We present for the first time a comparison under similar circumstances between Laguerre-Gauss beams (LGBs) and Bessel beams (BB), and show that the former can be a better option for many applications in which BBs are currently used. By solving the Laguerre-Gauss differential equation in the asymptotic limit of a large radial index, we find the parameters to perform a peer comparison, showing that LGBs can propagate quasi-nondiffracting beams within the same region of space where the corresponding BBs do. We also demonstrate that LGBs, which have the property of self-healing, are more robust in the sense that they can propagate further than BBs under similar initial conditions.
We realize a robust and compact cylindrical vector beam generator which consists of a simple two-element interferometer composed of a beam displacer and a cube beamsplitter. The interferometer operates on the higherorder Poincaré sphere transforming a homogeneously polarized vortex into a cylindrical vector (CV) beam. We experimentally demonstrate the transformation of a single vortex beam into all the well-known CV beams and show the operations on the higher-order Poincaré sphere according to the control parameters. Our method offers an alternative to the Pancharatnam-Berry phase optical elements and has the potential to be implemented as a monolithic device. 1 arXiv:1908.07562v1 [physics.optics]
Perfect vortex beams (PVBs) have intensity distributions independent of their topological charges. We propose an alternative formulation to generate PVBs through Laguerre–Gauss beams (LGBs). Using the connection between Bessel and LGBs, we formulate a modified LGB that mimics the features of a PVB, the perfect LGB (PLGB). The PLGB is closer to the ideal PVB, maintaining a quasi-constant ring radius and width. Furthermore, its number of rings can be augmented with the order of the Laguerre polynomial, showing an outer ring independent of the topological charge. Since the PLGB comprises a paraxial solution, it is closely related to an experimental realization, e.g., using spatial light modulators [Phys. Rev. A 100, 053847 (2019)PLRAAN1050-294710.1103/PhysRevA.100.053847].
We show that structured light beams can be customized with a differential operator in Fourier space. This operator is represented as an algebraic function that acts on a seed beam for adjusting its shape. If the seed beams are perfect Laguerre–Gauss beams (PLGBs) and Bessel beams (BBs) without orbital angular momentum, we demonstrate that the custom beams generated on the seed-PLG preserve their distribution a longer distance than the propagation-invariant custom-caustic light fields obtained with the seed-Bessel, where both beams have similar initial conditions. In this sense, the custom-PLGBs can be a better option for many applications where the propagation-invariant light fields are used. We show some beam distributions—astroid, deltoid, and parabolic—generated with both seeds.
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.
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