A reduced-blocking system where a perfect shuffle equivalent network having a plurality of node stages successively interconnected by link stages, is advantageously combined with expansion before the node stages and/or concentration after the node stages in a manner allowing the design of a system with arbitrarily low or zero blocking probability. An illustrative photonic system implementation uses free-space optical apparatus to effect a low loss, crossover interconnection of two-dimensional arrays of switching nodes comprising, for example, symmetric self electro-optic effect devices (S-SEEDs). Several low loss beam conbination techniques are used to direct multiple arrays of beams to an S-SEED array, and to redirect a reflected output beam array to a subsequent node stage.