<title>Spatial ray dynamics in the formation of optical speckle fields</title>

Internal flows and energy circulation in light beams

“…Quantitatively, transformation of the intensity pattern of a propagating beam is described by relation (3.46) that can be rewritten in the form is introduced. Equations (7.4), (7.5) form a ground for the 'hydrodynamic' approach to the beam evolution that appears especially helpful in complex situations of stochastic wave propagation [157][158][159]. Note that by introducing the electromagnetic mass with the density 2 e m w c = we can formulate the law (7.4) of the beam transformation exactly in terms of the fluid mechanics; however, this analogy is not complete because, except the continuity equation (7.4), the electromagnetic 'fluid' also obeys the Maxwell equations rather than mechanical equations of the fluid motion.…”

“…In the extreme case, the beam transverse section is divided into a number of 'beamlets' that propagate in directions determined by the local transverse momentum density. This concept is employed in regular approaches to wavefront sensing, such as the Hartmann method [160]; in essence, they measure the transverse orbital momentum [158] whence the phase profile is reconstructed via (3.44) or (3.45). However, this approach is only applicable to the rather wide and smooth beams that occur, e.g., in astronomy or in optical testing, including vision correction.…”

Optical Scully vortex and its spatial evolution

“…1 shows the dependence of the circulation ΓR; z calculated by Eq. (13). The calculation is performed for the longitudinal coordinate z z d , where z d ka 2 is the diffraction length.…”

“…The spatial dynamics of the vector field α is illustrated by the set of streamlines [1,[13][14]. These lines (mean diffraction rays) are integral curves of the first-order differential equation of the form…”