Time delay with active single-ring and double-ring microresonator

Utilizing the coupling matrix of optical couples, we analyze the time delay of the transmitted and reflected wave in active single-ring and double-ring microresonator (MR) systems. Our research reveals that the group delay of output field relays on the coupling coefficient in the single-ring miscroresonator system. In the presence of gain in the microresonator, the increase of the gain will lead to an increase of output time delay at the resonance point. Furthermore, for the double-ring microresonator system, the number of resonance points depends on the coupling coefficients. For the smaller coupling coefficients, the increase of the gain leads to a decrease of the time delay of transmitted wave at the resonance point, but an increase of the time delay of the reflected wave.