Abstract
Frequency microcombs, alternative to modelocked laser and fiber combs, enable miniature rulers of light for applications including precision metrology, molecular fingerprinting and exoplanet discoveries. To enable frequency ruling functions, microcombs must be stabilized by locking their carrierenvelope offset frequency. So far, the microcomb stabilization remains compounded by the elaborate optics external to the chip, thus evading its scaling benefit. To address this challenge, here we demonstrate a nanophotonic chip solution based on aluminum nitride thin films, which simultaneously offer optical Kerr nonlinearity for generating octave soliton combs and quadratic nonlinearity for enabling heterodyne detection of the offset frequency. The agile dispersion control of crystalline aluminum nitride photonics permits highfidelity generation of solitons with features including 1.5octave spectral span, dual dispersive waves, and subterahertz repetition rates down to 220 gigahertz. These attractive characteristics, aided by onchip phasematched aluminum nitride waveguides, allow the full determination of the offset frequency. Our proofofprinciple demonstration represents an important milestone towards fully integrated selflocked microcombs for portable optical atomic clocks and frequency synthesizers.
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Introduction
Optical frequency combs, developed from solidstate or fiber modelocked lasers, have evolved into photonic chipbased sources that feature the potential towards a miniaturized footprint and reduced cost^{1}. Among various chipscale schemes^{2,3,4,5}, microresonator Kerr frequency combs (“microcombs” hereafter) are of particular interest because of their high scalability for photonic integration^{6,7,8}. To enable phasecoherent microcombs, substantial efforts have been made towards soliton modelocking on the one hand^{9,10,11,12,13,14,15,16,17}, unveiling rich soliton physics on the other hand^{18,19,20}. Specifically, octavespanning soliton microcombs are important because it permits phase locking of the carrierenvelope offset (CEO) frequency (f_{ceo}) via wellknown f–2f interferometry^{21}, and are prerequisite for chipscale implementation of precision metrology^{22}, frequency synthesizers^{23} and optical clocks^{24}. To date, silicon nitride (Si_{3}N_{4}) nanophotonics has proved viable for octave soliton operations with a terahertz repetition rate (f_{rep})^{25,26,27}. Nevertheless, such a large f_{rep} is not amenable for direct photodetection and poses challenges to access the CEO frequency with a value up to f_{rep}. In the meantime, the lack of intrinsic quadratic χ^{(2)} nonlinearities in Si_{3}N_{4} films typically requires an external frequency doubler and offchip optical circuitry for deriving the CEO frequency^{28,29}. These offchip optical components compromise the scaling advantage of microcombs and significantly set back selflocked microcombs for portable applications.
Aluminum nitride (AlN) semiconductors exhibit a noncentrosymmetric crystal structure, thereby possessing inherent optical χ^{(2)} nonlinearity as well as Pockels electrooptic and piezoelectric properties^{30}. Apart from the advances in ultraviolet lightemitting diodes^{31} and quantum emitters^{32,33}, AlN has also proved viable for lowloss nanophotonics in highefficiency secondharmonic generation (SHG)^{34,35} and highfidelity Kerr and Pockels soliton modelocking^{15,36}. Therefore, it is feasible to establish an onchip f–2f interferometer provided that an octave AlN soliton microcomb is available. This is a solution that is favored here comparing with the heterogeneous integration approach such as proposal based on hybrid gallium arsenide (GaAs)/Si_{3}N_{4} waveguides^{37}. Despite that onchip f_{ceo} detection was achieved from supercontinuua driven by a femtosecond laser in nonresonant χ^{(2)} nanophotonic waveguides made from AlN^{38} or lithium niobate (LN) thin films^{39,40}, resonator microcombbased f–2f interferometry using nanophotonics, to our knowledge, remains elusive.
In this article, we demonstrate highfidelity generation of octave soliton microcombs and subsequent f_{ceo} detection using AlNbased nanophotoinc chips. Thanks to mature epitaxial growth, AlN thin films with highly uniform thickness are available, thus permiting lithographic control of group velocity dispersion (GVD) for comb spectral extension via dispersive wave (DW) emissions^{11}. Our octave soliton microcombs possess separated dual DWs and moderate f_{rep} of 433, 360, and 220 gigahertz, and are found to be reproducible from batchtobatch fabrications. The results then allow us to capture the f–2f beatnote through onchip SHG in phasematched AlN waveguides. Our work establishes the great potential of noncentrosymmetric AlN photonic platforms for achieving portable selflocked microcomb sources in the near future.
