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Low-noise frequency-agile photonic integrated lasers for coherent ranging

Abstract

Frequency modulated continuous wave laser ranging (FMCW LiDAR) enables distance mapping with simultaneous position and velocity information, is immune to stray light, can achieve long range, operate in the eye-safe region of 1550 nm and achieve high sensitivity. Despite its advantages, it is compounded by the simultaneous requirement of both narrow linewidth low noise lasers that can be precisely chirped. While integrated silicon-based lasers, compatible with wafer scale manufacturing in large volumes at low cost, have experienced major advances and are now employed on a commercial scale in data centers, and impressive progress has led to integrated lasers with (ultra) narrow sub-100 Hz-level intrinsic linewidth based on optical feedback from photonic circuits, these lasers presently lack fast nonthermal tuning, i.e. frequency agility as required for coherent ranging. Here, we demonstrate a hybrid photonic integrated laser that exhibits very narrow intrinsic linewidth of 25 Hz while offering linear, hysteresis-free, and mode-hop-free-tuning beyond 1 GHz with up to megahertz actuation bandwidth constituting 1.6 × 1015 Hz/s tuning speed. Our approach uses foundry-based technologies - ultralow-loss (1 dB/m) Si3N4 photonic microresonators, combined with aluminium nitride (AlN) or lead zirconium titanate (PZT) microelectromechanical systems (MEMS) based stress-optic actuation. Electrically driven low-phase-noise lasing is attained by self-injection locking of an Indium Phosphide (InP) laser chip and only limited by fundamental thermo-refractive noise at mid-range offsets. By utilizing difference-drive and apodization of the photonic chip to suppress mechanical vibrations of the chip, a flat actuation response up to 10 MHz is achieved. We leverage this capability to demonstrate a compact coherent LiDAR engine that can generate up to 800 kHz FMCW triangular optical chirp signals, requiring neither any active linearization nor predistortion compensation, and perform a 10 m optical ranging experiment, with a resolution of 12.5 cm. Our results constitute a photonic integrated laser system for scenarios where high compactness, fast frequency actuation, and high spectral purity are required.

Introduction

Low-phase-noise lasers1,2,3,4 are imperative in a wide range of technological and scientific applications, ranging from distributed fibre sensing5, coherent LiDAR6,7,8,9,10 to microwave photonics11. Over the past decade, the development of heterogeneously integrated lasers has led to a new class of CMOS-compatible highly integrated laser sources12,13,14 that are now commercially employed in data-centre interconnects. The fundamental linewidth, i.e., the phase noise, of lasers is given by the modified Schawlow-Townes linewidth limit15,16, which dictates that low-loss laser cavities with a high number of photons stored in the cavity allow inherently low phase noise. In addition to quantum noise, thermodynamical noise, such as thermo-refractive noise due to refractive index fluctuations, constitutes another limit17,18. To date, the lowest laser phase noise of compact semiconductor lasers is achieved by self-injection locking with discrete crystalline resonators (sub-Hz white frequency noise level)19,20, and extensively to silicon-based lasers21,22. Using Si3N4 TriPleX waveguides23,24 as first demonstrated by the pioneering work of the group of K.J. Boller, has enabled hybrid integrated lasers with Hz-level Lorentzian linewidth, that have shown steady improvements1. Using weak confinement Si3N4 waveguides and laser self-injection locking it has culminated recently in the demonstration of frequency noise of 0.006 Hz2/Hz at 4 MHz offset3. A particularly interesting application for integrated photonics-based low noise lasers is coherent FMCW LiDAR. Recently, autonomous driving and areal mapping have increased the interest in such sources and a fully hybrid integrated low-noise, high and frequency-agile source could hence unlock further applications of coherent FMCW LiDAR. Laser phase noise limits the maximum operating distance and ranging precision in FMCW LiDAR25,26. However, a key requirement for FMCW at long range is in addition to low phase noise, frequency agility, i.e to achieve fast, linear and hysteresis-free tuning26. Currently, integrated laser sources require external linearization or precompensation. Most digital approaches towards photonic integrated FMCW LiDAR, which employ injection-locking of a high power laser diode to an electro-optically modulated sideband of a coherent laser can deliver excellent linearity and low noise27,28, but today require bulk optical circulators and fibre laser oscillators for operation.

