Introduction

Optical frequency combs, consisting of discrete spectral lines aligned to equidistant frequency grids, serve as a coherent link between optical and microwave signals1. They have become the cornerstone for precision spectroscopy2 and metrology3, and their potential to enhance a diverse range of applications hinges on instrumental advancements that prioritize reduced size, weight, and power consumption. This aspiration has been realized in optical microresonators as microcombs, which harness resonantly-enhanced nonlinear optical processes for comb generation4. To date, mode-locked microcombs have been demonstrated in many microresonator platforms, such as MgF25, silica6, Si3N47, SiC8, and LiNbO39.

LiNbO3 has become an appealing comb-generating material due to its various optical nonlinearities, broad transparency window, and compatibility with integrated photonics10. The most well-known Pockels and Kerr effects have enabled electro-optic combs11,12,13 and soliton microcombs9,14,15,16,17,18 in LiNbO3 microresonators. Furthermore, their combination is expected to complete microcomb functionalities. Since electro-optically modulated soliton microcombs19 and highly-efficient frequency doublers20 are accessible on Z-cut LiNbO3 microresonators, self-referenced microcombs are underway for compact spectrometers21,22,23,24,25, miniaturized optical clocks26,27, low-noise microwave generation28,29,30, and high-precision ranging31,32,33.

The inclusion of Raman nonlinearity in comb-forming processes has introduced a range of novel phenomena. In materials with broadband Raman gain, such as silica, stimulated Raman scattering (SRS) can result in a redshift of the comb spectra34 or provide co-propagating, pulsed Raman gain for the formation of a secondary soliton microcomb35. In contrast, LiNbO3, a Raman-active crystal with several narrow-band vibrational energy levels (Fig. S7 in supplementary information (SI)), is inclined to produce continuous-wave Raman gain from individual comb lines. This results in continuous-wave Raman lasing in microresonators, thereby complicating the comb formation process15,36,37.

Mitigating SRS in LiNbO3 microresonators is essential for soliton microcomb generation18,19. The challenge is amplified for another important class of Kerr microcombs known as dark pulse microcombs. Unlike the sech2-shaped soliton microcombs, dark pulse microcombs appear as flat-top pulses in the microresonator38,39,40,41,42,43, exhibiting superior pump-to-comb conversion efficiency and high comb line power. Although these features are appealing for communications44,45,46 and microwave photonics47, the high-power comb lines near the spectral center of dark pulse microcombs also promotes continuous-wave SRS (Section I in SI), especially in microresonators with small free spectral ranges (FSRs) where optical modes more easily resonate with Stokes photons36,48. Consequently, dark pulse microcombs remain challenging to realize in LiNbO3 microresonators.

In this article, we present a dissipation engineering approach to mitigate SRS in an integrated high-Q LiNbO3 microresonator, where pulley waveguide couplers are designed to introduce wavelength-dependent losses to the microresonator. Consequently, we demonstrate the generation of dark pulse microcombs with repetition frequencies as low as 24.8 GHz and spectra spanning over 200 nm. Furthermore, we show the tuning of repetition frequency over 292 kHz by adjusting the laser-cavity detuning and characterize the phase noise performance, highlighting their potential for various applications at optical and microwave frequencies.

Results

Dissipation engineering

SRS and Kerr-induced four-wave mixing are both third-order nonlinear optical processes, with the threshold power for their initiation following similar scaling laws based on the dissipation rates of the microresonator (κ). For Raman lasing to occur, the pump energy inside the microresonator must exceed

$${E}_{{{{\rm{th,R}}}}}=\frac{{\kappa }_{R}}{2{g}_{R}},$$
(1)

where gR is the Raman gain coefficient and κR is the dissipation rate of the mode involved in Raman lasing. In the case of Kerr nonlinearity, and ignoring dispersion requirements, the pump energy required to initiate degenerate four-wave mixing is given by

$${E}_{{{{\rm{th,K}}}}}=\frac{\sqrt{{\kappa }_{{{{\rm{S}}}}}{\kappa }_{{{{\rm{AS}}}}}}}{2{g}_{K}},$$
(2)

where κS and κAS represent the dissipation rates for the Stokes and anti-Stokes modes, respectively. In LiNbO3, the Kerr nonlinear coefficient gK is often significantly smaller than the Raman gain coefficient gR. To raise the Raman lasing threshold to a level that does not interfere with Kerr microcomb formation, the dissipation rate of the Raman lasing mode should be substantially larger than that of the Stokes and anti-Stokes modes near the pump mode. This is the target of dissipation engineering in this work.

