Fig. 2: Nulling method of self-configuration.
a Configuring MZI Tmn updates matrix W. b Corresponding nulling update to X = UW†, which is c equivalent to zeroing an output of Tmn given a fixed input. d Allowed range of \(s={T}_{11}/{T}_{12}\in {\mathbb{C}}\), showing the forbidden regions centered at s = 0 and s = ∞ that arise from hardware imperfections (α = 0.23, β = 0.07 chosen for illustrative purposes). Contours for (θ, ϕ) are plotted in the accessible region (gray). e Probability density P(s) plotted on the Riemann sphere for meshes of size N = 4, 16, 64, and 256.
