Time response of a microring resonator to a rectangular pulse in different coupling regimes

We discuss the analytical temporal response of a microring resonator excited through a bus waveguide by an optical rectangular pulse. Finite difference time domain simulations illustrate the analytical solution and help in understanding the meaning of the different coupling regimes. In addition, we show that the temporal dynamics allow determining the coupling regime while the commonly used spectral characterization in the stationary regime does not. We also take advantage of the simulation to highlight the phase shift between the input and the output signals in the different coupling regimes. Finally, measurements on an $Si_3N_4$ microring resonator are performed and analyzed in the case of an under-coupling regime to illustrate how the time response study leads to the Q-factor determination.