Effect of velocity mismatch and microwave attenuation on time-domain response of traveling-wave electrooptic modulators

The dynamic response of a traveling-wave (TW) electrooptic phase modulator is treated using a Fourier transform technique. An integral expression for the induced phase shift which takes into account the optical-microwave velocity mismatch and the microwave attenuation is derived. In the case of a Gaussian modulating pulse and negligible microwave attenuation, the temporal dependence of the modulated pulse amplitude can be expressed in terms of error functions. Calculated pulse shapes showing the transition from a Gaussian to a flat top output pulse with increasing phase mismatch in the absence of microwave attenuation are presented. The effect of microwave attenuation on pulse shape, amplitude, and width is also explored. The method used to obtain these results is generally applicable to the time-domain analysis of TW modulators.