The optical dissipation in microresonators comprises both intrinsic and external components. The former (κo) is primarily influenced by material absorption and surface scattering, which is challenging to engineer in the frequency domain. On the other hand, external dissipation (κext) is dictated by waveguide coupling, which can be tuned in the frequency domain by designing phase-matching conditions between the waveguide and microresonator. Therefore, controlling κext provides a route for dissipation engineering.

We first consider the most widely-used coupler design, i.e., straight waveguide couplers, whose coupling to a ring resonator results in a confined coupling region due to limited spatial overlap. As the wave propagates along the waveguide, the effective distance between the waveguide and microring rapidly increases, leading to phase mismatching and a gradual increase in κext with wavelength due to modal leakage (Fig. 1a). We simulate comb formation in a normal-dispersion LiNbO3 microresonator with a straight waveguide coupler based on the generalized Lugiato-Lefever equation augmented by SRS (see “methods”). The FSR of the microresonator is set significantly smaller than the Raman gain bandwidth. The nearly constant dissipation profile gives rise to Raman lasing when the microresonator is pumped by a continuous-wave laser (Fig. 1b). Additionally, four-wave mixing interactions between the pump and Raman laser initiate modulational instability (MI), resulting in chaotic waveforms within the microresonator. Numerical simulations using a broader selection of pumping parameters (pump power and laser-cavity detuning) reveal the phase diagram, which excludes dark pulse microcombs (Fig. 1c).

Fig. 1: Dissipation engineering for dark pulse microcomb generation.
figure 1

a Dissipation rate versus wavelength for microrings coupled to straight bus waveguides. κo: intrinsic loss; κext: external coupling loss. b Simulated optical spectrum and temporal profile of microcomb in microresonators without dissipation engineering. The color gradient indicates the Raman gain. c Simulated phase diagram as a function of pump power and laser-cavity detuning in microresonators without dissipation engineering. The normalization of detuning and pump power is defined in Methods, and the details of simulating the phase diagrams are provided in the supplementary information. d Dissipation rate versus wavelength for microrings coupled to pulley bus waveguides. e Simulated optical spectrum and temporal profile of microcomb in microresonators with dissipation engineering. f Simulated phase diagram as a function of pump power and laser-cavity detuning in microresonators with dissipation engineering. The blue area indicates the maximum existence range of dark pulses generated from an initial seed, which are determined by verifying their stability in the generalized Lugiato-Lefever equation.

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This situation can be overturned by employing pulley waveguide couplers, which wrap around the resonator with a consistent gap, thereby considerably enhancing the coupling length compared to traditional straight waveguide coupling (Fig. 1d). By carefully designing the geometry of the waveguide and the microring, it is possible to achieve phase-matching conditions at specific wavelengths. Consequently, κext experiences a rapid increase towards the phase-matching wavelength. When modes within the Raman gain bandwidth experience much larger dissipation rates than modes near the pump, dark pulse microcombs can form in the microresonator, with a typical optical spectrum shown in Fig. 1e. Despite the presence of Raman lasing and modulational instability at high pump power levels, a distinct region indicating the existence of dark pulse microcombs emerges in the phase diagram (Fig. 1f), highlighting the efficacy of dissipation engineering.

Device characterization

We fabricate dissipation-engineered microring resonators on 570-nm-thick Z-cut lithium niobate on insulator wafers (Fig. 2a). The geometry of the microresonator, characterized by a radius of 817 μm, an etching depth of 300 nm, and a top width of 2.2 μm, is chosen to induce normal group velocity dispersion (GVD). Experimentally, we measure the resonant frequencies of the fundamental transverse-electric (TE) mode family over a wavelength range of 1460 nm to 1630 nm using tunable continuous-wave lasers calibrated by a Mach-Zehnder interferometer. The measured integrated dispersion, defined as Dint = ωμ − ω0 − D1μ = ∑n≥2 Dnμn/n!, where μ is mode index relative to the pump mode, ωμ represents the resonant frequency of the μth mode, and D1/2π is the free spectral range (FSR), is plotted in Fig. 2b. The FSR of the microresonator is found to be 24.803 GHz. Polynomial fitting of the integrated dispersion data reveals the second-order dispersion D2/2π = −6.2 kHz. Nevertheless, the experimentally measured mode family dispersion exhibits local deviations from the simulated results at several wavelengths. These discrepancies are likely attributed to interactions with other transverse modes in the multimode waveguides.