Here we demonstrate a laser that combines both low noise and frequency agility - enabling laser tuning at 1.6 × 1015 hertz/second. While both have been attained separately in integrated devices, and faster tuning (e.g. MEMS VCSEL lasers) and even lower phase noise has been attained for individual lasers, our work marks these two properties are simultaneously achieved in an integrated device, while maintaining fast (MHz) tuning and narrow linewidth (low phase noise). This is attained by using self-injection locking (SIL) of an III-V InP laser to an ultralow-loss Si3N4 microresonator2,29,30 monolithically integrated with AlN MEMS-based actuators31,32, we achieve both frequency agility and narrow linewidth, exhibiting phase noise that is on par at mid range offsets with fibre lasers - the workhorse for fibre sensing. Owing to the high Q of the Si3N4 microresonator resonances, the InP laser shows a reduced intrinsic linewidth of ~25 Hz. Using the AlN piezoelectrical actuators engineered based on novel contour mode cancellation and differential drive schemes allows the photonic microresonator to be frequency-modulated via the stress-optic effect with a flattened response up to the actuation frequency of 10 MHz - order of magnitude improvement33 due to the planar co-integration. This enables a class of compact LiDAR sources that do not require external linearization of the FMCW signal. We generate narrow-linewidth triangularly chirped lasers capable of chirp repetition frequencies as high as 800 kHz and nonlinearities as low as 1% without digital predistortion or complex direct microwave signal synthesis and perform an FMCW LiDAR demonstration at 100 kHz chirp frequency. The versatility permitted by the optical and mechanical properties of the system shows great promise in applications including, field-deployable frequency referencing34, frequency-agile rapid-scanning spectroscopy35,36 and low-cost FMCW LiDAR engines32.

Results

Hybrid self-injection-locked laser system

As illustrated in Fig. 1a, the hybrid laser system comprises a III–V laser chip with a distributed feedback (DFB) structure and a photonic chip-based ultralow-loss Si3N4 resonator with a monolithically integrated AlN piezoelectrical actuator. The DFB laser diode is mounted on a 3D piezoelectrical translation stage and butt-coupled to the Si3N4 photonic chip as shown in Fig. 1b, c operating at a lasing wavelength of 1556 nm with a free space output power of up to 120 mW. The Si3N4 photonic chips are fabricated using the photonic Damascene reflow process30,37,38, and feature intrinsic quality factor Q0 > 1.5 × 107. Frequency-dependent transmission, reflection and cavity linewidth data is presented in the SI Fig. 5 for all chips used in this work. Made from polycrystalline AlN as the main piezoelectric material, the actuator has molybdenum (Mo) and aluminium (Al) as the bottom (ground) and the top electrodes, respectively31 as shown in Fig. 1d. Applying a voltage between the electrodes tunes the microresonator frequency via the stress-optic effect39. Such hybrid packaging approach23 and also heterogeneous integration with InP laser and Si3N4 PIC fabricated on a single silicon substrate21, have recently been demonstrated with Si3N4 microresonators. By tuning the current of the laser diode, we sweep the relative frequency between the laser and the resonator modes to attain self-injection locking via the coupling of counter-propagating microresonator modes induced by backscattering predominatly from the core-cladding interface40 (cf. SI Figs. 5 and 1e). The gap between the laser chip and the Si3N4 photonic chip is adjusted for optimal feedback phase41, which yields the maximum self-injection locking range of up to 2.1 GHz (cf. Fig. 1e).

Self-injection locking in this manner has been attained in previous work, however, the ultralow-loss photonic integrated resonator enables the substantial reduction in the phase noise via self-injection locking that is hitherto only surpassed in low confinement Si3N4 microresonators2 without non-thermal actuation or crystalline microresonators19. In our work we only consider the linear regime of laser operation by adjusting the feedback phase and keeping the output optical power below 1.5 mW. In order to achieve frequency agility, we bias the diode in the centre of the locking plateau. In this manner, changes in the microresonator frequency will maintain injection locked operation and therefore lead to frequency tuning (cf. Fig. 1f). The AlN actuator will therefore transduce the applied voltage directly to changes in the optical frequency. Figure 1h shows the range over which the photonic resonator frequency can be tuned while still maintaining injection locking (corresponding to a tuning range of up to 2.1 GHz).

