Beam width of highly-focused radially-polarized fields.

On the basis of a formal analogy with the irradiance moments, analytical definitions are proposed for the width of both the transverse and the longitudinal component of rotationally-symmetric radially-polarized fields at the focal plane of a high-focusing optical system. The beam width of the whole field is also introduced. The transverse beam size is thus associated with the overall spatial structure of the field. The beam-width definitions are applied to an illustrative example, which enables us to show that, at the focal plane, the power contained within a circle whose radius is given by the proposed beam widths represents the main part of the total power.

Angular momentum decomposition of nonparaxial light beams.

The total angular momentum per unit length of a general non-paraxial beam is decomposed into an orbital component associated with the spiral spectrum at the far field and a component concerning the balance between right- and left-handed circular-polarization content of the angular spectrum. Expressions for the linear momentum and energy per unit length are also provided. The well-known division into orbital and spin components is shown to be recovered in the paraxial limit.

Cross-correlation between spiral modesand its influence on the overall spatial characteristics of partially coherent beams.

The overall spatial structure of a general partially coherent field is shown to be connected with the cross-correlation between the so-called spiral modes, understood as the terms of the spiral-harmonics series expansion of the field. The formalism based on the beam irradiance-moments is used, and the light field is globally described by the beam width, the far-field divergence, the beam quality factor, the orientation of the beam profile and the angular orbital momentum, given as the sum of its asymmetrical and vortex parts. This overall spatial description is expressed in terms of the intermodal coherence features (cross-correlation between spiral modes). The above analytical results are also illustrated by means of an example.

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.

Maximizing Young's fringe visibility under unitary transformations for mean-square coherent light.

Given the values of the degree of polarization of the fields at the pinholes in a Young interferometer, the maximum attainable visibility under unitary transformations is determined when the illuminating beam is mean-square light. Analytical expressions are also obtained for both the field vector (in the mean-square sense) and the cross-spectral density matrix associated with this kind of beams. A comparative summary is also provided of the main characteristics of well-known types of random electromagnetic fields frequently handled in the literature.

Propagation of light fields with radial or azimuthal polarization distribution at a transverse plane.

In terms of the angular spectrum representation, general expressions are given to describe the free-space propagation of electromagnetic fields with radial or azimuthal polarization structure at a transverse plane. The transverse distributions of the radial, azimuthal and longitudinal components of these fields are also analysed. In particular, the on-axis behavior upon free propagation is studied. Furthermore, the special but important case of those fields that retain their polarization character (radial or azimuthal) under propagation is also considered. The analytical results are illustrated by application to some examples.

Evanescent field of vectorial highly non-paraxial beams.

In terms of the Fourier spectrum, a simple but general analytical expression is given for the evanescent field associated to a certain kind of non-paraxial exact solutions of the Maxwell equations. This expression enables one to compare the relative weight of the evanescent wave with regard to the propagating field. In addition, in those cases in which the evanescent term is significant, the magnitude of the field components across the transverse profile (including the evanescent features) can be determined. These results are applied to some illustrative examples.

On the spatial orientation of the transverse irradiance profile of partially coherent beams.

On the basis of the irradiance-moments formalism, four matrices are proposed whose elements, defined for any partially coherent field, are closely related with the second-order measurable parameters handled in the ISO standard 11146. These matrices are shown to exhibit a number of properties concerning the orientation of the transverse profile of a partially coherent beam. This behavior is described by the rotation of the principal axes of the field around its propagation axis. In addition, these matrices provide information about the spatial structure of the field (beam spread product and orbital part of the angular momentum). A new overall parameter is introduced in terms of the above matrices, which remains invariant under rotation of the Cartesian coordinate axes and upon propagation through rotationally-symmetric first-order optical systems.

Beam propagation through uniaxial anisotropic media: global changes in the spatial profile.

The propagation of electromagnetic beams through uniaxial anisotropic media is investigated. The Maxwell equations are solved in the paraxial limit in terms of the plane-wave spectrum associated with each Cartesian field component. Attention is focused on the global changes in the spatial structure of the beam, which are described by means of the second-order intensity moment formalism. In particular, the propagation law for the intensity moments through this kind of media is obtained. As a consequence it is inferred that it is possible to improve the beam-quality parameter by using these media.

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.

Time-resolved spatial profile of TEA CO2 laser pulses: influence of the gas mixture and intracavity apertures.

The evolution of the intensity profile of transversely excited atmospheric CO2 laser pulses is investigated within the intensity moment formalism. The beam quality factor M2 is used to study the mode evolution. Attention is focused on the influence of both the gas mixture (N2 :CO2 :He) and the diameter of an intracavity diaphragm placed to attenuate higher-order modes. The degree of accuracy that can be attained by approximating the laser field amplitude by means of the lower-order terms of a Hermite-Gauss expansion is also analyzed. In particular, a bound for the truncation error is given in terms of two time-resolved spatial parameters, namely the beam width and the M2 parameter.

Quality improvement of partially polarized beams.

Improvement of the beam-quality parameter of partially polarized beams is investigated. We focus on the use of a Mach-Zehnder-type interferometric arrangement with crossed polarizers. The analysis has been carried out within the framework of the intensity moment formalism. Conditions are given under which the beam-quality parameter is optimized.

Spatial characterization of general partially polarized beams.

The spatial characterization of light beams given in terms of intensity moments is extended to partially polarized beams by means of a generalization of the Stokes-Mueller formalism. A simple classification scheme of partially polarized fields is proposed, and laws of propagation through nonpolarizing and polarizing optical systems are provided. Some invariant parameters are also investigated.

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 phase at the far field.

By use of the intensity moment formalism, a new tridimensional beam parameter is defined that is rotationally invariant and remains constant under propagation through certain classes of first-order optical systems. The special case of rotationally symmetric beams is considered in some detail. Also, for coherent beams this parameter is shown to be closely connected to the quadratic form of the phase of the directional power spectrum.

Time-resolved spatial parametric characterization of pulsed light beams.

New time-resolved spatial parameters are given that characterize the behavior of pulsed beams along with their propagation laws through first-order optical systems. The analytical conditions that should be fulfilled so that the intensity-moment formalism remains valid are investigated. Their physical meaning is also discussed, along with the implications for the evolution of the spatial profile of a pulsed beam.

Beam quality changes in Hermite-Gauss mode fields propagating through Gaussian apertures.

The beam quality behavior of Hermite-Gauss laser modes propagating through Gaussian apertures is analyzed.

Quality improvement of partially coherent symmetric-intensity beams caused by quartic phase distortions.

The effects that quartic phase distortions produce in the beam-quality parameter of partially coherent symmetric-intensitybeams are studied. An analytical expression for the beam-quality parameter at the output plane of a pure phase plate with quartic phase aberration has been derived. Explicit conditions to improve the beam quality are provided, and the corresponding optimized beam-quality value that can be attained for a given field has been determined.