Results
Experimental scheme description
Figure 1a illustrates the implementation of microcombbased f–2f interferometry from a nanophotonic chip. The strategy is to leverage noncentrosymmetric photonic media for cointegration of χ^{(3)} octave soliton microcombs and χ^{(2)} SHG doublers. For a proofofprinciple demonstration, we adopt an auxiliary laser (at f_{aux}) to obtain sufficient SHG power (at 2f_{aux}) from phasematched optical waveguides. The use of the auxiliary laser can be eliminated by exploiting microringbased architectures to boost the SHG efficiency^{34}. By subsequently beating f_{aux} and 2f_{aux} with the f_{n} and f_{2n} comb lines at their corresponding beatnotes of δ_{1} and δ_{2}, the f_{ceo} signal reads:
The AlN thin films in this work were epitaxially grown on a cplane sapphire substrate via metalorganic chemical vapour deposition^{41,42}. As illustrated in Fig. 1b, the AlN epilayer exhibits a hexagonal wurtzite structure with a unit cell shown in the bottom, highlighting the noncentrosymmetry. We also show an overall 2inch AlNonsapphire wafer featuring a broadband transparency and a favored film thickness (Fig. 1c)—both are crucial factors to ensure octave GVD control. Great attention was also paid to the film crystal quality and surface roughness for lowloss photonic applications. The AlN nanophotonic chips were manufactured following electronbeam lithography, chlorinebased dry etching, and silicon dioxide (SiO_{2}) coating processes and were subsequently cleaved to expose waveguide facets^{43}. The intrinsic optical quality factors (Q_{int}) of the AlN resonators were characterized to be ~1–3 million depending on the waveguide geometries. The detailed film and device characterization is presented in “Methods” and Supplementary Fig. 1.
Since wurtzite AlN manifests optical anisotropy for vertically or horizontallypolarized light^{44}, we engineer the waveguide structures for optimizing the performance of fundamental transverse magnetic (TM_{00}) modes, which allows the harness of its largest χ^{(2)} susceptibility to ensure highefficiency SHG. To expand microcomb spectra out of the anomalous GVD restriction, we exploit solitoninduced DW radiations by tailoring the resonator’s integrated dispersion (D_{int})^{11}:
where D_{2}, D_{3}, and D_{i} are i_{th}order GVD parameters, while μ indexes the relative azimuth mode number with respect to the pump (μ = 0). In the dispersion modeling, we have accounted for both the material (AlN) and geometry (cross section, bending radius, and slanted sidewall) dispersion^{42}. To prevent avoided mode crossing from interrupting soliton modelocking, we adopt a weak pulleycoupling configuration (concentric angle of 6°), which helps suppress the excitation of higherorder resonator modes (Supplementary Fig. 1c).
Octave soliton microcombs
Our GVD engineered AlN resonators are coated with a SiO_{2} protection layer, making it less susceptible to the ambient compared with the aircladded Si_{3}N_{4} counterpart^{25,26,27,28,29}. An example of the resonator modal profile is shown in the inset of Fig. 2a. The top panel of Fig. 2a plots the D_{int} curve from a 50 μmradius AlN resonator through numerical simulation (see “Methods”). In spite of the limited anomalous GVD window (solid light blue region), octave microcomb operation is feasible via DW radiations at phasematching conditions D_{int} = 0, allowing for spectral extension into normal GVD regimes (solid light orange regions). Note that the occurrence of such dual DWs benefits from the optimal film thickness in our AlN system, while the DW separation is agilely adjustable over one octave through the control of resonator’s dimensions (Supplementary Fig. 2). Around the telecom band, the D_{int} value (red dots) was characterized by calibrating the resonator’s transmission with a fiberbased MachZehnder interferometer^{15,17}. The experimental result matches well with the simulated one (inset of Fig. 2a) with an extracted D_{2}/2π of ~6.12 MHz.
We then explore soliton modelocking based on a rapid frequency scan scheme to address the abrupt intracavity thermal variation associated with transitions into soliton states^{15}. The soliton spectrum is recorded using two gratingbased optical spectrum analyzers (OSAs, coverage of 350–1750 nm and 1500–3400 nm). The experimental setup is detailed in Supplementary Fig. 4. The bottom panel of Fig. 2a plots the soliton spectrum from a 50 μmradius AlN resonator, featuring a moderate f_{rep} of 433 GHz and an observable spectral span of 1.05–2.4 μm, exceeding one optical octave. Meanwhile, solitoninduced DW radiations occur at both ends of the spectrum, in agreement with the predicted D_{int} curves. Note that the highfrequency DW exhibits an evident blue shift from the D_{int} = 0 frequency, which is mainly ascribed to Ramaninduced soliton red shifts (relative to the pump frequency)^{45,46}. The soliton recoils make less impact here due to dual DW radiations^{47}. This conclusion is supported by our modeling when comparing the soliton spectra with and without Raman effects (Supplementary Fig. 2b).
