that laser-induced periodic surface structures (LIPSSs) covered by fine SiO2 nanoparticles form on the fs laser-processed areas. Under optimal parameters, the redeposition of SiO2 nanoparticles can be minimized, and the surface roughness Sa of processed areas reaches 120 ± 8 nm after the removal of a 10 μm thick surface layer. After the laser processing, micro-burrs on original surfaces are effectively removed, and thus the average profile roughness Rz of 2 mm long surface profiles decreases from 920 ± 120 nm to 286 ± 90 nm. No visible micro-pits can be found after removing ~1 μm thick surface layer from the laser-processed substrates.

Achievement of regular-polygon-like focus through tightly focusing phase modulated radially polarized beam

In this paper, we propose a facile and universal method to design a phase diffractive optical element (DOE) in tightly focusing system for achieving regular-polygon-like focus, including flattop focus and ring-like focus on the focal plane. The edges of the regular-polygon-like focus can be simply adjusted by adjusting the amount of subareas on the DOE. For a specified regular polygon distribution, the focus can be modulated to flattop focus as well as ring-like focus through adjusting only one parameter. As a demonstration, flattop focus as well as ring-like focus with focal distributions as regular triangle, square, pentagon, hexagon and heptagon are well achieved on the focal plane. It provides a simple method to achieve regular-polygon-like focus, which may find potential applications in optical manipulation and material processing fabrications.

Hyperbolic phase function used in a spatial light modulator for flat top focus generation.

We report on a novel transversal beam shaping approach to convert a Gaussian beam to a flat top focus profile by employing a hyperbolic phase function in a liquid crystal on silicon (LCOS) spatial light modulator (SLM). The well-known Powell lens approach is compared to ours. The analytically obtained phase function for the flat top focus conversion problem is compared to our approach theoretically and experimentally. A strategy for the generation of squared and circular top hat foci is derived.

Generation of equilateral-polygon-like flat-top focus by tightly focusing radially polarized beams superposed with off-axis vortex arrays.

In this paper, the general formula for tightly focusing radially polarized beams (RPB) superposed with off-axis vortex arrays is derived based on Richard-Wolf vector diffraction theory. The off-axis vortex breaks the rotational symmetry of the energy flow along the axial direction and leads to the spatial redistribution of intensity within the focal plane. The dependence of the consequent focal intensity redistribution on the off-axis distance of vortices as well as the numerical aperture of the lens is theoretically studied. Based on this intriguing feature, generation of equilateral-polygon-like flat-top focus (EPFF) with a flat-top area on the level of sub-λ2 is realized. The demonstrated method provides new opportunities for focus shaping and holds great potentials in optical manipulation and laser fabrication.

Engineering of multi-segmented light tunnel and flattop focus with designed axial lengths and gaps

Based on the radiation pattern from a sectional-uniform line source antenna, a three-dimensional (3D) focus engineering technique for the creation of multi-segmented light tunnel and flattop focus with designed axial lengths and gaps is proposed. Under a 4Pi focusing system, the fields radiated from sectional-uniform magnetic and electromagnetic current line source antennas are employed to generate multi-segmented optical tube and flattop focus, respectively. Numerical results demonstrate that the produced light tube and flattop focus remain homogeneous along the optical axis; and their lengths of the nth segment and the nth gap between consecutive segments can be easily adjusted and only depend on the sizes of the nth section and the nth blanking between adjacent sectional antennas. The optical tube is a pure azimuthally polarized field but for the flattop focus the longitudinal polarization is dominant on the optical axis. To obtain the required pupil plane illumination for constructing the above focal field with prescribed characteristics, the inverse problem of the antenna radiation field is solved. These peculiar focusing fields might find potential applications in multi-particle acceleration, multi-particle trapping and manipulation.

Generating multiple focal structures with high NA parabolic mirror using azimuthally polarized pair of vortices

In this article, a simple method to tailor the focal patterns of high NA parabolic mirror by manipulating the position of vortex pair of opposite topological charge nested in an azimuthally polarized Gaussian beam is demonstrated numerically using Vector Diffraction Theory. It is observed that proper manipulation of position between the vortex pair generates novel focal patterns including focal hole, transversely polarized focal spot and flat top focus of sub wavelength scale are generated.

Changeable focused field distribution of double-ring-shaped cylindrical vector beams

Based on vector diffraction theory, the focusing features of double-ring-shaped cylindrical vector (DCV) beams are studied in this paper. The intensity pattern in the vicinity of the focus can be tailored by appropriately adjusting the parameters of the ratio of the inner-to-outer ring radius and the polarization state of the incident DCV beams. It is shown that focused field with flattop or optical cage profile is easily obtained. Moreover, we also propose a new approach to generate a flattop focus with extended depth of focus and lower side-lobe levels by adding a diffractive optical element (DOE) which is cleverly loaded on the spatial light modulator (SLM). The results from this study would especially facilitate light manipulation of two types of particles with different refractive indices in only one optical-trap system.