Laser frequency noise measurements

To measure and confirm the very low phase noise of the laser, we adopt two approaches (see Fig. 2a) to measure the frequency noise power spectral density Sν(Ω) (single-sided PSD, in units of Hz2/Hz), including (1) beating the injection-locked laser with an ultra-narrow-linewidth reference laser (see the SI for details) and measuring the beat signal’s frequency noise spectrum with an electric spectrum analyser (ESA), and (2) optical cross-correlation-based noise spectrum characterisation42 using two auxiliary lasers. (cf. Figs. 2b and SI). Since the laser linewidth narrowing factor, i.e. the ratio of the free-running laser linewidth to the linewidth of the injection-locked laser, is quadratically proportional to the Q of the resonator mode to which the laser is self-injection-locked41, the high loaded Q of the Si3N4 microresonator (see Fig. 2c) can significantly reduce the optical linewidth and improve the side mode suppression ratio (SMSR). We present simulations of the self-injection locking dynamics in the SI. Figure 2d shows the optical spectrum of the laser while it is self-injection locked, demonstrating an SMSR of 60 dB. The relative intensity noise (RIN) of the laser is displayed in the SI. Figure 2e shows the frequency noise spectra of the hybrid lasers in free-running condition and self-injection locking states, respectively. For the injection locking, three microresonators with distinct sizes and different free spectral ranges (FSRs) of 190.7, 9.87 and 2.45 GHz are tested. In general, the self-injection locking suppresses the frequency noise of the laser by more than 30 dB across the entire spectrum. At frequencies below 1 kHz, technical noises due the ambient temperature fluctuations, and the coupling gap instabilities caused by acoustic vibrations (which can be eliminated by packaging) leads to hybrid integrated laser RIN and also to a transduction to frequency noise at offsets < 1 kHz (see SI). The optical crosscorrelation-based characterisation reveals that the laser frequency noise reaches a plateau (white noise floor) of only 8 Hz2/Hz for the 2.45 GHz device, 10 Hz2/Hz for the 9.87 GHz and 300 Hz2/Hz for the 190.7 GHz device at 3 MHz offset. The frequency noise power spectral density was found to be in good quantitative agreement with fundamental thermo-refractive noise (TRN) limit43 of the Si3N4 microresonator at mid range offsets from 5 to 100 kHz. Thus, we demonstrate using high confinement Si3N4 platform the laser performance limited by thermo-refractive noise, which has only been shown in Si3N4 low-confinment waveguides2,3. We note that this intrinsic linewidth can be further reduced by using microresonators with even larger optical mode volume and therefore reduced TRN. To illustrate the performance of this integrated laser, we compare the laser frequency noise to two commonly used lasers. Figure 2f reveals that our hybrid integrated laser is better than a state of the art commercial external cavity diode laser (ECDL,Toptica CTL) and on par with a commercial fibre laser (NKT Koheras Adjustik E15) at the offset frequency range of 1–50 kHz. Another method to quantify and compare the linewidth from the measured frequency noise spectral density Sν(f) is to invoke the beta-line44. By integrating frequency noise up to the frequency of the interception point with a line Sν(f) = 8·ln(2)f/π2, we obtain an area A which we use for FWHM measure of the linewidth (8·ln(2)A)1/2. The full width at half maximum linewidth, which is calculated by integration of the frequency noise from the beta-line to the inverse integration time, is for the 9.87 GHz FSR Si3N4 device 7.5 kHz at 1 ms integration time, 18.7 kHz at 10 ms, and 21.5 kHz at 100 ms. For the 190.7 GHz FSR Si3N4 device the integrated linewidth is 43.27 kHz at 1 ms integration time, 73.7 kHz at 10 ms and 81.7 kHz at 100 ms. For the 2.45 GHz FSR Si3N4 device the integrated linewidth is 14 kHz at 1 ms integration time, 127 kHz at 10 ms and 130 kHz at 100 ms (cf. SI Fig. 6).

