Extended Data Fig. 4: Modal analysis of the BSV beam.

(a) Spatial mode of the BSV averaged over 100 shots. (b) First principal component from the most prominent eigenvector of the covariance matrix of flattened single-shot images, displaying nearly identical structure to the average spatial mode. (c) Average spectrum before (orange) and after (blue) spectral filtering and representative single-shot spectra from the two distinct clusters (black lines). (d) Monte Carlo sampling of two uncorrelated distributions, one with thermal (exponential) statistics, representing the non-degenerate mode (dashed black line in panel c), and one with BSV statistics, representing the degenerate mode (dotted black line in panel c). The orange and blue curves represent the case where the two modes have equal intensity and where the non-degenerate mode has 10 percent of the intensity of the degenerate mode, respectively. These situations correspond approximately to the filtered and unfiltered spectra in (c).