Application of flat-top focus to 2D trapping of large particles

The 2D optical trapping ability of larger-than average-particles is compared for three different beam types: a flat-top, a Gaussian beam, and a donut shaped beam. Optical force-displacement curves are calculated in four different size regimes of particle diameters (1.5-20 μm). We find that the trapping efficiency increases linearly with ratio of particle diameter to wavelength for all three beams. As the ratio reaches a specific threshold value, the flat-top focus exhibits the largest trapping efficiency compared to the other two beam types. We experimentally demonstrate that flat-top focusing provides the largest transverse trapping efficiency for particles as large as 20 μm in diameter for our given experimental conditions. The overall trend in our experimental results follows that observed in our simulation model. The results from this study could facilitate light manipulation of large particles.

Demonstration of flat-top focusing under radial polarization illumination

We experimentally demonstrate the generation of a flat-top intensity distribution using a radially polarized vector beam. Our approach uses higher numerical aperture focusing than what has been previously reported for a single, fixed, vector beam. In addition, the flat-top focus generated in our scheme exhibits a polarization gradient along the radial coordinate in the focal volume, with an on-axis longitudinal field component that persists over 2λ, which is a stark difference from conventional flat-top fields, which exhibit intensity profiles that are uniformly polarized. Our experimental results are found to be in good agreement with the theoretical prediction.

Compact flattop laser beam shaper using vectorial vortex

In this paper, we demonstrate a compact flattop beam shaper to realize two-dimensional flattop focus through generating a second order full Poincaré beam. Liquid crystal material is used in the device as the voltage-dependent birefringent material to provide appropriate phase retardation modulation. The beam shaper is fabricated and tested. Experimental results show that high quality flattop profiles can be obtained with steep edge roll-off. The tolerance of different input beam sizes of the beam shaper is also verified in the experimental demonstration.

Simulation of Flat-Top Focus Shaping Using Effect of Polarization in High Numerical Apertures Optical Systems

Flat-top focus shaping using effect of polarization is investigated theoretically by vector diffraction theory. We demonstrate how to make a properly selected polarization component to achieve a flat-top focus in high numerical apertures optical systems, hence achieving a potential goal of beam shaping. The results show that the values of the polarization angle corresponding to different numerical apertures (NA)values for a flat-top focus and the polarization angle increases on increasing NA for achieving a flat-top focal spot, but the flat-top focal pattern will become -sensitive when NA is larger than 1. One will have to add a diffractive optical element to achieve a flat-top focal spot in NA larger than 1 system.

Flattop focusing with full Poincaré beams under low numerical aperture illumination

In this Letter, we propose and experimentally demonstrate the generation of second-order full Poincaré beams and its applications in two-dimensional flattop beam shaping with spatially variant polarization under low NA focusing condition. High-quality flattop profiles with steep edge roll-off can be obtained with this technique. The experiment results also demonstrate that flattop profile can be maintained for different input beam sizes by conveniently rotating a half-wave plate.

Three-dimensional focus engineering using dipole array radiation pattern

A systematic three-dimensional focus engineering method based on the dipole-array radiation pattern is proposed. High numerical aperture focusing of generalized cylindrical vector beam is interpreted as the reversing of the radiation from electrically small dipole arrays. Required pupil plane illumination can be found for the desired focal field with specific characteristics. Magnetic-dipole array radiation is utilized to create ultra-long (~ 8λ) diffraction limited three-dimensional optical tube with maximal uniformity. Combined with a recently reported optical needle field generation with the help of electric dipole array radiation, ultra-long (~ 8λ) three-dimensional flattop focus that has top hat profiles in both transversal and longitudinal directions can be realized with the help of radiations pattern from co-located magnetic and electric dipole arrays.

Transverse superresolution and extended axial focal depth realized by three-zone annular phase pupil filter

When linearly polarized light is focused using a high numerical aperture lens with three-zone annular phase pupil filter, vector diffraction method was applied to study the optical intensity distribution in transverse and axial directions. Numerical simulation results show that optical intensity distribution in transverse and axial directions need to be treated simultaneously. When three-zone annular phase pupil filter is added in front of a high numerical aperture lens, transverse super resolution, extended axial focal depth and flat-top focusing can be achieved at the same time. Furthermore, When phase modulation depth is changed, the phenomenon of axial focal shift can be found. The structure of three-zone annular phase pupil filter was optimized and the optimized results were given.

Smallest flattop focus by polarization engineering

Spatial engineering of polarization as a new method of beam shaping is analyzed by using scalar diffraction theory. For the one-dimensional case, it is shown that the smallest flattop far-field distribution can be obtained by adopting a linear polarization that changes direction as a linear function of location in the pupil plane. The resulting light field is functionally equivalent to a cosinusoidal function modulation of the wavefront but maintains high efficiency. This polarization beam shaping technique proves to be highly useful in applications where diffraction effects need to be taken into account. The extension of this technique to two-dimensional beam shaping is also demonstrated.

Polarization beam shaping

Spatial engineering of polarization is proposed as a novel method of beam shaping. It is shown that a flat-top-shaped focus can be obtained in the far field by changing the polarization in the pupil plane in a spatially inhomogeneous manner. Experiments have been carried out to verify the validity of this method in one dimension. By comparison with traditional beam shaping methods, polarization beam shaping yields the smallest flat-top focus while maintaining high efficiency.