We propose to realize an optical device based on the properties of photon orbital angular momentum (POAM) to detect the presence of closeby faint companions in double systems using Laguerre-Gaussian (L-G) modes of the light. We test also the possibility of using L-G modes to build coron-agraph mask. We realized in the laboratory a prototype using a blazed l=1 hologram to simulate the separation...

Problems of the system identification using orthonormal functions are discussed and algorithms of computing parameters of the discrete time state-space model of the plant based on the generalized orthonormal functions and the Laguerre functions are derived. The adaptive LQ regulator and the predictive controller based on the Laguerre function model are also presented. The stability and the robu...

We introduce novel classes of higher-order spatial optical solitons in analogy with Laguerre-Gaussian and Hermite-Gaussian linear eigenmodes. We reveal that stable higher-order optical solitons can exist in nonlocal nonlinear media in the various forms of soliton necklaces and soliton matrices. Modulational instability can lead to nontrivial transformations between energetically close solitons ...

The quantized vortex state is investigated in a Bose-Einstein condensate, confined in a multiply connected geometry formed by a Laguerre-Gaussian optical trap. Solving the Gross-Pitaevskii equation variationally, we show that the criterion for vortex stability is that the interatomic interaction strength must exceed a critical interaction strength. The time evolution of a freely expanding Lague...

Recently there has been some renewed interest in Laguerre differential geometry [1], [2], [3]. This geometry was to a large extent developed by Blaschke and his school and a large amount of material about it can be found in [4]. Consider the set of oriented spheres in Euclidean space. If we add to this set the space of oriented planes, i.e. the spheres of infinite radii, then we obtain the spac...