A simple analytical model is proposed to describe the transversal spatial structure of a tridimensional rotationally symmetric pulsed beam. The spatial behaviour of the pulse amplitude is shown to be linked to its (measurable) second-and higher-order intensity moments, namely, beam width, quality parameter and kurtosis. As an illustrative experimental example, this model has been applied to high-quality TEA CO 2 laser pulses.

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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.

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.

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.