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 directwrite 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.