Abstract
We introduce and formalize a time-frequency dualism between first-order dispersion and quadratic phase modulation (time lens). As a particular case of this dualism, we demonstrate that when a time lens operates on an input optical pulse, this pulse can enter a regime which is the frequency-domain equivalent of the temporal Fraunhofer regime (real-time Fourier transformation by dispersion). In this new regime, which we will refer to as spectral Fraunhofer regime, the input pulse amplitude is mapped from the time domain into the frequency domain ( time-to-frequency conversion). Here we derive the conditions for achieving time-to-frequency conversion using a single time lens as well as the expressions governing this operation. Besides its intrinsic physical interest, time-to-frequency conversion can be used for measuring ultrafast temporal waveforms with a spectrum analyzer.
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