Polygonal Apertures Research Articles

On the streamwise vorticity generation and distribution in an angular particle wake

We investigate the streamwise vorticity generation mechanism and distribution pattern in an unbounded steady inertial flow past a fixed Platonic polyhedron. Three angular positions are selected: an edge facing the flow (E), a face facing the flow (F) and a vertex facing the flow (V). We provide compelling evidence that the generation of the streamwise vorticity is primarily caused by the tilting of the transverse vorticity that originates from the particle front surface. Each inclined face on the front surface generates a pair of opposite-signed streamwise vortices. They are advected to the particle wake and form a chiral vorticity pattern which preserves the symmetry of the particle front surface. Two particles at dual angular positions exhibit highly similar vorticity patterns. Our study reveals a striking similarity between the vorticity patterns and the far-field optics diffraction pattern of a light beam past a polygonal aperture. We discover the deterministic vorticity generation mechanism to predict the streamwise vorticity patterns based on the distribution of edges and inclined faces on the particle front surface. Conversely, the vorticity patterns themselves can serve as a diagnostic tool to infer the geometry of the opaque particle front surface. Additionally, the vorticity patterns can be used to predict the stable angular position of a freely settling angular particle, which tends to be such that the number of streamwise vorticity pairs in the wake is maximized.

Rayleigh-Sommerfeld scalar diffraction by rotating apertures

We have analytically explored the Rayleigh-Sommerfeld scalar diffraction for various rotating apertures such as rotating single-slit, rotating double-slit, rotating linear diffraction grating, and rotating regular polygonal aperture. Here the apertures are considered to be uniformly rotating along the axes perpendicular to the plane of the apertures and the diffracted fields are analysed in the far-field zone. We have compared the time-averaged intensity distributions for the rotating apertures with the intensity distributions for static circular apertures of the same area. We also have obtained angular speed of rotation dependent Fraunhofer diffraction formulae for the rotating apertures, in particular, the rotating single-slit, the rotating double-slit, and the rotating linear diffraction grating.

Characteristic and Mechanism Analysis of Aperture Barrel Erosion at Edge of Decelerator Grid of Three-Grid Ion Thrusters

To study the characteristics and mechanism of ion thruster decelerator grid aperture erosion at the edge, immersed finite element particle-in-cell (IFE-PIC) method combined with the sputtering erosion model was used to simulate the distribution of beam ions between grids. The characteristics and mechanism of ion thruster decelerator grid aperture barrel erosion at the edge were obtained. The results show that the direct impact of beam ions leads to polygonal erosion morphology. The reason for the uneven erosion depth in the circumferential direction is that the influence of the upstream sheath of the surrounding aperture on the edge aperture is too large, resulting in uneven distribution of beam ions. Hence, to avoid this kind of direct ion etching, the polygonal aperture is suggested at the edge of ion optics.

Generalized shift-rotation absolute measurement method for optical surface shapes with polygonal apertures based on migration recognition by Radon transform.

A generalized shift-rotation absolute measurement method for optical surface shapes with polygonal apertures based on migration recognition by Radon transform is proposed. The rotation angles and translation distances of the test surface, measured three times, are calculated through migration recognition. The absolute shape of the test surface with the polygonal aperture is fitted by orthogonal Zernike polynomials. Compared to the existing absolute measurement method for polygonal apertures, our method ensures test surface measurement accuracy without high-precision attitude control and repeated adjustments. The measurement is simple and coherent, which reduces the measurement time and improves the efficiency.

Exact paraxial diffraction theory for polygonal apertures under Gaussian illumination

Paraxial diffraction of monochromatic Gaussian beams by arbitrarily shaped polygonal apertures is analytically explored within the recently proposed paraxial boundary diffraction wave theory framework [J. Opt. Soc. Am. A 36, 1048 (2019)10.1364/JOSAA.36.001048)]. Surprisingly enough, exact closed-form expressions of the diffracted wavefield can be obtained by using only elementary calculus and Euclidean geometry. An interesting connection between paraxial optics and probability theory is also outlined.

Method to reduce the aberration of a polygonal aperture focus-tunable lens array for high fill factor.

Focus-tunable liquid lens arrays have been used to improve depth in glass-free three-dimensional devices where high fill factor is required. For high fill factors, polygonal apertures should be used, but due to the difficulty of controlling aberrations during focus tuning, polygonal aperture focus-tunable lenses have rarely been studied. This Letter proposes a new structure with walls at the lens boundaries using a square parabolic lens model to control the quadrafoil aberration induced by the square aperture. ANSYS simulation confirmed that the lens surface was closest to the parabolic lens model when the wall thickness was 1.4mm. A fabricated lens array demonstrated the quadrafoil inhibitory effect and confirmed the utility of the new structure.

Design quadrilateral apertures in binary computer-generated holograms of large space bandwidth product.

