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.
We present a study on electrical and optical trade-offs of the doping map in a ring modulator. Here, we investigate the effects of the high-doped region distance to edge of the waveguide sidewall. Four groups of ring modulators with different rib-to-contact distances are fabricated and measured where the key parameters such as extinction ratio, insertion loss, transmission penalty, and bandwidth are compared quantitatively. Small-signal responses for the selected ring modulators are simulated where results are in agreement with measurement results. We show that, at 4dB extinction ratio, decreasing the high-doped region distance to rib from 800nm to 350nm will increase the bandwidth by 3.8 ×. However, we observed 8.4dB increase the insertion loss. We also show that the high-doped region location affects the trade-off between bandwidth and frequency response magnitude at low frequencies. At 350nm, this trade off is 2.5 × and 3.8× more efficient compared to 550nm and 800nm, respectively.
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