Capturing ultra-broadband complex-fields of arbitrary duration using a real-time spectrogram

Abstract

One of the most intuitive representations of a waveform is achieved through time-frequency analysis, which depicts how the frequency components of a wave evolve over time. Time-frequency representations, such as the spectrogram, are well-known for allowing full-field characterization of a signal in terms of amplitude and phase. However, present methods to capture the spectrogram of a waveform are only suited for either relatively slow (<GHz bandwidth) waveforms of arbitrary duration or fast (>THz bandwidth) waveforms of short duration. It remains very challenging to capture the time-frequency representation of broadband waves extending over long durations, as required for many important fields in science and technology. Here, we introduce a linear optics temporal imaging concept based on electro-optic time-lensing and dispersive propagation to map the 2D spectrogram as a 1D waveform along the temporal domain. This technique enables ultra-broadband spectrogram analysis without any gaps in the acquisition and with no inherent limitation on maximum signal duration. The spectrogram is captured at unmatched processing rates, up to 16 × 109 Fourier transforms per second (∼60 ps per spectral frame), using a single photodetector and in a fully self-referenced manner. Under certain conditions, we show how this method enables the single-shot full-field characterization of optical waveforms spanning multiple THz. The method is further showcased through accurate amplitude and phase recovery of high-speed complex-modulated optical telecommunication signals using direct intensity detection. This concept will enable the study of physical phenomena unreachable to date and disruptive advancements in high-speed communications, sensing, and information processing.