Analysis of negative group delay response of all-pass ring resonator with Mach-Zehnder interferometer

The chromatic dispersion characteristics of waveguide all-pass filters were theoretically analyzed, in which the round-trip loss of a ring resonator was taken into account. Although an all-pass filter based on a ring resonator is lossless in principle, a finite round-trip loss of an actual filter changes an amplitude response and a group delay response drastically. The negative group delay resonance peak was confirmed both theoretically and experimentally.