A Dynamic Model of Silicon Bragg Grating Modulators

We present a dynamic model of silicon Bragg grating modulators that takes into account the distributed feedback of the grating coupled to depletion-based phase-shifters. We further consider the on-chip degradation of the radio-frequency excitation. This dynamic model allows the optimization of the grating design parameters such as its strength and length. We apply the proposed model to uniform Bragg grating modulators and show that grating modulators operated in reflection have larger 3 dB E/O bandwidth (BW), while gratings operated in transmission have larger optical modulation amplitude. As a result, higher speed on-off keying signal will be obtained using the reflection port while higher quality multi-level pulse amplitude modulation signal should be obtained in transmission, albeit at a lower baud rate. We also show that longer gratings have larger 3 dB modulation BW but noisier responses. Finally, we find that optical propagation losses results in either higher driving voltage or reduced modulation BW. The model is experimentally validated and we examine how RF propagation losses also limit the E/O BW.