Microresonator Dissipative Kerr Solitons Synchronized to an Optoelectronic Oscillator

Using phase-modulation-induced potential gradient whose period is synchronized to a microwave optoelectronic oscillator, dissipative Kerr solitons generated in a crystalline optical microresonator are trapped by the soliton tweezing effect, exhibiting a stabilized soliton repetition rate. In the meantime, side-mode suppression of the microwave signal is enabled by the photodetection of the soliton train. Substantiated both experimentally and theoretically, the hybrid system produces a drift-reduced microcomb and a spectrum-purified optoelectronic oscillator simultaneously, yielding a low-cost toolkit for microwave and optical metrology.

Figure 1

Using the phase gradient of a pump laser to synchronize microresonator DKSs to a GSL-based OEO. (a) The principle of DKS trapping. (b) Schematic of the experimental setup. A picture of the ${\mathrm{Mg}\mathrm{F}}_2$ microresonator is displayed too. SMF is the single-mode fiber; VOA is the variable optical attenuator; EDFA is the erbium-doped fiber amplifier; FBG is the fiber Bragg grating notch filter. (c) The upper panel shows the optical spectrum of the DFB laser (manufactured by NTT Electronics) when the OEO is in operation. The inset shows the unmodulated spectrum of the semiconductor laser driven by a dc bias current of 50 mA. The simulated optical spectrum and the temporal intensity profile of the DFB laser pulse are presented in the lower panel. (d) The upper panel shows the optical spectrum of the DKS microcomb. The inset shows that the relative intensity difference between the central pumping line and the two first-order PM sidebands is 11.4 dB, corresponding to a PM depth of $\beta \approx 0.5$. The lower panel shows the simulated microcomb spectrum. The inset is the intensity profile of the DKS in the time domain.

Figure 2

Experimental results of using an OEO to synchronize DKSs. (a) Frequency drifts of the repetition rate of the free-running DKS (upper panel) and the OEO (lower panel). (b) Relative Allan deviations of the frequency instabilities in (a). The error bars are barely visible in the figure due to their small values. (c) The rf spectra of the OEO oscillation signal (upper panel) and the synchronized DKS repetition rate (lower panel). The resolution bandwidth (RBW) of the measurement is 1 kHz. (d) Spectrogram of the DKS repetition rate when the microwave generated by the OEO is used to drive the PM. Two snapshots at the positions denoted by the red dashed lines are displayed in the lower panels, showing the spectral profiles of the synchronized and the unsynchronized DKS repetition rate, respectively.

Figure 3

Spectral purification enabled by soliton trapping. (a) Spectra of the OEO oscillation and the repetition rate of the trapped DKS. The DKS spectrum shows suppression ratios of 17 dB for the first-order side modes and 25 dB for the second-order side modes, respectively. (b) Phase noise spectra of the microwave signals. The OEO oscillation signal is tapped from the OEO using a microwave power splitter. The DKS signals are generated by the photodetection of the soliton pulse train with a fast photodetector.

Figure 4

Simulation of synchronized-DKS-based OEO side-mode suppression. (a) Schematic of the computational model of an optical-modulator-based OEO. The Mach-Zehnder interferometer structure of the modulator and the qualitative saturable curve of the modulation response are illustrated. OM is the optical modulator; G is the gain; BF is the bandpass filter; RN is the random noise. (b) The simulated phase variation of the 10-GHz OEO signal. (c) A 10-$\mu \mathrm{s}$-long piece in the curve in (b), showing the details of five consecutive roundtrips of the phase of the OEO signal. (d),(e) Computed phase evolutions of the synchronized DKS when the phase variation in (b) is applied to the intracavity soliton trap. The parameters related to the microresonator are set to be in accordance with an integrated ${\mathrm{Si}}_3{\mathrm{N}}_4$ microring resonator. The result in (d) is derived with the LLE-based simulation, while the result in (e) is calculated by numerical integration of Eq. (2). (f) Phase noise spectra of the 10-GHz OEO signal and the synchronized-DKS-purified signal computed with the data in (b), (d), and (e), respectively. (g)–(l) Simulation results similar to (a)–(f). The modeling of the 14-GHz OEO is based on a GSL and a loop length that is the same as that in the experiments. An adjustable loss (AL) is included in the loop to mimic the effect of the variable optical attenuator to obtain stable oscillations. For the simulation of the DKS dynamics, the microresonator-related parameters are set to be in close agreement with the ${\mathrm{Mg}\mathrm{F}}_2$ whispering-gallery-mode resonator used in the experiments.