“…Optical paths are composed only of vertical or horizontal segments joined by 90-degrees turns. Each element of the grid identified by the position (row, column) can be only of a finite number of types: horizontal straight segment (e.g., (1,1) in the grid), vertical straight segment (e.g., (4, 4)), left turn 2 (e.g., (7,4)), right turn (e.g., (2, 8)), turn pair 3 (e.g., (2,4)), path crossing intersection (at 90 • ) (e.g., (2,6)) and path crossing intersection with an optical 2 × 2 switching device 4 (that is supposed to have the two states cross and bar) (e.g., (1,4)). In this work we do not consider wavelength division multiplexing: all signals are at the same wavelength.…”