Exploring the dynamics of finite-energy Airy beams: a trajectory analysis perspective.

In practice, Airy beams can only be reproduced in an approximate manner, with a limited spatial extension and hence a finite energy content. To this end, different procedures have been reported in the literature, based on a convenient tuning of the transmission properties of aperture functions. In order to investigate the effects generated by the truncation and hence the propagation properties displayed by the designed beams, here we resort to a new perspective based on a trajectory methodology, complementary to the density plots more commonly used to study the intensity distribution propagation.

Affine diffractive beam dividers.

Diffractive optical elements that divide an input beam into a set of replicas are used in many optical applications ranging from image processing to communications. Their design requires time-consuming optimization processes, which, for a given number of generated beams, are to be separately treated for one-dimensional and two-dimensional cases because the corresponding optimal efficiencies may be different. After generalizing their Fourier treatment, we prove that, once a particular divider has been designed, its transmission function can be used to generate numberless other dividers through affine transforms that preserve the efficiency of the original element without requiring any further optimization.

Three-dimensional polarization of fields radiated by partially coherent electromagnetic cylindrical sources.

Partially coherent electromagnetic sources with cylindrical symmetry and infinite extent radiating outward are introduced. Their 3 × 3 cross-spectral density matrix is given through expansions of the field components in terms of basis functions related to the Hankel functions. The spectral density and the three-dimensional degree of polarization of such sources and the fields they radiate are examined.

Partially coherent spherical sources with spherical harmonic modes.

A class of partially coherent spherical sources is introduced whose cross-spectral density across the surface has a modal expansion made up of spherical harmonics. For such sources, the solution of the propagation problem in all the outer spaces can be written through a series of the propagated modes, which maintains the spherical harmonic structure. The main features of this class of cross-spectral densities are derived illustrating their coherence properties with examples.

Cylindrical partially coherent scalar sources.

Partially coherent scalar sources with cylindrical symmetry radiating outwards are introduced. Homogeneous cross-spectral densities are shown to possess angularly modulated Hankel modes, whose amplitudes are subject to a filtering process during propagation. Simple criteria for treating such sources are given.