Linear-optics time-frequency analysis of complex multi-THz-bandwidth waveforms from a single optical spectrum

The analysis of sophisticated ultrabroadband (multi-THz bandwidth) optical waveforms is essential for many advanced applications, yet current techniques are limited, energy-inefficient, and/or often require multiple spectral measurements. Here, we propose and experimentally demonstrate a simple linear-optics technique for measuring the joint time-frequency distribution of such waveforms. The technique relies on energy-efficient linear phase-only manipulations to map the waveform's short-frequency Fourier transform (SFFT) onto a single optical spectrum. The proposed architecture, involving temporal dispersion and electro-optic phase modulation, has no intrinsic analysis-bandwidth limitation; it is constrained only by the usable span of practical photonic components. Using this approach, we demonstrate the characterization of intricate waveforms spanning up to 11 THz over nanosecond durations, corresponding to ultrahigh time-bandwidth products exceeding 16,000.