A new approach for designing the binary computer-generated hologram (CGH) of a very large number of pixels is proposed. Diffraction of the CGH apertures is computed by the analytical Abbe transform and by considering the aperture edges as the basic diffracting elements. The computation cost is independent of the CGH size. The arbitrary-shaped polygonal apertures in the CGH consist of quadrilateral apertures, which are designed by assigning the binary phases using the parallel genetic algorithm with a local search, followed by optimizing the locations of the co-vertices with a direct search. The design results in high performance with low image reconstruction error.

Computer-Generated Very Large Space-Bandwidth Product Binary Hologram for Laser Projector

A new approach for designing the binary phase-only hologram with arbitrary-shaped polygonal apertures is proposed. The diffraction of the aperture was computed with the analytical Abbe transform. To explore the very high number of degrees of freedom available in the computer-generated hologram (CGH) of very large pixel count, a two-step optimization including the genetic algorithm with local search for encoding binary phases of apertures followed by the direct search for floating covertices of the elementary triangular apertures was developed for high performance and low image-reconstruction error of the binary CGH.

Polarization dependent enhanced optical transmission through a sub-wavelength polygonal aperture surrounded by polygonal grooves.

Enhanced optical transmission (EOT) and its polarization extinction ratio (PER) of a sub-wavelength polygonal aperture surrounded by polygonal grooves are investigated numerically by finite difference time domain (FDTD) method. Effects of light polarization on EOT were analyzed and compared for four types of geometrical structures: triangle aperture surrounded by triangle grooves, square aperture surrounded by square grooves, rhombus aperture surrounded by rhombus grooves, and pentagon aperture surrounded by pentagon grooves. The effects of relative angles between the symmetry axes of polygons and the light polarization were thoroughly analyzed. Among these plasmonic polygonal bull's eye structures, the rhombus showed a maximum EOT several times larger than others. In contrast to the prior normal incident condition, we further analyzed the impacts of the incident angle and we found a wideband tunability of EOT wavelengths.

Performance of compound parabolic concentrators with polygonal apertures

The optical performance of CPCs having n-sided polygonal inlet and outlet apertures is investigated by Monte-Carlo ray-tracing. The polygonal CPCs are formed by circumscribing regular polygons about the circular apertures of an underlying revolved CPC. The resulting side walls are extruded 2D CPC profiles with 1-dimensional curvature thus profiting from improved manufacturability compared to the revolved CPC. Furthermore, these designs may be uniformly tiled on flat or curved planes with minimal gap loss for applications requiring multiple absorbers. The principal property of interest is the optical efficiency defined as the fraction of radiant power incident on the inlet aperture which reaches the outlet aperture. The effect of geometry, reflectivity, and surface errors on the optical efficiency is presented. In analyzing these effects, a new approach for calculating the average number of reflections is derived and utilized. Additionally, the flux distributions at the outlet of the concentrators are examined. Especially for large acceptance angles, the performance of polygonal CPCs with reasonable numbers of sides is found to approach that of the revolved CPC, which may be considered a limiting case of the polygonal CPC for n→∞. It is found that the square CPC (n=4) has some favorable anomalous behavior, with performance surpassing that of designs with 5 and 6 sides for small acceptance angles. Polygonal CPCs show promise as less expensive alternatives to the revolved CPC for applications including stationary solar concentrators, and secondary concentrators for dish, tower, and trough primaries.

Efficiently Simulating the Bokeh of Polygonal Apertures in a Post‐Process Depth of Field Shader

AbstractThe effect of aperture shape on an image, known in photography as ‘bokeh’, is an important characteristic of depth of field in real‐world cameras. However, most real‐time depth of field techniques produce Gaussian bokeh rather than the circular or polygonal bokeh that is almost universal in real‐world cameras. ‘Scattering’ (i.e. point‐splatting) techniques provide a flexible way to model any aperture shape, but tend to have prohibitively slow performance, and require geometry‐shaders or significant engine changes to implement. This paper shows that simple post‐process ‘gathering’ depth of field shaders can be easily extended to simulate certain bokeh effects. Specifically we show that it is possible to efficiently model the bokeh effects of square, hexagonal and octagonal apertures using a novel separable filtering approach. Performance data from a video game engine test demonstrates that our shaders attain much better frame rates than a naive non‐separable approach.

Enhancing the light transmission of plasmonic metamaterials through polygonal aperture arrays

While plasmonic metamaterials find numerous applications in the field of nanophotonic devices, a device may work as a normal or plasmonic device, depending on whether it operates at the resonance mode. In this paper, the extraordinary light transmission through coaxial polygonal aperture arrays, including circle, hexagon, square, and triangle geometries, is studied using FDTD simulation. Circular, hexagonal and squared aperture arrays have similar high transmission rate, while triangular aperture array has considerably lower transmission rate. It is found that the transmission peaks reflect the resonance modes propagating along the direction of neighboring apertures. We hence rearrange the apertures from square lattice to triangle lattice to obtain a uniform resonance mode along the neighboring apertures. This leads to enhanced light transmission. The study gains understanding of new properties of the metamaterials based on plasmonic resonance.