Frequency-agile tuning

We next demonstrate the frequency agility of our hybrid laser. To this end, we carry out frequency-modulation of the self-injection-locked laser by applying a time-varying voltage to the single integrated AlN actuator (cf. Fig. 3a) manufactured on top of the 190.7 GHz ring resonator on a square (4.96 × 4.96 mm) non-apodized chip. Triangular ramp signals of ramping frequencies from 10 kHz to 800 kHz are generated with an arbitrary frequency generator and amplified to 150 Vpp which induces a 1.1 GHz laser frequency modulation. The tuning efficiency is composed of two contributions: first, the microscopic photoelastic effect and, second, the change of ring radius due to the generated mechanical stress. The latter leads to a 30% increase in tuning efficiency for the 190.7 GHz resonator compared to larger ring resonators. In the self-injection locking range, the change of microresonator frequency imprints directly on the laser output frequency, even without additional feedback on the pump current of the laser. The time-varying laser output frequency is characterised by measuring a heterodyne beatnote with a reference ECDL (free running Toptica CTL) on a fast photodetector. We define chirp nonlinearity as the root mean square (RMS) deviation of the measured frequency tuning curve from a perfect triangular ramp that is determined with least-squares fitting. The phase noise PSD of the tuned laser can also be directly retrieved by Hilbert’s transform from the heterodyne beat note (cf. SI Fig. 10). Figure 3b, c summarise the main results of the heterodyne beat experiment with the SIL laser locked to a 190.7 GHz microresonator. The large tuning range of >1 GHz at high ramping speeds up to 800 kHz, with small chirping RMS nonlinearities below 1% as shown in Fig. 3b showcases the remarkable frequency agility of our system. This excellent linearity and the almost vanishing hysteresis of the monolithically integrated AlN actuator32 facilitates the generation of highly linear triangular chirps for modulation frequencies up to 100 kHz without the need for active or passive linearization. Figure 3d presents the processed laser frequency spectrograms and the corresponding nonlinearities at five different ramping frequencies respectively. At 10 kHz modulation frequency, the achieved RMS nonlinearity is as low as 600 kHz (relative nonlinearity 5 × 10−4), which only degrades slightly for 100 kHz tuning rate to 1.5 MHz. In Fig. 3c, we plot the frequency-dependent transduction from the frequency modulation amplitude of the first 17 harmonics of each modulation frequency (10 kHz–800 kHz) from the experimental data presented in Fig. 3d. The peak around 900 kHz matches well with the first mechanical mode of the chip presented in Fig. 3e. The 4 MHz low pass cut-off of the high voltage amplifier is indicated in red. Together with more than 1 GHz tuning range, such actuation bandwidth exceeds the performance of common benchtop laser systems that rely on bulk piezo making this laser source an ideal candidate for direct implementation in long-range FMCW LiDAR systems45, that can operate at rates reaching megapixel-per-second.

Flattening actuation response via photonic chip mechanical modes suppression

To achieve the optimal performance of the hybrid integrated laser as an FMCW LiDAR engine at high measurement rates, in addition to a large optical frequency excursion B (which determines LiDAR resolution c/2B), a flattened actuation transfer function is highly desired for minimising chirping nonlinearity. The lower inset of Fig. 3e shows the setup of the actuation response measurement. In this measurement, the actuation voltage derived from a vector network analyser (VNA) is applied on the actuator, and a laser is frequency-tuned to sit on the side of resonance, to measure the response. Figure 3e presents the measured optomechanical response of the single-actuator configuration (grey) and the dual-actuator configuration (green, red and blue). As shown in Fig. 3e (grey), the fabricated AlN piezoelectrical monolithic actuator excites many mechanical bulk or contour modes of the photonic chip, leading to a nonflat actuation response. The inset of Fig. 3e shows finite element simulations of the flexural modes of the photonic chip, that match the observed actuation resonances. The increasing mode density of the Si3N4 photonic chip with actuation frequency severely limits the flat effective actuation bandwidth. We mitigate this effect, first, by developing the active cancellation scheme with a difference-actuation. In this scheme, an additional AlN actuator with the same geometry is fabricated adjacent to the microresonator. The two actuators are driven by the same signal but with a 180-degree phase shift to cancel the actuation of the mechanical modes of the photonic chip. As a result, while the stress-optic effect exerted on the microresonator is the same, the excitation of mechanical resonances can be effectively suppressed as shown in Fig. 3e (green). The scheme effectively reduces modes below 1 MHz, mainly cancelling the flexural modes due to far-field destructive interference, a scheme inspired by nanomechanical membranes46. Many mechanical modes of relatively low resonance frequencies are flexural modes whose vibrations are caused by transverse standing waves. The bulk mechanical modes whose vibrations are caused by longitudinal standing waves (displacement amplitude profile visualisation shown at 967 kHz frequency) can be eliminated by judiciously shaping the geometry of the photonic chips47. To improve the actuation further, and suppress the bulk acoustic modes, we next apodized the photonic Si3N4 chip by dicing the released chip. We observe a reduction in the number of bulk mechanical modes in an apodized photonic chip. Figure 3e (red) shows that the mechanical resonances below 1 MHz are completely removed with the first resonance of apodized chip at 1.69 MHz, matching the finite element simulation (FEM). We further flatten the actuation response by attaching the apodized chip on a piece of carbon tape and then differentially driving the actuators as explained before. In this way, both the flexural and the bulk mechanical modes are damped up to the first fundamental high-overtone bulk acoustic resonator mode (HBAR) at 17 MHz32. The active cancellation scheme on an apodized chip placed over a carbon tape limits the variations of the actuation response within 1 dB yielding a record-flat response bandwidth of nearly 20 MHz (see the SI for the full plot). Such flat actuation response can improve the linear chirping performance of the FMCW LiDAR (see the SI for the analysis of the required actuation bandwidth), and in particular allows an increase of the FMCW signal frequency, thereby directly increase the speed of the LiDAR to beyond megapixel-per-second rates.

