PROPAGATION OF HIGHER-ORDER INTENSITY MOMENTS IN QUADRATIC-INDEX MEDIA

A more detailed characterization of partially coherent optical beams requires the determination of higher-order intensity moments. If the beam is propagating in quadratic-index media its transformation is completely given by the ABCD matrix. This holds for all intensity moments, as will be shown in this paper. Analytic expressions are given for the transformation of the generalized moments [x(m)THETA(n)], where x is the beam width and THETA the far-field divergence. The complete determination of the radiation field requires the knowledge of all intensity moments. From the experimental point of view, only moments up to fourth-order make sense. Higher-order moments are subject to large errors and are too difficult to measure. Of special interest are the higher moments of near- and far-field [x(m)], [THETA(m)]. The transformation of these moments by an optical system, characterized by its ABCD matrix is derived up to order 8. For m less-than-or-equal-to 4 the transformations is: [x2m] = [(Ax1 + BTHETA1)m] + delta(m4) 3 . A2B2/k2 [THETA2m] = [(Cx1 + DTHETA1)m] + delta(m4) 3 . C2D2/k2 with k the wavenumber and delta(m4) the Kronecker function. The brackets denote the corresponding integrals. This is a more comprehensive representation of the formulation given by Martinez-Herrero et al. [1].