Characterizing the radial content of orbital-angular-momentum photonic states impaired by weak-to-strong atmospheric turbulence

Abstract

The changes in the radial content of orbital-angular-momentum (OAM) photonic states described by Laguerre-Gaussian (LG) modes with a radial index of zero, suffering from turbulence-induced distortions, are explored by numerical simulations. For a single-photon field with a given LG mode propagating through weak-to-strong atmospheric turbulence, both the average LG and OAM mode densities are dependent only on two nondimensional parameters, i.e., the Fresnel ratio and coherence-width-to-beam-radius (CWBR) ratio. It is found that atmospheric turbulence causes the radially-adjacent-mode mixing, besides the azimuthally-adjacent-mode mixing, in the propagated photonic states; the former is relatively slighter than the latter. With the same Fresnel ratio, the probabilities that a photon can be found in the zero-index radial mode of intended OAM states in terms of the relative turbulence strength behave very similarly; a smaller Fresnel ratio leads to a slower decrease in the probabilities as the relative turbulence strength increases. A photon can be found in various radial modes with approximately equal probability when the relative turbulence strength turns great enough. The use of a single-mode fiber in OAM measurements can result in photon loss and hence alter the observed transition probability between various OAM states. The bit error probability in OAM-based free-space optical communication systems that transmit photonic modes belonging to the same orthogonal LG basis may depend on what digit is sent.