  Fabrication imperfections must be considered during configuration to ensure
that the setup is suitable for the actual fabricated programmable photonic
integrated circuits (PPICs). Therefore, characterization of imperfections is
crucial but difficult, especially for PPICs made from recirculating waveguide
meshes. The flexibility required by these meshes demands a more complex
topology and compact TBU structure, complicating the characterization. In this
paper, we propose a characterization method applicable to recirculating
waveguide meshes based on an optimization approach, along with a step-by-step
procedure to reduce the parameter space of optimization, allowing for
characterizing imperfect parameters of each individual component within the
waveguide mesh. To the best of our knowledge, this method can greatly broaden
the range of characterized parameters compared to currently reported methods.
In order to verify the effectiveness of our method, we used the characterized
parameters to build a multi-frequency model of a mesh with fabrication errors
and successfully demonstrated accurate prediction of its behavior. Furthermore,
we applied our method on implementations of 6 different kind of FIR/IRR
filters, to further prove the effectiveness of our method in configuring
applications on meshes with fabrication errors. At last, our method was carried
out under various scenarios considering beam splitter splitting ratio variance,
inaccurate measurements of mesh and imprecise TBU insertion loss
characterization, to demonstrate its strong robustness under various practical
scenarios.
