Abstract
The calculation of the propagation of partially coherent and partially polarized optical beams involves using 4D Fourier Transforms. This poses a major drawback, taking into account memory and computational capabilities of nowadays computers. In this paper we propose an efficient calculation procedure for retrieving the irradiance of electromagnetic Schell-model highly focused beams. We take advantage of the separability of such beams to compute the cross-spectral density matrix by using only 2D Fourier Transforms. In particular, the number of operations depends only on the number of pixels of the input beam, independently on the coherence properties. To provide more insight, we analyze the behavior of a beam without a known analytical solution. Finally, the numerical complexity and computation time is analyzed and compared with some other algorithms.
Highlights
Three-dimensional electromagnetic field distributions generated in the focal region of a high numerical aperture (NA) focused system has been extensively investigated in the last years [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]
Equation (18) provides the relationship between the properties of coherence-polarization of the incident beam and the elements of the polarization matrix of the focused field. This equation appears to be specially suitable for the numerical evaluation of the focused field since it only involves 2D arrays. This means that the calculation of the elements of the cross spectral density matrix (CSDM) can be performed in a reasonable short amount of time
We proposed a computational procedure for calculating the CSDM W(r, r, z) in the focal region of a high NA optical system, assuming electromagnetic Schell input beams
Summary
Three-dimensional electromagnetic field distributions generated in the focal region of a high numerical aperture (NA) focused system has been extensively investigated in the last years [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]. The incident beam is assumed to be an electromagnetic Schell field This kind of paraxial fields is one of the more remarkable models of partially coherent and partially polarized beams, mainly due to their simple mathematical form and the wide range of applications [46,47,48,49]. Taking advantage of their particular properties, it is possible to reduce the 4D problem to a set of six 2D convolutions, independently on the shape of the beam.
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