In this paper, we analyze dynamics and frequency response of GaAs-based microring modulators at the 1.55 $\mu$m using the finite-difference time-domain method. Two types of modulation are investigated: pump-probe configuration and modulation of the coupling coefficient. The pump-probe signals are tuned at separate resonance wavelengths of the microring. Change of effective refractive index of the microring by two-photon absorption is used to modulate the probe beam. By applying probe beam in four timing configurations, it is shown that the wavelength shift of the probe depends not only on the pump intensity but also on the interaction length over which the pump and probe pulses overlap. It is also shown that free-carrier absorption increases when the temporal width of pump signal is wide enough. Modulation bandwidth of microring in the presence of nonlinear effects is investigated and it is shown that the bandwidth is in 10 GHz range. In order to increase the bandwidth of the intensity modulator, controlled coupling is used. It is shown that in this case, modulation bandwidth of waveguide-ring coupling strength becomes three times wider.
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