Optical FMCW LiDAR using the hybrid integrated laser

As an actual demonstration of the potential of the hybrid integrated laser, we perform optical FMCW LiDAR mapping in the laboratory environment. Importantly, we can – due to the excellent linearity, low hysteresis, and narrow linewidth – perform ranging without any adaptive clock sampling and without pre-distortion linearization. Figure 4a shows the experimental setup of FMCW LiDAR measurement, for the description of the experiment refer to Methods. We apply a triangular chirp with 100 kHz frequency to piezoelectric AlN actuator to obtain 1.2 GHz optical frequency excursion of self-injection locked laser, corresponding to 12.5 cm resolution in distance measurement. Beam steering is realised using mechanical galvo scanner with two mirrors. For the ranging target scene, we use a polystyrene foam donut in front of a PC monitor 10 m away from the laser collimator (Fig. 4b). We record a beat signal of light reflected from the target and the laser in the local oscillator path on a balanced PD. To construct the point cloud from a recorded oscillogram, we first employ a short-time Fourier transform with a window size equal to half of the chirping period. Obtained time-frequency plots for the target are presented in Fig. 4c. Time-frequency spectrograms contain 82k timeslices with typical 15 dB SNR for the target. We remove points with SNR below 10 dB from the point cloud. Noticeable reflection at 27 MHz in Fig. 4c is due to the reflection from the collimator. Peaks at 40–46 MHz offsets correspond to the target scene. We find a peak with maximal spectral amplitude in the time-frequency plot for each timeslice. The frequency of the peak provides the distance information (radial coordinate) for each timeslice. Figure 4d provides a histogram of distance distribution for the target point cloud. We used zero-padding to increase FFT window size four times and to obtain a continuous distribution of radial distance. The point cluster at 9 m distance corresponds to the Styrofoam donut, 9.35 m to the PC monitor, and 9.7 m to the back wall. A small cluster of points at 9.6 m distance corresponds to the soldering station on the table. All peak widths are limited by the fundamental resolution of 12.5 cm. Polar and azimuthal coordinates were retrieved from the galvo scanner mirrors’ driving signals, which were recorded on the same DSO. Interactive code for LiDAR data processing can be found in the code availability section. Figure 4e,f,g shows the point cloud of the scene with distance-based colouring, the donut is depicted in blue, PC monitor in green, and part of the wall in yellow. The scene has been properly reconstructed, although the dual layering of objects is visible in Fig. 4g due to discretization from 12.5 cm LiDAR resolution (no zero-padding was used in FFT).

To increase optical frequency excursion limited in our method and particular Si3N4 sample by injection locking range and improve LiDAR resolution, one might consider a different tuning scheme where the laser diode current and the piezoactuator voltage are synchronously tuned in a way that the laser is kept in injection-locked state. In this case, a diode current tuning might not be precisely linear as self-injection locking implies and preserves the linearity of cavity resonance tuning by the piezoelectrical actuator. In such a feed-forward scheme, the laser tuning range would be limited by piezoactuator’s tuning range. Another option might be to use a two microring-based Vernier configuration for the laser48,49, with the fast tuning provided by integrated piezoactuators.

