We performed a scaling analysis of programmable hexagonal two-dimensional (2D) waveguide meshes with different shapes. We show that the shape of the meshes can impose restrictions such as high path losses or large foot-prints for certain configurations and applications. We use the graph-based strategy to guide our applicationspecific scaling analysis. The design practices are discussed for implementing the programmable mesh for beam splitters and NxN switches. This will provide a guideline of the shape and size for the future programmable photonic circuits.
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