Title: Variational processing of partially coherent light in photonic integrated circuits Abstract: Classical and quantum optical fields are naturally described in terms of modes. Modal decompositions underpin our understanding of the generation, propagation, and measurement of multimode light, as exemplified by the Karhunen–Loève expansion for partially coherent fields, density-matrix eigendecompositions, Schmidt decompositions of bipartite states, and the Bloch–Messiah decomposition of Gaussian …