Hybrid integrated laser with fast tuning based on integrated low voltage PZT piezoactuator

We investigate the reduction of tuning voltage requirement by introducing an integrated piezoelectric actuator based on lead zirconium titanate (PZT)50,51. The actuator has PZT as the main piezoelectric material and platinum (Pt) as the top and the bottom (ground) electrodes, as shown in Fig. 5a. The key difference to AlN is that the PZT process has a patterned ground plane to eliminate bond-pad capacitance, since the relative permittivity of PZT is >800 compared to ~9 for AlN. Using disk-shaped PZT actuator on top of Si3N4 microresonator with 100 GHz FSR (see Fig. 5b), we perform the heterodyne beat experiment with a free running ECDL reference laser. The DFB is self-injection locked at 240 mA driving current to the Si3N4 cavity resonance. By applying a triangular voltage ramp with an 81 kHz frequency and an amplitude from 0.5 V to 3.5 V and positive bias of 3.5 V, we measured optical frequency excursion from 230 MHz to 1832 MHz correspondingly, and fit a tuning efficiency of 520 MHz/V (see Fig. 5c). Figure 5d, e presents the laser frequency spectrogram and the corresponding tuning nonlinearity at 500 kHz ramp frequency with 1.1 V applied, confirming the PZT actuator nonlinearity 0.95% over 525 MHz frequency excursion.

Discussion

We have demonstrated a hybrid integrated laser with low noise while exhibiting up to 10 MHz flat laser frequency actuation. This is achieved using piezo-electrical actuators in conjunction with suppression of mechanical modes of the chip via apodization. The approach is based on foundry-ready processes that include photonic integrated circuits based on Si3N4 as well as AlN and PZT MEMS processing, and is therefore amenable to large-volume manufacturing. The combination of narrow linewidth (kHz level) along with the fast and flat actuation response, makes the source ideally suited for medium to long-range coherent LiDAR, as required for autonomous driving, drone navigation, or industrial and terrain mapping. The combination of low noise and fast on chip tuning, alleviates the need for external components such as AOMs or single sideband modulators for fast frequency actuation, and may also find use in other areas such as locking of lasers to reference cavities, or atomic transitions - where a tight lock is required, and can be achieved with a high actuation bandwidth as demonstrated here. In addition, while our lasers were demonstrated at 1556 nm, the centre wavelength can be readily extended to other ranges, including the near IR and mid-infrared, due to the transparency of Si3N4. To further improve the performance of the laser system here, one can use laser chips with higher output power. Also, microresonators with larger mode volumes can be used to reduce the fundamental thermo-refractive noise. In addition, with careful design of the geometry of the piezoactuator and the dimension of the Si3N4 photonic chip to suppress HBAR modes, the linear actuation bandwidth could extend into the GHz regime - limited only by the internal modes of the piezoactuator31. Last, viewed more broadly, our results show that low noise hybrid integrated photonic lasers based on the Si3N4 - as pioneered by Boller et al. - can now achieve unique performance metrics in terms of combining linearity, frequency agility, and phase noise. In many cases our laser supersede commercial bulk external-cavity diode lasers and fibre lasers, today’s workhorses of distance metrology, spectroscopy and quantum optics. Detailed comparison with commercial ECDL and fibre lasers as well as many compact and photonic integrated tunable lasers based on monolithic InP chips is given in Table II of the supplementary information. Our results indicate the significant potential of hybrid integrated photonics with low loss dielectric feedback and fast non-thermal actuation to replace decades-old prevailing technologies based on bulk fibre laser and bulk grating-based external cavity lasers.

Methods

Thermorefractive noise calculation

To calculate TRN limit, we use the following expression for the effective temperature fluctuations43,52:

$${S}_{\delta T}({{{{{\rm{\omega }}}}}})=\frac{{k}_{B}{T}^{2}}{\sqrt{{\pi }^{3}\kappa \rho C\omega }}\sqrt{\frac{1}{2p+1}}\frac{1}{R\sqrt{{d}_{r}^{2}-{d}_{z}^{2}}}\frac{1}{{[1+{({{{{{\rm{\omega }}}}}}{\tau }_{d})}^{3/4}]}^{2}},$$
(1)

where R is the microring resonator radius; Si3N4 material parameters ρ = 3.29 × 103 kg m−3 is density; κ = 30 W m−1 K−1 is thermal conductivity; C = 800 J kg−1 K−1 is specific heat capacity; T = 300 K, dz = 1.5 μm and dr = 0.75 μm stand for halfwidths of the fundamental mode, with orbital number l, azimuthal number m and meridional mode number p = lm, $${\tau }_{d}=\frac{{\pi }^{1/3}}{{4}^{1/3}}\frac{\rho C}{\kappa }{d}_{r}^{2}$$.

