Spectral Purification of Microwave Signals with Disciplined Dissipative Kerr Solitons

Continuous-wave-driven Kerr nonlinear microresonators give rise to self-organization in terms of dissipative Kerr solitons, which constitute optical frequency combs that can be used to generate low-noise microwave signals. Here, by applying either amplitude or phase modulation to the driving laser we create an intracavity potential trap to discipline the repetition rate of the solitons. We demonstrate that this effect gives rise to a novel spectral purification mechanism of the external microwave signal frequency, leading to reduced phase noise of the output signal. We experimentally observe that the microwave signal generated from disciplined solitons is injection locked by the external drive at long timescales, but exhibits an unexpected suppression of the fast timing jitter. Counterintuitively, this filtering takes place for frequencies that are substantially lower than the cavity decay rate. As a result, while the long timescale stability of the Kerr frequency comb’s repetition rate is improved by more than 4 orders of magnitude, the purified microwave signal shows a reduction of the phase noise by 30 dB at offset frequencies above 10 kHz.

Figure 1

The concept of a microcomb-based microwave spectral purifier. A commercially available electronic microwave oscillator (Rohde&Schwarz SMB100A) is used to modulate the pump laser, leading to the injection locking of solitons, thus providing a long-term frequency reference to the soliton repetition rate. The generated microwave exhibits a reduced phase noise level due to the nonlinear soliton dynamics, leading to noise reduction of the microwave signal for Fourier frequencies far away from the carrier.

Figure 2

(a) The experimental setup. (b) The ${\mathrm{MgF}}_2$ resonator used in the experiment. (c) Illustration of the PDH offset locking and the prestabilization scheme. (d) Optical spectrum of the soliton microcomb. (e) Generated comb power as the laser is scanned across the pumped resonance (upper) and the corresponding PDH error signal (lower). The red dot indicates the locking point. (f) Allan deviations of $f_{\mathrm{rep}}$ when the Kerr comb is prestabilized and DKS-disciplined, respectively. We counted $f_{\mathrm{rep}}$ with a $\mathrm{\Pi }$-type frequency counter that is referenced to the same frequency source (relative frequency instability $<1\times {10}^{-12}$ at 1 s averaging time) to which $f_{\mathrm{mod}}$ is referenced.

Figure 3

(a) In frequency domain, the difference between the pump laser and the modulated sidebands sets the microcomb $f_{\mathrm{rep}}$. (b) In time domain, the potential of the modulated cw field traps solitons, thus locking $f_{\mathrm{rep}}$ of the soliton train. (c) Evolution of the spectrum around 14.09 GHz. (d) Snapshots with different $f_{\mathrm{mod}}$ detuned from free-running $f_{\mathrm{rep}}$ (indicated in the upper-right corners) showing the typical states of unlocked ($-500$ and 500 Hz), quasilocked ($-300$ and 300 Hz), and injection-locked (0 Hz). (e) Locking ranges with varied AM strengths for modulation frequencies around $f_{\mathrm{rep}}$ (blue circles) and $2\times f_{\mathrm{rep}}$ (red circles), respectively.

Figure 4

Phase noise spectra of the soliton repetition rate with and without PM injection locking. The phase noise of the input microwave signal is also presented, showing that the injection locking reduces the noise level by nearly 40 dB for offsets at 100 kHz. The crosses and the dashed line show the noise floor of the phase noise analyzer.

Figure 5

Experimentally measured and numerically simulated phase noise transfer indices for the PM-to-PM noise transfer from injected microwave signal to $f_{\mathrm{rep}}$ of the DKS stream. The flat floors of the experimental data at frequencies above 100 kHz are due to the noise floor of the phase noise analyzer during the IQ measurement, which are indicated by the dash-dot lines.