P. M. Mejías

Parametric characterization of general partially coherent beams propagating through ABCD optical systems

Within the formalism of the Wigner distribution function, a new parameter is proposed, which characterizes arbitrary tridimensional partially coherent beams and is invariant through ABCD optical systems. The relationship between such a parameter and the bidimensional concept of beam quality is analyzed. An absolute lower bound that the new parameter can reach is also shown.

Second-order spatial characterization of hard-edge diffracted beams

Second-order characteristic beam parameters, including beamwidth and far-field divergence, are generalized for hard-edge diffracted fields. On the basis of, the so-called moments formalism these parameters are shown to propagate through ABCD optical systems according to laws similar to those applied to systems with no hard-edge openings. The power–content ratio of any diffracted beam within a certain region is evaluated in terms of such generalized parameters. An alternative analytical expression of such generalized far-field divergence is also provided that is suitable for experimental measurements. Application to Gaussian beams diffracted by slits is included.

Vectorial structure of nonparaxial electromagnetic beams

A representation of the general solution of the Maxwell equations is proposed in terms of the plane-wave spectrum of the electromagnetic field. In this representation the electric field solution is written as a sum of two terms that are orthogonal to each other at the far field: One is transverse to the propagation axis, and the magnetic field associated with the other is also transverse. The concept of the so-called closest field to a given beam is introduced and applied to the well-known linearly polarized Gaussian beam.

On the propagation of the kurtosis parameter of general beams

Abstract The behaviour of the kurtosis parameter of a partially coherent beam that freely propagates is investigated. A general classification scheme of light beams is given in terms of the number of extremals of the kurtosis in free space. Propagation through ABCD optical systems is also considered and a number of general properties of the kurtosis parameter are provided concerning the relationship between the extremals of the kurtosis and the position of the beam waist.

Parametric characterization of coherent, lowest-order Gaussian beams propagating through hard-edged apertures

Analytical expressions for the width, far-field divergence, crossed moment, and generalized beam-quality parameter of a coherent, lowest-order Gaussian beam propagating through hard-edged slits are given in terms of the size of the opening and of the position of the aperture plane with respect to the beam waist. Some optimization criteria of these beam-shape parameters are also inferred.

Parametric characterization of the spatial structure of non-uniformly polarized laser beams

We present an approach for describing the spatial structure of partially polarized light fields. Unlike the treatments usually encountered in the literature, in which the polarization state is represented by position-dependent functions, the formalism shown here characterizes the polarization by means of a family of measurable overall parameters averaged over the transverse spatial region where the beam intensity reaches significant values. Generalized degrees of polarization are introduced to evaluate the uniformity of the spatial distribution of the polarization state of the beam-like field. The possibility of improvement and optimization of the quality of a polarized laser beam (understood as the general usefulness of such field for collimation and focussing) is analyzed by employing first-order optical systems. Finally, attention is briefly devoted to non-paraxial electromagnetic vector beams, whose parametric description of their polarization properties constitutes, at present, a challenge for theoreticians.

Sharpness changes of gaussian beams induced by spherically aberrated lenses

Sharpness changes of the spatial profile of a gaussian beam induced by spherically aberrated lenses are investigated in terms of the so-called kurtosis parameter. It is shown both theoretically and experimentally that, after a single aberrated lens, it is possible to get flatter and sharper beam intensity distributions than the input gaussian beam depending on the plane where the field is observed. Agreement between analytical and experimental results is discussed.Abstract Sharpness changes of the spatial profile of a gaussian beam induced by spherically aberrated lenses are investigated in terms of the so-called kurtosis parameter. It is shown both theoretically and experimentally that, after a single aberrated lens, it is possible to get flatter and sharper beam intensity distributions than the input gaussian beam depending on the plane where the field is observed. Agreement between analytical and experimental results is discussed.

Third- and fourth-order parametric characterization of partially coherent beams propagating throughABCD optical systems

Within the formalism of the Wigner distribution function, third- and fourth-order measurable beam parameters are proposed and their physical meaning is investigated. The general propagation law of such characteristic quantities inABCD optical systems is derived and a number of paramters are shown to be invariant under propagation inABCD devices.

Genuine cross-spectral densities and pseudo-modal expansions

A necessary and sufficient non-negative definiteness condition for the cross-spectral density (CSD) is provided. It is also shown that any genuine CSD can be expanded in terms of the so-called pseudo-modes of the source, understood as coherent contributions, not orthogonal to one another, that, superposed in an uncorrelated way, give rise to the CSD. Their evaluation is analyzed by means of an illustrative example.

Parametric characterization of non-uniformly polarized beams

A new overall parameter is defined, namely, the generalized degree of polarization, which involves the spatial distribution of the polarization of a light beam. This parameter is introduced on the basis of a general treatment recently proposed [Optics Lett. 22 (1997) 206] to characterize partially polarized fields, which extends the Stokes-Mueller formalism to describe the intensity moments of a quasimonochromatic beam. The main properties and the physical meaning of this parameter with regard to the spatial inhomogeneities of the polarization state are analysed, and a general measurement procedure is proposed.