In this work, the paraxial evolution of fields generated by pseudo-Schell vortex sources is analyzed through some global parameters. In particular, it is shown that the kurtosis parameter of these fields presents a minimum at the beam waist and a maximum which value and position depends on the coherence characteristics of the source.
In this work a new type of partially polarized and partially coherent sources is proposed. The coherence characteristics of these sources are dependent on the difference of the radial distances from the source center of the two points to be compared. The coherence is perfect for points located on the same circle centered on the source center and decreases for points that belongs to different concentric circles. The maximum attainable coherence is related to the degree of polarization of the source. Coherence and polarization characteristics of this kind of fields at the source plane and upon free space propagation are analyzed in detail for a simple case. For the particular presented example, a partially polarized and partially coherent field is obtained, whose polarization properties are invariant in propagation.
We show that the terms of a Lax series, commonly used to evaluate propagated optical fields in nonparaxial conditions, present a factorially divergent asymptotic behavior in the case of highly nonparaxial beams, under rather general conditions.
This allows some resummation algorithms, such as the Weniger transformation, to be used in order for the evaluation of the propagated field to be successfully performed starting from the terms of the divergent Lax series.
Examples are presented, concerning cases for which the terms of the Lax series can be evaluated explicitly.
We introduce the beam coherence-polarization matrix as a tool for dealing with beam shaped fields that are at the same time partially coherent and partially polarized. Such matrix can capture differences between physically distinct beams that would appear identical in a scalar description. Examples are given.
A typical axially symmetric beam on paraxial free propagation maintains the same transverse shape as at its waist plane for a certain range along its axis. We introduce a general procedure for estimating this range.