Ring modulator small-signal response analysis based on pole-zero representation

We present a closed-form expression for the small-signal response of a depletion-mode ring modulator and verify it by measurement results. Both electrical and optical behavior of micro-ring modulator as well as the loss variation due to the index modulation is considered in the derivation. This expression suggests that a ring modulator is a third-order system with one real pole, one zero and a pair of complex-conjugate poles. The exact positions of the poles/zero are given and shown to be dependent upon parameters such as electrical bandwidth, coupling condition, optical loss, and sign/value of laser detunings. We show that the location of zero is different for positive and negative detuning, and therefore, the ring modulator frequency response is asymmetric. We use the gain-bandwidth product as a figure of merit and calculate it for various pole/zero locations. We show that gain-bandwidth for the over-coupled ring modulator is superior compared to other coupling conditions. Also, we show that the gain-bandwidth product can be increased to a limit by increasing the electrical bandwidth. (C) 2016 Optical Society of America