Fig. 1: Generalized scattering matrix and augmented partial factorization (APF).
From: Fast multi-source nanophotonic simulations using augmented partial factorization
a,b, Schematic of light scattering from a nanostructure (grey circles). Outgoing waves (light-blue and orange arrows) resulting from inputs at two different incident angles (dark-blue and brown arrows) correspond to two different columns of the scattering matrix S (insets). c, Illustration of equation (2), which relates a generalized scattering matrix S to the inverse of the discretized Maxwell operator A, source profiles B that generate the incident waves, projection profiles C that extract the outputs of interest and the matrix D that subtracts the baseline. Each small circle indicates a nonzero element of the sparse matrix, coloured based on its spatial location shown in d. d, Discretization grids of the illustration in c, with colour coding for different regions of the system. e, The augmented sparse matrix K of equation (3), whose partial factorization gives the generalized scattering matrix S.
