Symmetry between the transfer properties of micro-ring resonators with gain and with loss

摘要

Gain and loss affect the performance of dispersive micro-ring resonator systems significantly. Through analysing the transfer functions of two-port ring-resonator (TPRR) circuits and coupled micro-ring resonators, the symmetry between the transfer properties of micro-ring resonators with loss and with gain is discovered. For two TPRRs whose attenuation and gain coefficients are equal to each other, or for two coupled micro-ring resonators whose counterparts have equal gain and loss respectively, their intensity transmissions are reciprocal, while the phase shifts and dispersions are the same. This symmetry demonstrates the action mechanism of loss and gain on the transmissions and dispersions of these micro-ring resonators. It is useful for analysing and designing micro-ring resonators in group velocity control and dispersion compensation applications.