Fig. 2: Modal fidelity measurement.

a, b The measured amplitude, phase, and polarization of the scrambled probe beams and unscrambled signal beams for horizontally polarized LG(3,2) and HG(4,4) mode respectively. c, d The unnormalized modal fidelity for unscrambled Laguerre–Gauss modes and Hermite–Gauss modes. A single index is used to denote the two-mode indices for simplicity (see Supplementary Note 3), and the light and dark blue bands denote the odd and even mode group number respectively.