Ultrabroad bandwidth signal generation based on frequency-to-time mapping in the temporal Fresnel regime

We show that there are some waveform examples that achieve frequency-to-time mapping while violating the above far-field inequality, thus suggesting that the Fraunhofer requirement is not always a necessary condition. In the context of E-AWG, achieving the frequency-to-time mapping operation at smaller GDD amounts than expected allows us to obtain pulses with significantly broader radio-frequency content.