Radial–angular entanglement in Laguerre–Gaussian mode superpositions

Classical optic entanglement between the radial and angular degrees of freedom in Laguerre-Gaussian mode superpositions is explored within the framework of symmetric first-order optical systems. The Gouy phase picked by a Laguerre-Gaussian mode on free propagation is seen to be of consequence to the radial-angular entanglement in the mode superpositions. We illustrate examples of mode superpositions for which radial-angular entanglement is preserved on passage through symmetric first-order optical systems. An indicator of radial-angular entanglement in two-mode Laguerre-Gaussian superpositions is demonstrated to be a robust free space signaler in the presence of atmospheric turbulence, through examples.