Nanometric dual-comb ranging using photon-level microcavity solitons

Abstract

Absolute distance measurement with low return power, fast measurement speed, high precision, and immunity to intensity fluctuations is highly demanded in nanotechnology. However, achieving all these objectives simultaneously remains a significant challenge for miniaturized systems. Here, we demonstrate dual-comb ranging (DCR) that encompasses all these capabilities by using counter-propagating (CP) solitons generated in an integrated Si$_3$N$_4$ microresonator. We derive equations linking the DCR precision with comb line powers, revealing the advantage of microcomb's large line spacing in precise ranging. Leveraging the advantage, our system reaches 1-nm-precision and measures nm-scale vibration at frequencies up to 0.9 MHz. We also show that precise DCR is possible even in the presence of strong intensity noise and loss, using a mean received photon number as low as 5.5$\times$10$^{-4}$ per pulse. Our work establishes an optimization principle for dual-comb systems and bridges high performance ranging with foundry-manufactured photonic chips.

Figures (5)

• Figure 1: Coherent dual-comb ranging (DCR) using counter-propagating (CP) solitonsa, Experimental setup for the CP solitons generation and DCR. ECDL, external cavity diode laser; SSBM, single-sideband modulator; AOM, acousto-optical modulator; FBG, fibre Bragg grating; EDFA, erbium-doped fibre amplifier; PC, polarization controller; Col, collimator; BPD, balanced photodetector. b, Optical spectra of the CP solitons. The inset shows the nanophotonic chip. c, Dual-comb inteferogram in the signal and reference arms. d, Power spectrum of the signal arm and the corresponding phase spectrum. e, Allan deviation of phase different between the 4th and the 9th lines. f, Phase difference between the signal and the reference arms measured in 50 $\mu$s. g, Fitting the phase difference in panel f yields the distance over 10$^4$ time slots. h, DCR Allan deviation when selecting different number of comb lines for fitting, all showing $t^{-1/2}$ scaling. The inset shows all the selections yield the same distance, but with different standard deviation (see error bars).
• Figure 2: Measurement precision of DCR.a, Allan deviation of the phase of the 4th comb line, which equals 1/$\sqrt{\rm rSNR}$. The inset shows an illustration of the relationship between rSNR and phase deviation. b, DCR precision for a fixed comb bandwidth $B$=3.2 THz, but selecting comb lines with different spacing (thus, different used comb line number $N$). The inset shows the normalized precision improves as $N^{-1/2}$. c, Measured DCR precision agrees with the theoretical precision determined by Eq. \ref{['eq2Sigma']}. The inset confirms the $N^{-3/2}$ trend in our theory.
• Figure 3: DCR with low received power and strong intensity noise.a, Dual-comb interferogram signal with a received power of 7 pW. b, RF spectrum of the signal in panel a after $t$=0.5 s coherent averaging. c, DCR Allan deviation of a series of received powers, all exhibiting $t^{-1/2}$ scaling. d, Normalized DCR precision, showing an inverse square-root relationship with the received power. e, Measured RF pulses have randomly fluctuating amplitudes when introducing intensity noise on the received microcomb. f, Measured distance in five 5 ms slots separated by 0.1 s (50 $\mu$s per measurement point) and solid lines are the average distance. g, DCR Allan deviation under different intensity noise. The inset shows the distribution of the RF pulse amplitude. In the absence of intensity noise, the amplitude has a 2% fluctuation. The added intensity noise can introduce 30% amplitude fluctuation. h, Deterioration of the rSNR under different intensity noise, which results in the increase of the DCR Allan deviation.
• Figure 4: Near Megahertz dual-comb vibration (DCV) measurements.a, Measured distance change with drive frequencies of 20 or 900 kHz. b, DCV spectra measured at three drive frequencies, all yielding sharp peaks with a high signal-to-noise ratio (SNR). The inset shows the measured vibration amplitude versus the drive power of the phase modulator (PM). c, The DCV sensitivity (determined by the noise floor in panel b) scales in a square-root way with the received microcomb power. d, Deduced rSNR for a single-frame inteferogram under different received powers. This rSNR should exceed 3 dB for a reliable DCV measurement. e, The highest vibration frequency that can be measured with different received powers. Below 200 nW power, the highest frequency decreases linearly with the power. When the comb line number becomes larger for a fixed total power, DCV at $\delta f_r$/2 will need a higher received power.
• Figure 5: Performance comparison with other dual-comb ranging systems. Our system feature low received pulse energy and high precision. EO comb, electro-optical comb.