Fig. 2: Device design and characterization.
figure 2

a Optical microscope images of LiNbO3 microring (left, top) and scanning electron microscope images detailing various components: waveguide-coupled region (left, bottom), the cross-section of the microring waveguide (right, top), and a zoom-in view of the pulley waveguide coupler (right, bottom). The intensity profile of the fundamental TE mode is overlaid on the cross-section. b Integrated dispersion (Dint) of the fundamental TE mode family. The values of D1 and D2 are also listed. c Top panel: normalized transmission spectra of four typical resonances at different wavelengths. Middle panel: broadband transmission spectrum. The fringes caused by the reflection at the bus waveguide facets are removed using Fourier filtering. Bottom panel: measured and simulated total dissipation rates as a function of wavelength. Color shadings represent different coupling conditions. The pump mode and the corresponding Raman gain are also indicated.

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The pulley coupler, characterized by a bus waveguide width of 1.756 μm, a pulley angle of 15 degrees, and a constant gap of 450 nm (Fig. S6 in SI), is anticipated to exhibit increased coupling losses at wavelengths exceeding 1600 nm. These wavelengths feature strong Raman gain for 1563.2 nm pump lasers, as depicted in Fig. 2c and Fig. S7 (see SI). To investigate the impact of the pulley waveguide, we analyze the broadband transmission spectrum of the microresonator. Given that the intrinsic loss remains relatively stable within this spectral range, we utilized this knowledge (Qo ≈ 4 ~ 5 M) to distinguish between intrinsic and external coupling losses by applying Lorentzian fitting to the transmission spectra. Our analysis reveals that the microresonator transitions from over-coupling to under-coupling and then returns to over-coupling as the wavelength increases from 1460 nm to 1630 nm. Notably, the total dissipation rates reach 2π × 350 MHz at 1600 nm, representing a threefold increase compared to those observed near 1563.2 nm. This increase is expected to result in a corresponding threefold rise in the Raman lasing threshold. The excellent agreement between our measured and simulated results underscores the precision with which the device geometry is controlled during fabrication.

Generation of dark pulse microcombs

An amplified continuous-wave laser pumps the microresonator at around 1563.2 nm for comb generation. The laser is scanned from the red-detuned side towards the blue-detuned side of the mode. The transmission spectra of the pump and other comb lines are selected using a tunable fiber Bragg-grating filter (Fig. 3a). Low-noise steps appear first on the transmission spectra, corresponding to mode-locked microcombs. Further increasing the laser frequency results in chaotic transmission spectra, referred to as MI. As shown in Fig. 3b, the optical spectra of MI manifest two Raman lasers with frequency shifts of 153 cm−1, and 628 cm−1, respectively, corresponding to the optical phonon modes of E(TO)1 and A(TO)4 (Fig. S7 in SI)49,50. Other sidebands arise from the four-wave mixing processes and are not coherent with each other.

Fig. 3: Formation of dark pulse microcombs.
figure 3

a Normalized transmitted pump power (top panel) and comb power (bottom panel) as a function of the increased pump laser frequency. b Optical spectrum of microcomb at MI state. Two Raman lasing modes are labeled with corresponding Raman shifts of 153 cm−1 and 628 cm−1. c Optical spectra of dark pulse microcombs with different comb line spacing. The left insets show the zoom-in views of the comb lines. The right inset shows the measured electrical beatnote of the 1-FSR microcomb with 10-Hz resolution bandwidth (RBW). d Optical spectra of dark pulse microcombs for two different laser-cavity detunings. The simulated spectral envelopes of the microcombs are also plotted. The detunings are inferred from the simulations as 364 MHz and 400 MHz for left and right panels, respectively. Insets: simulated intracavity waveforms.

