S. A. Balalayev's research while affiliated with Russian Academy of Sciences and other places

A binary diffractive optical element (1500 pixels × 1500 pixels, diameter 4.5 mm) is designed by partial encoding and fabricated by direct electron beam writing in SiO2. Two conjugate hyper-geometric laser modes are generated using the fabricated element. The root-mean-square transverse intensity deviation of the experimental from theoretical diffraction pattern, determined within a circle of radius 1 mm, is below 13%.

We develop an algorithm for calculating hyper-geometric modes of the coherent light field, which represent a solution to the paraxial wave (Schrödinger-type) equation. The propagation of the hyper-geometric modes containing a phase spiral singularity is computer simulated. A comparison is conducted of the exact analytical solution and an approximate solution derived using an integral Kirchhoff propagation operator. A specific feature of the hyper-geometric modes that distinguish them from the familiar paraxial (Gauss, Bessel) modes is that the major radius of the former increases as a square root of the distance passed and the spacing between the adjacent maxima (or minima) in the diffraction pattern decreases with increasing radial coordinate.