Inverse design of a spatial demultiplexer for free-space optical communications: direct optimization over turbulence statistics

Abstract

Atmospheric turbulence severely limits the coupling of received optical wavefronts into single-mode fibers in satellite-to-ground free-space optical links. Spatial demultiplexing receivers address this challenge by distributing the incoming field across a bundle of single-mode fibers whose outputs are recombined coherently, relaxing the requirements on wavefront correction. In this work, we investigate the design of such receivers from two complementary angles. We first compare the power coupling statistics achieved by several modal bases and show that the spatial support of the modes matters far more than the specific choice of basis, questioning the relevance of mode-selective approaches for this application. We then present the inverse design of a compact two-plane refractive system optimized directly over an ensemble of turbulence realizations using stochastic gradient descent, with no constraint imposed on the input modal decomposition. The optimized system significantly improves over direct coupling into the fiber bundle, approaches the performance of an ideal modal projection, and remains competitive across a broad range of turbulence conditions.

Figures (8)

• Figure 1: Left: normalized squared singular value spectrum of the Karhunen-Loève basis, showing the rapid decay of the eigenvalues. Right: four representative turbulent wavefront realizations at $D/r_0 = 8$, displayed within the circular collecting pupil. The phase is shown in radians.
• Figure 2: Power coupling efficiency $\eta$ of the Karhunen-Loève basis at $D/r_0 = 8$, without (blue) and with (orange) tip-tilt correction. Left: $\eta$ over 300 representative turbulent realizations. Right: distribution of $\eta$ over 3000 realizations, with fitted Kumaraswamy distributions overlaid.
• Figure 3: Total intensity of the four modal bases considered in this work, summed over the first 91 modes: wide packing (top left), dense packing (top right), Laguerre-Gauss (bottom left), and Karhunen-Loève (bottom right). The dashed red circle indicates the boundary of the collecting pupil of diameter $D = 160\,\mathrm{\mu}$m.
• Figure 4: Power coupling efficiency distributions for the four modal bases considered in this work at $D/r_0 = 8$. Left: without tip-tilt correction. Right: with tip-tilt correction. Histograms show the empirical distributions over 3000 turbulent realizations; solid curves show the fitted Kumaraswamy distributions.
• Figure 5: Schematic of the two-plane refractive demultiplexer. A telescope images the collecting aperture onto a $160\,\mathrm{\mu}$m input pupil. The optimized glass slab ($n = 1.5$, thickness $150\,\mathrm{\mu}$m) with two freeform surfaces redirects the incoming turbulent wavefront onto an array of 91 single-mode fibers placed $50\,\mathrm{\mu}$m after the second surface.