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

R. Martínez-Herrero, A. Manjavacas, P. M. Mejías

2009
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Optics Express
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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 irradiancemoments 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
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... n 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. 1 1 n n W − + (see Eq. (12)), which involve intermodal cross-correlations. Taking all this into account, a number of direct consequences follow for general partially coherent beams: i) The focusing properties in the near-and far-field (beam width, divergence and waistplane position, given by the elements of (0) M ) do not depend on the intermodal coherence. ii) Accordingly, the beam quality parameter is also independent of any cross-correlation between spiral modes that constitutes the field. iii) The intermodal coherence has no influence on the z-component of the orbital angular momentum, z J . In other words, different cross-correlation between spiral modes can give rise to the same value of z J . iv) The orientation of the profile of a freely-propagating beam and the asymmetrical OAM, ( ) a z J (both contained in matrices (1) M and (2) M ) depend on the crosscorrelation between pairs of spiral modes separated by two orders (n + 1 and n-1). When such a cross-correlation does not exist, the spatial profile does not rotate upon free propagation, even though the rest of intermodal correlations differ from zero. In addition, ( ) 0 a z J = . v) The vortex part, ( ) v z J , of the OAM also depends of the intermodal coherence of the pair of modes n-1, n + 1. Property iii indicates, however, that such cross-correlation has no influence on the sum ( ) Example To illustrate the above general conclusions, let us now consider a light field represented by the following stochastic process at some transverse plane:

doi:10.1364/oe.17.019857
pmid:19997207
fatcat:lmikuv7dffglrccke4fovvft7m