Finite hypergeometric series summation-based Fraunhofer diffraction analysis for optical vortices generated by spiral phase plates

Summation Formulae for Noncommutative Hypergeometric Series

Hypergeometric series with noncommutative parameters and argument, in the special case involving square matrices, have recently been studied by a number of researchers including (in alphabetical order) Durán, Duval, Grünbaum, Iliev, Ovsienko, Pacharoni, Tirao, and others. See [3, 6, 8, 9, 10, 11, 12, 16] for some selected papers. The subject of hypergeometric series involving matrices is closel...

Summation theorems for multidimensional basic hypergeometric series by determinant evaluations

Creation of Optical Vortices Using an Adjustable Spiral Phase Plate and Computer-Generated Holograms

An adjustable spiral phase plate and computer-generated holograms were investigated as methods for creating optical vortices. The phase plate was created by cutting a plastic microscope cover slip from a corner to its center and separating the resultant tabs by inserting a uniformly thick wedge between them. The computer-generated holograms were designed by mathematically interfering an oblique...

Hypergeometric Summation Techniques for High Order Finite Elements

The goal of this paper is to discuss the application of computer algebra methods in the design of a high order finite element solver. The finite element method is nowadays the most popular method for the computer simulation of partial differential equations. The performance of iterative solution methods depends on the condition number of the system matrix, which itself depends on the chosen bas...

Fraunhofer diffraction of light by human enamel.

Fraunhofer diffraction patterns of human enamel samples were photographed with a helium-neon laser beam (lambda = 633 nm). The first-order diffraction angle was in reasonable agreement with a prediction based upon enamel prisms acting as a two-dimensional grating. These results support the hypothesis that enamel diffracts light because of the periodic structure of enamel prisms with interprisma...