Scalable analysis for arbitrary photonic integrated waveguide meshes

The advances in fabrication processes in different material platforms employed in integrated optics are opening the path towards the implementation of circuits with increasing degrees of complexity. In addition to the more conventional application specific photonic circuit paradigm, the programmable multifunctional photonics (PMP) approach is a transversal concept inspired by similar approaches, which are already employed in other technology fields. For instance, in electronics, field programmable gate array devices enable a much more flexible universal operation as compared to application specific integrated circuits. In photonics, the PMP concept is enabled by two-dimensional (2D) waveguide meshes for which the number of possible input/outputs ports quickly builds up, and, furthermore, internal signal flow paths make the computation of transfer functions an intractable problem. Here we report a scalable method based on mathematical induction that allows one to obtain the scattering matrix of any 2D integrated photonic waveguide mesh circuit composed of an arbitrary number of cells and that is easily programmable. To our knowledge this is the first report of the kind, and our results open the path to unblocking this important design bottleneck.