Coherent frequency-to-time mapping revisited: Breaking the Fraunhofer limit to achieve ultrabroad radio-frequency waveforms

In this contribution, we revisit the criteria required to achieve the well-known frequency-to-time mapping phenomenon. It is found that the popular far-field inequality is too restrictive when applied to most of the waveforms of interest in radio-frequency arbitrary waveform generation. A new condition based on notions borrowed from the field of antenna engineering is investigated. This “antenna designer's formula” sets a more precise limit on the minimum dispersion required for the frequency-to-time mapping to occur. Numerical and experimental results show how spectrally engineered waveforms are mapped into the time domain using dispersion amounts smaller than expected. These results pave the way to synthesize electromagnetic pulses with ultrabroad frequency content using coherent frequency-to-time mapping.