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The photorefractive effect in LiNbO3 allows for bi-directional accessing the low-noise steps in terms of tuning the laser frequency9. Each step corresponds to a different state of the dark pulse microcomb, and several representative optical spectra are displayed in Fig. 3c. The combs span from 1440 nm to 1640 nm, and Raman lasing actions are not observed. The spacings of the microcombs can be adjusted from single FSR to 4 FSR. Microcombs with multiple-FSR spacing exhibit enhanced power per comb line and an extended spectral span captured by the optical spectral analyzer51. A few spikes are present on the spectra due to the coupling between the fundamental TE mode and other transverse modes52. These avoided mode crossings, along with SRS, indeed facilitate the initiation of parametric oscillations, and dark pulses can be generated at other pump wavelengths from 1552 nm to 1564 nm38,53 (Fig. S8 in SI). With 260 mW pump power on the bus waveguide, the conversion efficiency of the pump to the comb line can be up to 4% by calibrating the losses in the measurement setup (Fig. S9 in SI). Photodetection of the single-FSR microcomb reveals a monotone electrical beatnote at 24.8038 GHz, corresponding to the repetition frequency of the microcomb. It unambiguously demonstrates the mode-locking of the microcomb.

We fine-tune the microcomb with single-FSR spacing by adjusting the laser-cavity detuning. The spectra acquired at two different detunings exhibit characteristic modulations with different periods determined by the duration of the dark pulse38,54 (Fig. 3d). To infer the temporal profiles of the two states, we perform numerical simulations based on experimentally measured device parameters. The fittings of the optical spectra reveal flat-top pulses in the microresonator, with duration varied from 5.4 ps to 2.4 ps depending on the detuning. The relatively small duty cycle is a consequence of the near-zero dispersion of the microresonator. The deviation between the simulated intracavity spectra and the experimental results is attributed to the wavelength-dependent coupling to the bus waveguide. For instance, the dips observed in the experimental spectra near 1528 nm aligned with the under-coupled regime shown in Fig. 2c.

Microwave synthesis

We further investigate the tunability and noise performance of the microwave signal synthesized from the electrical beatnote (repetition frequency) of the dark pulse. The experimental setup is illustrated in Fig. 4a. In addition to the comb generation system, we actively monitor the comb power to stabilize the relative detuning between the pump laser and the resonance. As a result, we observe significant suppression of spectral drift over several hours, as demonstrated by the stability of the total power of the comb lines (Fig. 4b). This feedback control mechanism not only stabilizes the system but also allows precise tuning of the detuning, enabling access to different comb states, each characterized by distinct repetition frequencies. By adjusting the locking point, we achieve a tunability of the repetition frequency over a range of 292 kHz (Fig. 4c).

Fig. 4: Microwave synthesis using dark pulse microcombs.
figure 4

a Experimental setup. PM: phase modulator; EDFA: erbium-doped fiber amplifier; PC: polarization controller; FBG: fiber Bragg grating; PD: photodetector; AOM: acousto-optic modulator; PNA: phase noise analyzer. b Evolution of comb power versus time. c Electrical beatnotes of dark pulse microcombs for 5 different laser-cavity detunings. d Single-sideband (SSB) phase noise of the repetition rates of the dark pulse microcombs and the pump laser. The contribution of the pump RIN to the phase noise is plotted as the gray dashed line. Inset: zoom-in view of the noise spectra near 100 kHz offset frequencies. The spurs induced by phase modulation and pump RIN are indicated.

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The phase noise of the repetition frequency is measured using a phase noise analyzer (Rohde & Schwarz FSWP50), while the phase noise of the pump laser is characterized using a delayed self-heterodyne interferometer (see “Methods”). A comparison of the laser phase noise and beatnote phase noise reveals similar spectral features at low offset frequencies (Fig. 4d), suggesting the presence of noise transduction between the two. This transduction likely arises from a combination of stimulated Raman scattering52, higher-order dispersion7, and avoided mode crossings55, which introduce spectral shifts dependent on the laser-cavity detuning. As a result, the laser phase noise couples to the repetition frequencies. Furthermore, we find that the extent of this transduction varies with different detuning values. The lowest phase noise of the beatnote reaches -101 dBc/Hz at a 10 kHz offset and decreases to -143 dBc/Hz at a 1 MHz offset.

To quantify the transduction factor more precisely, we apply phase modulations to the pump laser, generating artificial spurs in the phase noise spectra. Given that the thermo-optic effect56, pyroelectric-electro-optic effect57, and photorefraction9 can contribute to the discrepancy between the detuning noise and the pump noise, the phase modulation is set to 100 kHz to exceed the bandwidths of these effects. By comparing the spur levels at 100 kHz (inset of Fig. 4d), we estimate that the transduction factor can reach as high as −43 dB. Additionally, we observe another spur at 117 kHz, which is identified as originating from the relative intensity noise (RIN) of the pump laser. By matching the peak levels, we determine that the contribution of the pump RIN to the microwave phase noise is not the dominant limiting factor (see “Methods”).

