Design of optically path-length-matched, three-dimensional photonic circuits comprising uniquely routed waveguides

A method for designing physically path-length-matched, three-dimensional photonic circuits is described. We focus specifically on the case in which all the waveguides are uniquely routed from the input to output-a problem that has not been addressed to date and that allows for the waveguides to be used in interferometric measurements. Circuit elements were fabricated via the femtosecond laser direct-write technique. We demonstrate via interferometric methods that the fabricated circuits were indeed optically path-length matched to within 45 μm, which is within the coherence length required for many applications.