Power Control in Non-Hermitian Lattices Through Singular Value Decomposition

Periodic structures in optics, like gratings or photonic crystals have played a pivotal role in both basic and applied research applications over the decades [1]. As far as, integrated photonics is concerned, another highly relevant optical structure, that of photonic lattices, has been an important platform for nonlinear and guided paraxial optics [2]. Here we theoretically examine the problem of power control in complex lattices, in the context of non-Hermitian photonics [3], [4], by applying singular value decomposition (SVD) techniques on the evolution propagators of non-normal matrices and operators [5]–[7].