The single crystal nature of AlN thin films permits reproducible optical refractive indices in each manufacture run. This, in combination with their uniform film thickness control, leads to a high predictability for the dispersion engineering, making it feasible to predict octave soliton combs at various repetition rates. For instance, our GVD model indicates that octave spectra with repetition rates further decreased by two times are anticipated from 100 μmradius AlN resonators at optimal widths of 3.3–3.5 μm (Supplementary Fig. 3a). Figure 2b plots the recorded soliton comb spectrum at a resonator width of 3.5 μm, where a f_{rep} of ~220 GHz and dual DWs separated by more than one octave are achieved simultaneously. Such a low f_{rep} is amenable for direct photodetection with stateoftheart unitravellingcarrier photodiodes^{48}. We also noticed the occurrence of a weak sharp spectrum around 130 THz, which might arise from modified local GVD due to avoided mode crossing^{49}. In our nanophotonic platform, we could further predict resonator geometries for achieving octave solitons with an electronically detectable f_{rep} of ~109 GHz (Supplementary Fig. 3b). Nonetheless, the strong competition between Kerr nonlinearities and stimulated Raman scattering (SRS) must be taken into account since the free spectral range (FSR) of the resonator is already smaller than the \({A}_{1}^{{{{{{{{\rm{TO}}}}}}}}}\) phonon linewidth (~138 GHz) in AlN epilayers^{42}.
Since the SHG from the auxiliary laser (1940–2000 nm) available in our laboratory is beyond the soliton spectral coverage shown in Fig. 2, we further adjust the resonator dimensions for extending microcomb spectra below 1 μm. As plotted in Fig. 3a, the phasematching condition (D_{int} = 0) for highfrequency DW radiations below 1 μm is fulfilled by elevating the resonator radius to 60 μm while maintaining its width around 2.3 μm. In the meantime, lowfrequency DWs could also be expected and their spectral separation is adjustable by controlling the resonator width. Guided by the tailored D_{int} curves, we fabricated the AlN resonators and recorded octave soliton spectra at a f_{rep} of ~360 GHz (Fig. 3b). Lithographic control of DW radiations (indicated by vertical arrows) is also verified by solely adjusting the resonator width, allowing the spectral extension below 1 μm (width of 2.3 or 2.4 μm). The low and highfrequency DWs are found to exhibit distinct frequency shifting rates, consistent with the D_{int} prediction. The observable soliton spectra (from top to bottom of Fig. 3b) cover 1.5, 1.3, and 1.2 optical octaves by normalizing the total span (Δf) to its beginning frequency (f_{1}), that is Δf/f_{1}. Such a definition permits a fair comparison among soliton microcomb generation in distinct pump regimes across different material platforms, suggesting high competitiveness of our AlN microcomb span comparing to stateoftheart values reported in Si_{3}N_{4} microresonators^{26}.
Onchip second harmonic generator
We then explore the cointegration of SHG based on the χ^{(2)} susceptibility of AlN for matching the DW peak below 1 μm (middle panel of Fig. 3b). To fulfill the demanding requirement of spectral overlaps with the microcomb, we adopt a straight waveguide configuration, which allows a broader phasematching condition albeit at the cost of reduced conversion efficiencies comparing to its counterpart using dualresonant microresonators^{34,50}. Through modeling, we predict an optimal waveguide width of ~1.38 μm for fulfilling the modalphasematching condition (Supplementary Fig. 5a), while the actual waveguide width was lithographically stepped from 1.32 to 1.46 μm (spacing of 5 nm) accounting for possible deviations during the manufacturing process.
Figure 4 a shows a section of 6 cmlong SHG waveguides cofabricated with the microcomb generator. At a fixed fundamental wavelength (1970 nm), we located the phasematching waveguide at the width of 1.395 μm, close to the predicted width. The corresponding SHG spectra are plotted in Fig. 4b, where we achieve a high offchip SHG power over 50 μW by boosting the fundamental pump power from a thuliumdoped fiber amplifier to compensate the SHG efficiency (Supplementary Fig. 5b). In the meantime, the wavelengthdependent SHG power shown in the inset indicates a large 3dB phasematching bandwidth of ~0.8 nm, which, together with an external heater for thermal finetuning, is sufficient to cover the target comb lines for subsequent heterodyne beating.
