Spectral Fraunhofer regime: time-to-frequency conversion by the action of a single time lens on an optical pulse

We analyze a new regime in the interaction between an optical pulse and a time lens (spectral Fraunhofer regime), where the input pulse amplitude is mapped from the time domain into the frequency domain (time-to-frequency conversion). Here we derive in detail the conditions for achieving time-to-frequency conversion with a single time lens (i.e., for entering the spectral Fraunhofer regime) as well as the expressions governing this operation. Our theoretical findings are demonstrated both numerically and experimentally. A comparative study between the proposed single-time-lens configuration and the conventional dispersion + time-lens configuration for time-to-frequency conversion is also conducted. Time-to-frequency conversion with a single time lens can be used for applications similar to those previously proposed for the conventional time-to-frequency converters, e.g., high-resolution measurement of fast optical temporal waveforms. Moreover, our results also indicate that the spectral Fraunhofer regime provides additional capabilities for controlling and processing optical pulses.