Photonic timing-engineered solitons for dual-microcomb metrology

Abstract

Dissipative microcavity solitons offer a route to integrate comb-based metrology systems on photonic chips. However, integrated solitons generally lack agile control of comb parameters, particularly pulse timing control, hindering their application in quantum-limited metrology. Here we introduce dynamical soliton trapping to enable optically timing-engineered microcombs (OTEM). By injecting an auxiliary laser to anchor one of the microcomb lines, we create a potential well to trap and steer the soliton. Thus, soliton timing can be engineered by phase modulating the injected laser. Theory and measurement reveal the fast response bandwidth of the OTEM, which enabled a soliton slew rate of 31.3 ps/$μ$s, surpassing existing time-programmable fiber laser combs by more than two orders of magnitude. Leveraging the timing scan, we used a single OTEM for single-pixel and parallel ranging by retrieving the phase of the multi-heterodyne beat spectrum. Picometer-scale ranging precision was achieved, establishing new record for optical absolute ranging. Our work can transform timing-engineering of microcavity solitons and endow integrated dual-microcomb metrology systems with enhanced precision.

Figures (5)

• Figure 1: Dynamical soliton trapping and optically timing-engineered microcombs (OTEM). A microcomb line at $\nu_n$ can be injection locked by a control laser. The locked line serves as a trapping well for the microcavity soliton. Phase modulation of the injected laser enables fast steering of soliton position or timing, $t_s(T)$, via dynamical trapping. By delaying an arm of the solitons, dual-comb metrology can be implemented using a single OTEM. The OTEM can be used for ranging/imaging and spectroscopy. PM, phase modulator; PD, photodetector; AOM, acousto-optical modulator.
• Figure 2: Timing-engineering of a soliton microcomb via dynamical trapping. a, Experimental setup to generate optically timing-engineered microcombs (OTEMs) and to characterize the soliton timing. The inset shows the spectrum of a soliton microcomb. b, Soliton motion retrieved by the heterodyne measurement under different drive waveforms. Numbers in the left panel show the phase of the corresponding sidebands. c, Measured soliton motion amplitude under different sine-drive frequencies and injected optical powers. The measured response exhibits a bandwidth exceeding 100 MHz and fits the theory (Supplementary Sec. 1). d, Soliton response bandwidth increases with injected laser power and agrees with the theory. e, Phase response of the OTEM under different modulation frequencies, in agreement with theory in Supplementary Sec. 1. f, Retrieved soliton motion amplitude versus the amplitude of $\phi_n(T)$, in agreement with Eq. \ref{['eq1']}. The inset shows the retrieved soliton motion under $\phi_n^a$=10.7 rad.
• Figure 3: Single OTEM enabled dual-comb ranging.a, Experimental setup for effective dual-comb ranging using an OTEM. Polarization-multiplexing was used to cancel the influence of fiber fluctuations in measurements. b, Measured interferograms in the signal arm with different soliton scan span $t_r^a$. The dashed curves show the relative delay change between the split solitons. c, Optical power and phase spectra derived from the measured interferograms. The optical frequency resolution can be adjusted by $t_r^a$, and the spectral power envelopes have a sech$^4$-shape. The radiofrequency (RF) lines can reach a peak signal-to-noise ratio from the average noise (rSNR) of 67 or 80 dB within 1 ms. d, Allan deviation of the absolute distance measured by the spectral phase fitted time-of-flight (ToF) and the interferometric phase of a single line, showing a normalized precision of 85 pm$\cdot$$\sqrt{\rm s}$ and 2 pm$\cdot$$\sqrt{\rm s}$, respectively. The inset shows the measured distance for these two methods.
• Figure 4: Absolute ranging and imaging using an OTEM.a, Experimental setup for ranging through fluctuating flames and 3D imaging of a scattering aluminum plate whose reflection loss can exceed 50 dB. b, Measured distance and optical power changes induced by a naturally fluctuating flame. c, Correlation between the distance and power changes. d, Measured distance change induced by a speaker playing the Symphony of Destiny, which agrees with the input signal. e, Audio spectrum of the measured distance change induced by the perturbed flames. f, 3D imaging of the aluminum plate with a panda image. g, Distance change along the dashed slice in panel f. The solid and dashed lines are linear fits of the measured distance change for the front and back surfaces, respectively. h, Residual error distribution for the measured distance subtracted by the solid linear fit.
• Figure 5: Parallel ranging using an OTEM.a, Experimental setup for parallel ranging by dispersing the OTEM by a grating. b, Measured displacement when the piezo drives the mirror at 5 kHz. c, Measured displacement amplitude for different comb mode index, i.e., different positions of the mirror. d, Spectral power density of vibrations for all the measured 25 comb modes with a resolution bandwidth of 50 Hz, reaching the highest sensitivity of 2.8 pm/$\sqrt{\rm Hz}$ (mode $-$9).