Relative Wavefront Error Correction Over a 2.4 km Free-Space Optical Link via Machine Learning

TL;DR

A machine learning-based wavefront correction algorithms are developed to compensate for observed WFEs, via phase retrieval, resulting in up to a 2/3 reduction in the relative phase error variance.

Abstract

In coherent optical communication across turbulent atmospheric channels, reference beacons can be multiplexed with information-encoded signals during transmission. In this case, it is commonly assumed that the wavefront distortion of the two is equivalent. In contrast to this assumption, we present experimental evidence of relative wavefront errors (WFEs) between polarization-multiplexed reference beacons and signals, after passing through a 2.4 km atmospheric link. We develop machine learning-based wavefront correction algorithms to compensate for observed WFEs, via phase retrieval, resulting in up to a 2/3 reduction in the relative phase error variance. Further, we analyze the excess noise contributions from relative WFEs in the context of continuous-variable quantum key distribution (CV-QKD), where our findings suggest that if future CV-QKD implementations employ wavefront correction algorithms similar to those reported here, an order of magnitude increase in secure key rates may be forthcoming.

Figures (3)

• Figure 1: Experimental setup for preparation and measurement of a reference and signal, with the 2.4 km link shown at the bottom right, and HG mode intensity and phase profiles shown at the receiver. AOM is an acousto-optic modulator, Pol is a polarizer, PC is a polarization controller, PD is a photodetector, ZBE is zoom beam expander, MC is the mode cleaner, Tx is the transmitter, Rx is the receiver, Ch is the channel, CCR is the corner-cube retroreflector, and BENLOg represents our logarithmic photodetectors.
• Figure 2: Derived variances ${\mathrm{Var}(\Delta\phi_{mn})}$ (red bars) versus correction variances ${\mathrm{Var}(\Delta\phi_{mn} - \Delta\tilde{\phi}_{mn})}$ (blue bars) for all campaigns, where purple shows where the derived variances and correction variances overlap. Covariances of relative mode phase errors are shown in the insets. $C^2_n$ was estimated to be $[2.70, 2.57, 2.68] \times10^{-15}$ m$^{-2/3}$ for the morning, noon and evening campaigns, respectively.
• Figure 3: Top-(a) Total relative phase error variances $\mathrm{Var}(\Delta\phi)$ and bottom-(b) average effective excess noise $\xi_t$ for a trusted detector, for accumulating HG modes, for all campaigns, where D represents derived (plotted as solid lines) and C represents corrected (plotted as dot-dashed lines).