Planar realization of all-optical 2D switching networks

Assuming advantages of all-optical 2D switching networks, the question arises which advantages are preserved by the planarization and what are the costs. The planarization of all-optical 2D switching networks show different results depending on (1) the geometry N >= 3 and the (2) implementation by directional couplers and Mach-Zehnder interferometers, respectively. The feed-forward graphs (FFGs), being the complete graph models of planar 2D switching networks, are the starting point for the planarization which is classified into (1) the direct realization where the 2D network is transformed into its isomorphic FFG according to a certain scheme (2) the recurrent realization of 2D networks (a network is represented by smaller networks) and (3) multi-layer realizations. The FFGs are optimized with regard to (4) a minimum number of crossings and (5) minimum skews.