FMCW laser ranging experiment

The DFB is directly butt-coupled to a 190.7-GHz FSR microresonator on a regular non-apodized chip placed on a carbon tape. The chip features a single AlN disk actuator. We employ laser frequency tuning by keeping the laser diode’s current fixed, the laser self-injection locked to a Si3N4 resonance and by tuning only the cavity resonance with AlN piezoactuator. Triangular ramp with 100 kHz frequency from an arbitrary waveform generator is amplified to 150 V (peak-to-peak amplitude) with a high voltage amplifier with 5 MHz bandwidth. The diode current is set near the centre of the injection locking range (281 mA for the particular resonance used) and AlN voltage is adjusted to keep the laser inside the self-injection locking range, resulting in a 1.2-GHz optical frequency excursion, corresponding to a FMCW LiDAR resolution of approximately 12.5 cm. While not required in actual operation, a small portion of the laser power was split of (95/5) to a fibre-coupled Mach-Zehnder interferometer for calibration of the frequency excursion. The length of the calibration MZI was measured with a frequency comb calibrated tunable diode laser scan. No active linearization or k-point sampling was necessary due to the excellent linearity and negligible hysteresis of the integrated AlN tuner. While 10% of the total laser power of 1.5 mW is used as a local oscillator (LO), 90% of the light is amplified by an EDFA to 10 mW and sent to a target through a collimator with an aperture of 8 mm, which was adjusted to fit the target range of 10 m. A double-axis galvanometric mirror scanner (Thorlabs GVS112) was used for the beam steering. Vertical and horizontal mirrors were rotated with constant speed at rates 3 Hz and 60 Hz correspondingly to cover the full scene during the measurement time of 400 ms.

Data availability

Data used to produce the plots within this paper is available at https://doi.org/10.5281/zenodo.6328345 All other data used in this study are available from the corresponding author upon reasonable request.

Code availability

Code used to produce the plots within this paper is available at https://doi.org/10.5281/zenodo.6328345.

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Acknowledgements

This work was supported by funding from the European Union H2020 research and innovation programme under FET-Open grant agreement no. 863322 (TeraSlice) and the Marie Sklodowska-Curie IF grant agreement No. 101033663 (RaMSoM). This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-19-1-0250. This work was supported by funding from the Swiss National Science Foundation under grant agreement No. 192293, No. 176563 (BRIDGE) and No. 201923 (Ambizione). This work was supported by funding from the European Space Technology Centre with ESA Contract No. 4000135357/21/NL/GLC/my. This work was also supported by the United States’ National Science Foundation under grant No. PHY 18-39164, DMR 17-47426, and QIS DCL 20-063. The chip samples were fabricated in the EPFL centre of MicroNanoTechnology (CMi), and in the Birck Nanotechnology Center at Purdue University. AlN deposition was performed at OEM Group Inc. PZT actuators were fabricated at Radiant Technologies Inc. We acknowledge Lin Chang and John Bowers for providing the DFB laser.

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G.L. and J.R. performed the experiments with the help from Vy.S.; W.W. developed a theoretical model and performed numerical simulations. A.S. performed mechanical response measurements. J.L., R.N.W. and J.H. designed, fabricated and characterised the Si3N4 chips. H.T. designed and fabricated the AlN actuators. R.N.W. performed chip apodization. Vl.S. and A.V. performed actuator’s bandwidth requirement simulations. G.L, J.R., A.S. and V.S analysed the data. W.W., G.L. and J.R. wrote the manuscript with input from all authors. T.J.K. and S.A.B. supervised the project.

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Correspondence to Tobias J. Kippenberg.

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Lihachev, G., Riemensberger, J., Weng, W. et al. Low-noise frequency-agile photonic integrated lasers for coherent ranging. Nat Commun 13, 3522 (2022). https://doi.org/10.1038/s41467-022-30911-6

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