Optical resonators with a double-coupler and double-ring configuration
incorporated into optical amplifiers that have negative gain are anal
yzed. The resonators are presented with a unique signal-flow graph tog
ether with z-transform variables for sampled optical signals. Their op
tical transfer functions are obtained by a graphical technique. The po
les and zeroes in the z plane of the transfer functions are examined,
which leads to some unique design features of the resonators for optic
al-filtering applications.