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 where all the waveguides are uniquely routed from the input to output; a problem which has not been addressed to date and 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 um which is within the coherence length required for many applications.