Dissipative Kerr solitons generated in microresonators driven by a continuous wave pump laser have promise for widespread applications in spectroscopy and telecommunications. From the perspective of basic physics research, DKSs exhibit rich nonlinear phenomena and serve as a unique platform to study nonlinear physics. In this paper, an optimized all-optical radio frequency (RF) spectrum analyzer, also named frequency domain light intensity spectrum analyzer (f-LISA), is used to characterize the various stable soliton states. Results show that the optimized f-LISA achieves a measurement bandwidth of 2.2 THz and a frame rate of 20.62 MHz. Therefore, the versatile RF spectral patterns of stable two-soliton states have successfully recorded by f-LISA. More importantly, the relative azimuthal angles between two solitons within the round-trip can be extracted by applying an inverse Fourier transform to the RF spectra, indicating that the ultra-fast and broadband RF spectral measurement enable the visualization of soliton motion. It is believed that the f-LISA can function as a powerful and useful tool to monitor the rich nonlinear dynamical phenomena such as soliton number switching in the microresonators
Autocorrelator, as a pulse measuring equipment, can effectively characterize pulse width and pulse waveform with high resolution. Limited by the refresh rate, conventional autocorrelator are incapable of capture the ultrafast processes of pulses, such as soliton transitions. In this paper, we proposed an ultrafast autocorrelator based on broadband radio frequency (RF) spectrum analyzer. The RF spectrum under test is firstly transformed to the continuous wave via the cross-phase modulation. Then the RF spectrum is mapped to the temporal domain through time stretch and finally measured by a real-time oscilloscope. The ultrafast autocorrelation trace is obtained from the inverse Fourier transform of the mapped RF spectrum. With the 60-GHz detected bandwidth of the photodetector adopted, the simulated ultrafast autocorrelator achieves the measurement rate of 50 MHz, the resolution of 300 fs, and the measuring window of 600 ps.
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