Vortex characteristics of Fraunhofer diffractions of a plane wave by a spiral phase plate limited by pseudoring polygonal apertures

We introduce a multilevel spiral phase plate (SPP) limited by a pseudoring polygonal aperture (PRPA). Such an SPP has the advantages of easier fabrication and greater suppression of the sidelobes of the diffraction field over that generated with a polygonal aperture (PA). The Fraunhofer diffraction fields generated by an SPP with a PRPA or with a PA have the same topological charge features and a similar diffraction pattern. Numerical evaluations show that the maximum bright annular-intensity difference between the diffraction patterns for the SPP with a PRPA and that of a PA does not exceed 3% under optimal design parameters.

Dynamic behavior of plastic circular plates with polygonal apertures

Using a model of a rigidly plastic body, a procedure has been developed permitting calculation of limiting loads and residual damageability of circular plates with a regular polygonal aperture if dynamic loads of explosion type distributed uniformly act on them. Both contours are supported by hinges or fixed. It is shown that three mechanisms of plate deformation are possible depending on the load level. For each of them, defining equations have been obtained and conditions of their realization have been analyzed. Examples of numerical solutions are presented.

Fraunhofer diffraction of the plane wave by a multilevel (quantized) spiral phase plate

We obtain an analytical expression in the form of a finite sum of plane waves that describes the paraxial scalar Fraunhofer diffraction of a limited plane wave by a multilevel (quantized) spiral phase plate (SPP) bounded by a polygonal aperture. For several topological charges of the SPP we numerically obtain the minimal number of SPP sectors for which the RMS between the Fraunhofer diffraction patterns for multilevel and continuous SPP does not exceed 2%.

Polarization properties of partially coherent flat-topped light beams diffracted through a regular polygonal aperture

Based on the beam coherence-polarization matrix and the propagation law, the polarization properties of partially coherent flat-topped light beams diffracted through a regular polygonal aperture are studied systematically. The expression for the degree of polarization of partially coherent flat-topped light beams is derived. And according to that, the expression for the degree of polarization of Gaussian Schell-model beams and the propagation of partially coherent flat-topped light beams in the free space are obtained. It is shown that the polarization properties of partially coherent flat-topped light beams diffracted through a rectangular aperture depends on the truncation parameter, spatial coherence parameters, diffraction angle, propagation distance and the order of flat-topped light beams.

Fresnel diffraction and fractal patterns from polygonal apertures

Two compact analytical descriptions of Fresnel diffraction patterns from polygonal apertures under uniform illumination are detailed. In particular, a simple expression for the diffracted field from constituent edges is derived. These results have fundamental importance as well as specific applications, and they promise new physical insights into diffraction-related phenomena. The usefulness of the formulations is illuminated in the context of a virtual source theory that accounts for two transverse dimensions. This application permits calculation of fractal unstable-resonator modes of arbitrary order and unprecedented accuracy.

Diffracted wavefield by an arbitrary aperture from Maggi–Rubinowicz transformation: Fraunhofer approximation

Fraunhofer diffraction patterns through apertures in opaque screens are the cases of most interest in optics. The major purpose of this paper is to establish a general and explicit formula for calculating diffracted wavefield from Maggi–Rubinowicz transformation. The 2-D integration (Rayleigh–Sommerfeld or Helmholtz–Kirchhoff integral formulas) is reduced to a 1-D integration over the rim of the aperture. Some examples for elliptical and polygonal apertures are given.

Sliding-blade MEMS iris and variable optical attenuator

An iris-type variable aperture fabricated using microelectromechanical systems (MEMS) technology is described. The device contains a number of shutter blades, which are each driven by a separate microactuator, and translated synchronously to create a variable polygonal aperture. The optical performance of devices with different numbers of blades is compared using simple analytic models and diffraction theory. The mechanism is simulated by finite element analysis. Four-blade devices driven by buckling mode electrothermal actuators are formed by double-sided patterning and deep reactive ion etching of bonded silicon-on-insulator and characterized experimentally. Symmetric deflections are obtained, and used to create a square pupil. Variable attenuation is demonstrated using optical fibres with thermally expanded cores.

Multiplexed computer-generated holograms with polygonal-aperture layouts optimized by genetic algorithm.

Using a novel genetic algorithm (GA) with a Lamarckian search we optimize the polygonal layout of a new type of multiplexed computer-generated hologram (MCGH) with polygonal apertures. A period ofthe MCGH is divided into cells, and the cell is further divided into polygonal apertures according to a polygonal layout, which is to be optimized. Among an ensemble of 1.21 x 10(24) possible polygonal layouts, we take a population of 102 solutions, which are coded as chromosomes of bits, and find the optimal solution with our GA. We introduce rank-based selection with cumulative normal distribution fitness, double crossover, exponentially decreasing mutation probability and Lamarckian downhill search with a small number of offspring chromosomes into our GA, which shows a rapid convergence to the global minimum of the cost function. In a second step of optimization the phase distributions over the subholograms in the MCGH are determined with our iterative subhologram design algorithm. Our MCGH designs show large-sie reconstructed images with high diffraction efficiency and low reconstruction error.