Hypergeometric Gaussian Research Articles

Hypergeometric-Gaussian modes

We studied a novel family of paraxial laser beams forming an overcomplete yet nonorthogonal set of modes. These modes have a singular phase profile and are eigenfunctions of the photon orbital angular momentum. The intensity profile is characterized by a single brilliant ring with the singularity at its center, where the field amplitude vanishes. The complex amplitude is proportional to the degenerate (confluent) hypergeometric function, and therefore we term such beams hypergeometric-Gaussian (HyGG) modes. Unlike the recently introduced hypergeometric modes [Opt. Lett. 32, 742 (2007)], the HyGG modes carry a finite power and have been generated in this work with a liquid-crystal spatial light modulator. We briefly consider some subfamilies of the HyGG modes as the modified Bessel Gaussian modes, the modified exponential Gaussian modes, and the modified Laguerre-Gaussian modes.

The relation between the lateral profile of giant extensive air showers and the age parameter

After performing extensive simulations with the code CoRSiKa, we have obtained an analytical description fitting with surprising accuracy the numerical densities up to distances larger than 5 km from the shower axis. This was achieved by using the hypergeometric formalism in place of the traditional NKG approach. The difficulty of cascade theory (validity limited to 3.5 Moliere radii), underlined with reason by the particle data group, is solved here, after overcoming the constraints of approximation B, to show that the distribution of lateral profiles at large distances is also correlated with the age parameter. This is an important step for a coherent interpretation of hybrid events recorded with both surface array and fluorescence telescopes, even with other information coming from Cerenkov or radio emission. A set of hypergeometric Gaussian functions, with a consistent relation between age parameter and total size, is proposed in the ultra-high-energy range (above 1 EeV) for electrons, muons and vertical equivalent muons.

Lateral distributions, localization methods, ϱ(600), size and energy determination in giant EAS

The radial analytical structure functions used in different experiments for charged particles and muons are compared. A minimization method is used, according to each function, to optimize the axis localization, the size and ϱ(600) approach and finally the primary energy determination. The procedure of evaluation has been employed for the giant EAS contained in Volcano Ranch and Yakutsk catalogues, as well as for the most energetic event published from AGASA. The best results are obtained using a hypergeometric gaussian function (JNC function) for electrons (or charged).