Rhythmic soliton interactions for integrated dual-microcomb spectroscopy

Abstract

Rotation symmetry of microresonators supports the generation of phase-locked counter-propagating (CP) solitons that can potentially miniaturize dual-comb systems. Realization of these dual-comb compatible solitons in photonic integrated circuits remains a challenge. Here, we synthesized such CP solitons in an integrated silicon nitride microresonator and observed forced soliton oscillation due to rhythmic, time-varying soliton interactions. The interactions result in seconds mutual-coherence passively. Temporal motion in the soliton streams is discerned by measuring a quadratic-scaling frequency noise peaks and an inverse quadratic-scaling microcomb sidebands. By generating a CP soliton trimer to have two synchronized solitons in one of the orbiting directions, we resolve the incapability of measuring two unsynchronized CP soliton dimer pulses by optical cross-correlation, and show CP solitons undergo complex motion trajectory. We further prove that precise dual-comb spectroscopy with an acquisition time as short as 0.6 $μ$s is feasible using these solitons, although the temporal motion limits the dynamic range. Besides revealing soliton interactions with different group velocities, our work propels the realization of photonic integrated dual-comb spectrometers with high passive coherence.

Figures (4)

• Figure 1: Counter-propagating (CP) solitons in a silicon nitride microresonator.a, Illustration of CP solitons in a Si$_3$N$_4$ microresonator. Due to the rhythmic soliton interactions in the Vernier frequency locking, the output CP solitons feature periodic motion in the pulse timing. b, Experimental setup for the generation of CP solitons. ECDL, external cavity diode laser; SSBM, single-sideband modulator; AOM, acousto-optical modulator; FBG, fiber Bragg grating; EDFA, erbium-doped fiber amplifier. The bottom panels show the picture of the Si$_3$N$_4$ photonic chip, as well as an SEM picture of the microresonator. c, Optical spectra of the CP soliton microcombs. d, Temporal interferogram of the CP solitons. e, Fourier transform of the interferogram of the CP soliton streams. f, Peak RF signal-to-noise ratio (rSNR) for the spectrum in panel e. The power (amplitude) rSNR scales linearly (as square-root) with the measurement time $\tau$, which suggests the mutual coherence time between the CP solitons exceeds 1 s. g, Photodetected electric power spectrum when selecting an individual comb line from one of the CP soliton microcombs. The spectrum comprises an array of RF lines spaced by $\delta f_r$.
• Figure 2: Fine microcomb line structures due to rhythmic soliton interactions.a, Experimental setup for the measurement of microcomb line frequency noise and heterodyne beat with an external cavity diode laser (ECDL) to measure the extinction ratio $R(m,N)$. b, Measured frequency noise spectra for three comb lines, showing strong peaks at $\delta f_r$ and its harmonics. c, The intensity of the first harmonic scales quadratically with the mode number $m$. d, Measured heterodyne beat spectrum between the $m$=4 line and the ECDL, showing multiple sidebands spaced by $\delta f_r$. e, Measured extinction ratio between the main line and the 1st VFL sidebands, showing an inverse quadratic trend as the theory predicts. The inset confirms this trend in a log-log plot.
• Figure 3: Soliton motion within a counter-propagating (CP) soliton trimer.a, Experimental setup to measure the soliton motion by a balanced optical cross-correlator (BOC). ODL, optical delay line; PBS, polarization beam splitter. b, Measured soliton spectrum in the direction hosting two solitons. The spectral fringes show decreasing contrast with increasing frequency spacing from the pump, see the two green dots. c, BOC measured soliton motion between two solitons within the soliton trimer, showing a complex motion trajectory with about 140 fs peak-to-peak amplitude. d, Power spectrum of the BOC measured soliton motion trajectory.
• Figure 4: Dual-comb spectroscopy (DCS) using counter-propagating (CP) solitons.a, Illustration of the experimental setup for the CP solitons-based DCS. b, Measured absorption spectrum when encoding the virtual sample (a pulse shaper) with a sinusoidal or Lorentzian spectrum. c, Allan deviation of the sine-absorption amplitude, which scales as $1/\sqrt{\tau}$ with measurement time $\tau$. d, Spectroscopic signal-to-noise ratio (sSNR) of the Si$_3$N$_4$ CP soliton dual-comb spectrometer, which scales as $\sqrt{\tau}$. An average sSNR as high as 300 is reached within 10 ms, that is higher than other reports. DFG, difference frequency generation; iDFG, interleaved DFG; CE-DCS, cavity enhanced DCS; OPO, optical parametric oscillator; SC, supercontinuum. e, Measured sine-absorption amplitude versus applied absorption amplitude for the pulse shaper. When the absorption is high, the VFL sidebands cause the measurement to deviate from the applied absorption. f, Example of the distorted DCS spectrum when the applied absorption sine-amplitude is 45% (peak-to-peak amplitude 90%). g, Conceptualization of a CP soliton dual-comb spectrometer in a Si$_3$N$_4$-based photonic integrated circuit. ECU, electronic control unit.