Structured light beams constituted of incoming and outgoing waves

Abstract

In the present work, we demonstrate that structured light beams are constituted by two traveling waves which transverse components are in opposite directions, that is, incoming and outgoing from the axis of propagation. These waves result from the complex sum of the two fundamental solutions of the transverse component of the spatial wave equation. After a partial obstruction of the beam, the incoming and outgoing waves can be easily observed during the self-healing process, providing a simple explanation of the phenomenon. Incoming and outgoing waves in Laguerre-Gauss beams are investigated analytically, numerically and experimentally. The proposed way to describe light beams might offer new insights into the phenomenon of diffraction.

Spiral light beams inspired by galaxies with dark matter

“…The mixture of the radial and azimuthal components in the phase of the SLGBs can open a new way to tailor the intensity distributions in the light beams. We consider that these SLGBs can be generated experimentally with a computer hologram in a spatial light modulator (SLM) [23,25], because the SLGBs equation is well defined, as is that of the Laguerre-Gauss beams [33]. Finally, we consider that this work has applications to the study of particle manipulation [41], and fiber-optic communication [42].…”

“…We can also use Bessel beams (BBs) seed u(r) considering similar conditions of LGBs [32]. Nevertheless, they conserve their properties only at a diffraction distance, and LGBs go further than the BBs, and they have better self-healing properties than Bessel beams [33]. It is noteworthy that the free-space propagation of the light beams transforms the seed beams using the phase i r exp , f F ( (…”

On the physical limitations of structured paraxial beams with orbital angular momentum

“…It is noteworthy that the coefficient C m,n , introduced in equation ( 15) and defined in equation ( 29), can only be obtained by means of an asymptotic analysis without which a consistent construction of Hankellike Laguerre functions cannot be performed. The lack of this asymptotic analysis in [32] prevented a proper definition of traveling-wave solutions, as we will see next.…”

“…Laguerre-Gauss beams are another example of paraxial beams for which traveling-wave solutions can be attributed. In fact, that kind of solutions have recently been introduced, but their mathematical formalism was briefly discussed, and neither their divergent nor asymptotic behavior were properly addressed [32], a thorough mathematicalphysics study is required.…”

Revealing the modal content of obstructed beams

“…Contrary to the initial belief, many different families of beams possess a self-healing property [16]; not just the non-diffracting type. The selfhealing of Laguerre-Gaussian beams [17] and Hermite-Gaussian beams [18] has been demonstrated. More generally, it turns out that any beam has the capacity to self heal [19].…”