Energy trajectories, that is, integral curves of the Poynting (current) vector, are calculated for scalar Bessel and Laguerre-Gauss beams carrying orbital angular momentum. The trajectories for the exact waves are helices, winding on cylinders for Bessel beams and hyperboloidal surfaces for Laguerre-Gauss beams. In the geometrical-optics approximations, the trajectories for both types of beam a...

For α = n− 1, n ∈ N\{0}, the operator D2 is the radial part of the sub-Laplacian on the Heisenberg groupHn (see [2, 4]). These operators have gained considerable interest in various fields of mathematics (see [1, 4]). They give rise to generalizations of many two-variable analytic structures like the Laguerre-Fourier transform L, the Laguerre-convolution product, the dispersion and the Gaussian...

A provably stable reduced order model, based on a projection onto a scaled orthonormal Laguerre basis, followed by a SVD step, is proposed. The method relies on the conformal mapping properties induced by the complete orthonormal scaled Laguerre basis, allowing a mapping from the discrete-stable case to the continuous-stable case and vice versa.

We introduce two axioms in Laguerre geometry and prove that they provide a characterization of miquelian planes over fields of the characteristic different from 2. They allow to describe an involutory automorphism that sheds some new light on a Laguerre inversion as well as on a symmetry with respect to a pair of generators.

We investigate finite elation Laguerre planes admitting a group of automorphisms that is two-transitive on the set of generators. We exclude the sporadic cases of socles in two-transitive groups, as well as the cases with abelian socle (except for the smallest ones, where the Laguerre planes are Miquelian of order at most four). The remaining cases are dealt with in a separate paper. As a conse...

The Volterra series can be used to model a large subset of nonlinear, dynamic systems. A major drawback is the number of coefficients required model such systems. In order to reduce the number of required coefficients, Laguerre polynomials are used to estimate the Volterra kernels. Existing literature proposes algorithms for a fixed number of Volterra kernels, and Laguerre series. This paper pr...

A reduced order modeling method based on a system description in terms of orthonormal Laguerre functions, together with a Krylov subspace decomposition technique is presented. The link with Padé approximation, the block Arnoldi process and singular value decomposition (SVD) leads to a simple and stable implementation of the algorithm. Novel features of the approach include the determination of ...

We summarise the construction of exact axisymmetric scalediscretised wavelets on the sphere and on the ball. The wavelet transform on the ball relies on a novel 3D harmonic transform called the Fourier-Laguerre transform which combines the spherical harmonic transform with damped Laguerre polynomials on the radial half-line. The resulting wavelets, called flaglets, extract scale-dependent, spat...

Using a spontaneous parametric down-conversion process to create entangled spatial states, we compare the information capacity associated with measurements in the Hermite-Gaussian and Laguerre-Gaussian modal basis in an optical system of finite aperture. We show that the cross-talk imposed by the aperture restriction degrades the information capacity. However, the Laguerre-Gaussian mode measure...

The multi-indexed Laguerre and Jacobi polynomials form a complete set of orthogonal polynomials. They satisfy second-order differential equations but not three term recurrence relations, because of the ‘holes’ in their degrees. The multi-indexed Laguerre and Jacobi polynomials have Wronskian expressions originating from multiple Darboux transformations. For the ease of applications, two differe...