Polygonal Apertures Research Articles

Classic-fractal eigenmodes of unstable canonical resonators

It was recently shown that intensity cross-sections through the eigenmodes of canonical unstable resonators with polygonal apertures can have the statistical scaling behaviour of fractals. Here we present computer simulations which show that a careful choice of the resonator’s parameters, in particular the hitherto unexplored sideways shift of the aperture, can result in intensity cross-sections related to many classic self-similar fractals, such as the Sierpinski Gasket and the Koch Snowflake. Our computer simulations use the monitor-outside-a-monitor effect, which we argue to be equivalent to the more commonly used virtual-source method.

Multiplexed computer-generated holograms with irregular-shaped polygonal apertures and discrete phase levels.

We propose a novel type of multiplexed computer-generated hologram (MCGH) with irregular-shaped polygonal apertures and discrete phase levels. Each elementary cell forming the new MCGH is divided into a central aperture and several peripheral apertures. The new MCGH allows us to exploit the huge space-bandwidth product provided by standard lithography technologies. With use of the Abbe transform, the Fraunhofer diffraction patterns from the polygonal apertures and, therefore, the layout coefficients can be computed with simple algebraic expressions. Several symmetries related to the polygonal apertures also facilitate the layout-coefficient computation. In the novel iterative subhologram design algorithm (ISDA), we consider all subholograms equally and apply the image-plane constraint to the total reconstructed image, which is the coherent addition of the subimages from the subholograms. We designed MCGHs with several billions of pixels per period, which cannot be achieved with the classical iterative Fourier transform algorithm, because of the prohibitive computational cost and memory limitation. MCGHs with irregular polygonal apertures and discrete phases, which were designed by the ISDA, reconstruct a desired image of large size with high diffraction efficiencies and low reconstruction errors.

Multiplexed computer-generated hologram with polygonal apertures.

A novel type of multiplexed computer-generated hologram (CGH) is designed with more than one billion of pixels per period. It consists of elementary cells divided into arbitrary-shaped polygonal apertures, the division being identical in all cells. The cells are further digitized into pixel arrays to exploit the huge space-bandwidth product of electron-beam lithography. The polygonal apertures in the same location inside the cells constitute a subhologram. With the Abbe transform that has never, to our knowledge, been used in other CGH designs, the subhologram images (subimages) are obtained with fast Fourier transforms. It is therefore possible to design a multiplexed CGH that has a size thousands of times larger than the manageable size of a conventional CGH designed with the iterative Fourier transform algorithm (IFTA). A much larger object window than that of the conventional CGH can also be achieved with the multiplexed polygonal-aperture CGH, owing to its extremely large dimensions. The multiplexed polygonal-aperture CGH is designed with the novel iterative subhologram design algorithm, which considers the coherent summation of the subimages and applies constraints on the total image, subimages, and subholograms. As a result, the noise appearing in the preceding multiplexed-CGH designs is avoided. The multiplexed polygonal-aperture CGH has a much higher diffraction efficiency than that resulting from either the preceding multiplexed-CGH designs or the conventional CGH designed by the IFTA.

Optimized secondary concentrators for a partitioned central receiver system

We present secondary concentrators with non-regular shapes for increasing the concentration of radiation from a given field of heliostats, well suited for partitioning the receiver into several units, arranged side by side. For a general heliostat field with a non-axisymmetric directional distribution of the radiation at the entrance aperture of the secondary concentrator, concentrators with non-regular shape can significantly increase the concentration as compared to their symmetric analogs. Our optimizations indicate best results for concentrators based on rectangular entrance and exit apertures. The concentration may be increased by a factor of 2.3 at an optical efficiency of 90%. If the shape of the exit aperture is required to be close to circular, concentrators based on non-regular hexagonal apertures may reach concentration higher than their symmetric analogs by a factor of 1.3. For the given radiation, concentrators with polygonal apertures perform significantly better than concentrators with smooth elliptic apertures.

Lepidotrachelophyllum fornicis, n. g., n. sp., a Ciliate with an External Layer of Organic Scales (Ciliophora, Litostomatea, Haptoria)1

Lepidotrachelophyllum fornicis n. g., n. sp. was discovered in White Lake, Ontario, Canada, under winter ice. The genus is Trachelophyllum-like, being highly flattened, elongate, and very extensible. The major feature that separates it from other genera in the family Trachelophyllidae is the presence of a dense layer of organic scales which covers the exterior of the cell and through which the cilia emerge. The scales are composed of filamentous material which is organized as an ovoid structure. The “rim” of the baseplate is formed of interwoven filaments. The baseplate is broken by circular or polygonal apertures. The same filaments form an arched superstructure broken by even larger, less regular apertures.

Simple derivation of formulas for Fraunhofer diffraction at polygonal apertures from Maggi–Rubinowicz transformation

The Maggi–Rubinowicz transformation is used to derive rigorous but simple formulas for Fraunhofer diffraction at apertures in the form of arbitrary polygons. The use of these formulas is illustrated by application to the two classical cases of rectangular and triangular apertures.

Simple derivation of formulas for Fraunhofer diffraction at polygonal apertures: errata

The Abbe transform is used to derive rigorous algebraic formulas for the wave function describing Fraunhofer diffraction at apertures in the form of arbitrary polygons. Two remarks bring the Abbe transform and the Abbe theorem into the context of the history of diffraction.

Simple derivation of formulas for Fraunhofer diffraction at polygonal apertures

The Abbe transform is used to derive rigorous algebraic formulas for the wave function describing Fraunhofer diffraction at apertures in the form of arbitrary polygons. Two remarks bring the Abbe transform and the Abbe theorem into the context of the history of diffraction.

Diffraction patterns of simple apertures

The Fraunhofer diffraction patterns of the triangle, trapezoid, and hexagon are calculated and displayed in moiré plots. The diffraction pattern of the general polygonal aperture with a finite number of vertices can be calculated in terms of elementary functions.

Stress concentration in plates and shells with polygonal apertures

Stress concentration in plates and shells with polygonal apertures