Fig. 1. (a) Illustration of the experimental setup of low noise microwave generation due to the hybridized mode using polarization diverse soliton. (b) Microscope images of the PAW resonator. Right panel illustrates the dual auxiliary (TM0) and soliton mode (TE0) interactions. (c) Measured optical spectrum of the polarization dissipative soliton. The spectrum does not fit a sech2 profile due to its asymmetry. Inset: optical spectrum near the pump showing a signature of an AMX.

Fig. 2. Characterization of the free-running soliton repetition rate. (a) Single-sideband (SSB) phase noise was measured with the free-running microresonator. The estimated shot noise floor is −150  dBc/Hz. Pump laser phase noise transduction to repetition rate noise is shown in black. The estimated noise induced by pump intensity fluctuation is plotted in orange, which is not the noise limiting factor. The simulated AMX-induced noise originating from intermode thermorefractive noise (TRN) is illustrated in green. Repetition rate TRN is the fundamental limit of the generated microwave beat and is shown in light gray. For comparison, the noise of a Rohde & Schwarz SMA100B signal generator is illustrated in purple. The phase noise analyzer FSWP26 instrument limit is shown as the dashed light brown line. Inset: pump laser phase noise transduction at 2 kHz offset for 0 to 4 GHz detuning. (b) RF spectrum of the microwave repetition rate beat signal with a resolution bandwidth (RBW) of 1 kHz. (c) Relative intensity noise (RIN) of the pump laser and EDFA. (d) A frequency counter measurement shows the real-time trace of the repetition rate, with a long-term average drift of −37.8  Hz/min over 85 min. (e) Repetition-rate beat Allan deviation computed from single-sideband phase noise metrology [(a) in red] and frequency counting [(d) in black].

Fig. 3. Intermode breather solitons induced phase noise. (a) SSB phase noise of the 19.69 GHz signal at 10 kHz offset versus pump detuning with the repetition rate shift shown below. (b) SSB phase noise at different detuning frequencies [indicated by color in accordance with (a)]. (c) Optical spectrum at different detuning. Inset: spectrum near the pump showing absence of the soliton spectrum shift. (d)–(f) RF spectrum of the repetition rate with RBW of 50 kHz at three different detunings that match (c).

Fig. 4. Stabilized chip-scale optical frequency comb. (a) Stabilizing the repetition rate to an ultralow noise microwave signal synthesized using self-referenced fiber frequency combs. ULE, ultralow expansion cavity; PC, polarization controller; 3X PRM, three-stage pulse rate multiplier; ECDL, extended cavity laser diode; EDFA, erbium-doped fiber amplifier; SG, signal generator; FBG, fiber Bragg grating; PD, photodiode; RF BPF, RF bandpass filter; RF LPF, RF lowpass filter; LPN AMP, low-phase noise amplifier; Attn, attenuator; and PNA, phase noise analyzer. (b) SSB phase noise of the stabilized repetition rate (blue) shows active stabilization below the TRN limit (gray). The phase noise analyzer instrument limit is shown in light brown. (c) RF spectrum of the stabilized versus free-running repetition rate shown with 1 Hz RBW to examine the long-term frequency drift. (d) RF spectrum of the locked soliton repetition rate showing fine-tuning control of the repetition rate. The RBW is 1 Hz. (e) Example spectrogram of the repetition rate before and after locking.

Fig. 5. Stabilization using optical frequency division (OFD). (a) Experimental setup. An optical coupler is used to couple the fiber comb with the microcomb. A dense WDM is used to filter out two frequency comb pairs. After each pair is photodetected, their beats are mixed. The resultant signal is down-mixed to DC and serves as the error signal. (b) Optical spectrum showing the separation between the comb pair. Three different frequency separations are illustrated as examples. (c) SSB phase noise of the locked repetition rate showing close to 20log10(N) division.

Fig. 6. Linear characterization of the microresonator. (a) Normalized transmission. (b) Hybridized TE–TM mode near 1603 nm. (c) Histogram of the loaded quality factor of the microresonator. (d) Integrated dispersion away from the avoided mode-crossing region.

Fig. 7. Simulation of thermorefractive noise of the microresonator. (a) TRN of the soliton mode TE0 and TRN of the differential mode of the soliton mode and other modes, taken at the frequency of the pump fp=187  THz. (b) Temperature correlation factor R between soliton mode and other different transverse modes.

Fig. 8. Dependence of locking sensitivity on pump properties. (a) Locking setup, where an intensity modulator is used to actuate the pump power, and laser current to actuate the detuning. (b) The repetition rate as a function of the pump power change in the ring, was determined at −116  kHz/mW. (c) The repetition rate as a function of the pump frequency change, determined between −99 and −115  Hz/MHz. (d) Phase noise measurement of the locked repetition rate in the two cases. The laser current shows a smaller locking bandwidth due to insufficient sensitivity.