Nanophotonicsbased f–2f interferometry
By combining outgoing light from optimal AlN soliton and SHG generators on the calibrated OSAs, we are able to estimate the f–2f beatnote frequency to be approximately 32 GHz limited by the resolution of the OSAs. To electronically access the f_{ceo} signal in real time, we employ a scheme sketched in Fig. 5a. The recorded soliton spectrum after suppressing pump light by a fiber Bragg grating (FBG) indicates a high offchip power close to −40 dBm for the highfrequency DW (Supplementary Fig. 6a). Meanwhile, a wavelengthdivision multiplexer (WDM) is utilized to separate the f and 2f frequency components before sent into the photodetectors (PDs). Two tunable radio frequency (RF) synthesizers are introduced as the local oscillators (LO1 and LO2) to down convert the photodetector signals for effective capture of the f–2f beat signal at a convenient lowfrequency band with an electronic spectrum analyzer (ESA, range of 20 Hz–26.5 GHz).
As highlighted in Fig. 5b, we record two downconverted beatnotes of Δf_{1} and Δf_{2} with a signaltonoise ratio (SNR) of 10 dB at a resolution bandwidth of 1 MHz. A much higher SNR is anticipated by applying a finer detection bandwidth upon locking the telecom pump laser as well as the f_{ceo} frequency^{23,24}. The corresponding f–2f beatnote is \(\overline{{f}_{{{{{{{{\rm{ceo}}}}}}}}}}\) = 2f_{LO1} + f_{LO2} – Δf_{2} (inset of Fig. 5b) since the local oscillator frequencies f_{LO1} and f_{LO2} are chosen to be larger than beatnotes of δ_{1} and δ_{2}. Based on the relative frequency positions of the auxiliary laser and its neighboring comb tooth (Supplementary Fig. 6b), we reach an actual f_{ceo} = FSR – \(\overline{{f}_{{{{{{{{\rm{ceo}}}}}}}}}}\) due to the involvement of f_{n} and f_{2n+1} comb lines in the heterodyne beating. On the other hand, the f_{LO1} and f_{LO2} frequencies are freely adjustable up to 40 and 20 GHz in our scheme, which could further expand the accessible range of the f_{ceo} frequency based on the downconversion process presented here. Meanwhile, the RF synthesizers are synchronized to a common external frequency reference, suggesting that the captured downconverted f–2f signals are available for further locking the comb teeth in a feedback loop^{28}.
Discussion
We demonstrate nanophotonicsbased implementation of f–2f interferometry by leveraging χ^{(3)} octave solitons and χ^{(2)} SHG cofabricated from a noncentrosymmetric AlN photonic platform. Thanks to agile GVD engineering offered by epitaxial AlN thin films, our octave soliton microcombs can be reliably produced with dual DWs and subTHz repetition rates (220–433 GHz) that are accessible with unitravellingcarrier photodiodes. The overall soliton spectral span is adjustable up to 1.5 octaves, on a par with stateoftheart values (1.4 octaves) reported in Si_{3}N_{4} microresonators. We further perform the f_{ceo} measurement with the aid of an auxiliary laser for enabling SHG in phasematched AlN waveguides, thus allowing for spectral overlap with the desired octave soliton.
For future development, the spectral restriction of octave solitons for matching with the auxiliary laser wavelength can be relaxed by exploiting highefficiency SHG in dualresonant microresonators, which allows direct doubling of a selected comb line in the low frequency DW band^{51}. Meanwhile, the octavespanning microcomb’s repetition rate can be further reduced by leveraging onchip Pockels electrooptical frequency division^{52}. By shifting the phase matching condition for SHG, it is also possible to extend octave solitons into the nearvisible band, giving access to selflocked nearvisible microcombs for precision metrology. Our results represent an important milestone to unlock the potentials of octave microcomb technologies for portable applications.
Methods
Nanofabrication
The surface roughness and crystal quality of our AlN epilayer were respectively characterized by an atomic force microscope and an Xray diffraction scan, indicating a rootmeansquare roughness of 0.2 nm in 1 × 1 μm^{2} region and an FWHM linewidth of ~46 and 1000 arcsec along [002] and [102] crystal orientations, respectively. The film thickness was mapped by a spectroscopic ellipsometer (J.A. Woollam M2000), providing a quick and preliminary selection of the desired AlN piece for octave soliton generation with dual DWs. As shown in Supplementary Fig. 1a, in spite of varied film thicknesses across a 2inch AlN wafer, we can reliably locate the desired region for reproducible octave device fabrication.
