Fig. 3: Experimental results on time-mapped spectrogram analysis of a linearly chirped RF waveform using photonic sampling and dispersion.
a A schematic of the photonics-based TM-SP experimental setup for real-time spectral analysis of broadband microwave signals. The microwave signal under test (SUT) is sampled with a picosecond optical pulse train generated from a mode-locked fiber laser, in a Mach–Zehnder modulator (MZM). The optical samples are propagated through dispersion compensating fiber (DCF) with a total dispersion \(\ddot \phi\), and the output TM-SP is captured in a real-time oscilloscope after photo-detection. b The temporal trace of the microwave signal under test (SUT), with a linearly increasing frequency, from 500 MHz to 2 GHz, along a duration of 2 µs. c The photo-detected output temporal waveform (voltage signal) that is directly captured in a real-time oscilloscope, over the same 2-µs duration. The inset plots show a zoom of the output waveform around three different time slots, each extending over one analysis period (TR = 205.6 ps). The temporal trace along each consecutive analysis period, TR, is a time-mapped copy of the FT of the input SUT, effectively windowed around the corresponding time of analysis. The top horizontal axis follows the frequency scale that is obtained using the mapping law \(\Delta t_2 \leftarrow \Delta \omega _1\ddot \phi\). The instantaneous spectrum of the input signal at any given instant of time consists of two individual pulses, corresponding to the frequency of the signal, ±ωRF(t1) linearly increasing with time. The observed signal background (including at the location corresponding to DC) is attributed to unwanted variations in the bias condition of the electro-optic modulation process with respect to the optimal design. d A 2D representation of the signal joint time–frequency energy distribution (spectrogram) that is directly recovered from the output temporal trace.