To further reduce the propagation loss, the AlN photonic chips were annealed at 1000 °C for 2 h. The resonator Qfactors were probed by sweeping a tunable laser (Santec TSL710) across the cavity resonances and then fitted by a Lorentzian function. In the 100 μmradius AlN resonators (width of 3.5 μm), we achieve a recorded Q_{int} of 3.0 million, while the 50 μmradius resonators (width of 2.3 μm) exhibit a decreased Q_{int} of 1.6 million, indicating the dominant sidewall scattering loss of our current fabrication technology. The related resonance curves are plotted in Supplementary Fig. 1c and d.
Numerical simulation
The D_{int} of the AlN resonators is investigated using a finite element method (FEM) by simultaneously accounting for the material and geometric chromatic dispersion. The overall D_{int} value is approximated with a fifthorder polynomial fit applied to the simulated modal angular frequencies: ω_{μ} = ω_{0} + μD_{1} + D_{int}, where D_{1}/(2π) is the resonator’s FSR at the pump mode μ = 0.
The spectral dynamics of octave soliton microcombs is numerically explored based on nonlinear coupled mode equations by incorporating the Raman effect^{46,53}:
Here a and \({{{{{{{\mathcal{R}}}}}}}}\) are the mode amplitudes of cavity photons and Raman phonons with subscripts k, l, n being the mode indices, while g_{K} and g_{R} represent the nonlinear coupling strength of Kerr and Raman processes, respectively. The driving signal strength is \({\xi }_{{{{{{{{\rm{P}}}}}}}}}=\delta (\mu )\sqrt{\frac{{\kappa }_{{{{{{{{\rm{e}}}}}}}},0}{P}_{{{{{{{{\rm{in}}}}}}}}}}{\hslash {\omega }_{{{{{{{{\rm{p}}}}}}}}}}}\) at an onchip pump power P_{in}, κ_{μ} (κ_{e,μ}) denotes the total (external) cavity decay rate of the μ^{th} photon mode, and γ_{R} is the Raman phonon decay rate. The detuning from a D_{1}spaced frequency grid is indicated by \({{{\Delta }}}_{\mu }^{a}\) = ω_{μ} – ω_{P} – μD_{1} and \({{{\Delta }}}_{\mu }^{{{{{{{{\rm{R}}}}}}}}}\) = ω_{R} – μD_{1} with ω_{P} and ω_{R} being pump and Raman shift angular frequencies, respectively.
In the simulation, we set the time derivative of Raman items in Eq. (4) to zero to speed up the computation since the decay rate of phonons is much larger than that of photons. We also consider frequencyindependent κ_{μ}/(2π) ≈ 120 MHz and κ_{e,μ}/(2π) ≈ 75 MHz based on measured Qfactors of 50 μmradius AlN resonators (Supplementary Fig. 1c). Because incident light is TMpolarized, the involved \({A}_{1}^{{{{{{{{\rm{TO}}}}}}}}}\) Raman phonon in AlN exhibits an ω_{R}/(2π) ≈ 18.3 THz with an FWHM of γ_{R}/(2π) ≈ 138 GHz^{41}. The g_{K}/2π is calculated to be 0.73 Hz for a given nonlinear refractive index n_{2} = 2.3 × 10^{−19} m^{2}/W, while an optimal g_{R}/2π = 0.29 MHz is adopted, resulting in a soliton spectrum matching well with the measured one in Fig. 2a. The simulated high frequency DW also exhibits an evident blue shift comparing with the case of g_{R}/2π = 0 MHz (Supplementary Fig. 2b).
Data availability
The source data that support the findings of this study are available in figshare repository: https://doi.org/10.6084/m9.figshare.15167895.v1.
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Acknowledgements
This work was supported by DARPA SCOUT (W31P4Q1510006). H.X.T. acknowledges partial support from DARPA’s ACES program as part of the DraperNIST collaboration (HR001116C0118) and DARPA’s APhi program with a subcontract from Sandia labs (DENA0003525). The authors thank Y. Sun, S. Rinehart, and K. Woods in Yale cleanrooms and M. Rooks in YINQE for assistance in the device fabrication, and J. Xie and M. Xu in the laboratory for the microwave circuit discussion.
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H.X.T and X.L conceived the idea. X.L. performed the device design, fabrication, and measurement with the assistance from Z.G., A.B., J.S. and J.L., Z.G. and X.L. performed the soliton simulation. X.L. and H.X.T. wrote the manuscript with the input from all other authors. H.X.T supervised the project.
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Liu, X., Gong, Z., Bruch, A.W. et al. Aluminum nitride nanophotonics for beyondoctave soliton microcomb generation and selfreferencing. Nat Commun 12, 5428 (2021). https://doi.org/10.1038/s41467021257519
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DOI: https://doi.org/10.1038/s41467021257519
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