Discussion

The demonstration of dark pulse microcombs in LiNbO3 microresonators offers several advantages. First, realizing anomalous GVD at visible wavelengths is challenging for LiNbO3, but dark pulse microcombs are compatible with the entire transparency window of LiNbO3. This flexibility could drive the development of compact optical clocks3, astronomical spectrometers24,25, and other interdisciplinary applications58. Additionally, integrating dark pulse microcombs into LiNbO3-based transmitters could leverage the high-power comb lines, offering excellent signal-to-noise ratios for massively parallel data transmission44,45,46.

Future work is poised to equip Kerr microcombs with Pockels effect9,17,19,59. In this regard, the next step is to apply dissipation engineering to X-cut LiNbO3 microresonators for comb generation. Despite the much stronger Raman response of TE-polarized extraordinary light in this platform, unlocking mode-locked Kerr microcombs in X-cut LiNbO3 allows for integration with highly efficient electro-optic modulators60 and frequency doublers61 through planar fabrication processes in foundries. It should also open avenues for exploring the interplay between Kerr and Pockels effects in the comb-forming regime62,63.

Methods

Device fabrication

Devices are fabricated from a commercial Z-cut LiNbO3-on-insulator wafer (NANOLN) with a 570-nm-thick LiNbO3 layer on top of a 4.7-μm-thick silica buffer layer. Electron-beam lithography is used to define the patterns of bus waveguides and microrings in ma-N 2405 resist with a thickness of 750 nm. The resist pattern is transferred to the LiNbO3 film using Ar+ plasma with an etching depth of 300 nm. The etching process yields a characteristic 60∘ angle of the sidewalls. The photoresist is removed by organic reagent and oxygen plasma. Finally, the redeposition on the surface of the sample is removed using SC1 solution.

Numerical simulations

The generalized Lugiato-Lefever equation (g-LLE), augmented with SRS and wavelength-dependent losses, provides a framework for simulating the evolution of intracavity optical fields5,64,65,66. This equation is expressed as

$$\frac{\partial A(\phi,t)}{\partial t}= -i\delta \omega A-{{{{\mathcal{F}}}}}^{-1}\left\{\frac{\kappa (\mu )}{2}{\tilde{A}}_{\mu }\right\}+\sqrt{\frac{{\kappa }_{{{{\rm{ext}}}}}(0){P}_{{{{\rm{in}}}}}}{\hslash {\omega }_{0}}}\\ \,+\, i\frac{{D}_{2}}{2}\frac{{\partial }^{2}A}{\partial {\phi }^{2}}+i(1-{f}_{R}){g}_{K}| A{| }^{2}A\\ \,+\, i{g}_{K}\frac{{f}_{R}A}{{D}_{1}}\int{h}_{R}\left(\frac{\phi -{\phi }^{{\prime} }}{{D}_{1}}\right)| A({\phi }^{{\prime} }){| }^{2}d{\phi }^{{\prime} }.$$
(3)

The slowly-varying field envelope A(ϕ, t) is normalized to photon number and studied in the rotation frame which rotates around the microresonator at the rate D1. \({\tilde{A}}_{\mu }\) is the optical field of the μth mode, which is defined as \(A(\phi,t)={\sum }_{\mu }{\tilde{A}}_{\mu }{e}^{i\mu \phi }\). δω is the frequency detuning of the pump laser relative to the mode. The pump power is denoted by Pin. The Kerr nonlinear coefficient is defined as \({g}_{K}=\hslash {\omega }_{0}^{2}{n}_{2}{D}_{1}/2\pi {n}_{o}{A}_{{{{\rm{eff}}}}}\), where no and n2 are the linear and nonlinear refractive indices, respectively. Aeff is the nonlinear effective mode area. The total optical dissipation of the μth mode, κ(μ) = κo(μ) + κext(μ), accounts for both intrinsic (κo(μ)) and external coupling (κext(μ)) losses. The wavelength-dependent loss term is implemented in the frequency domain for convenience, with \({{{{\mathcal{F}}}}}^{-1}\{\cdot \}\) representing the inverse Fourier transform. In Fig. 1, the normalized detuning is defined as ζ = 2δω/κ(0) and the normalized pump power is defined as ∣f∣2 = 8gKκext(0)Pin/κ3(0)ℏω0.

LiNbO3 has several vibrational modes as shown in Fig. S7 (see SI). For simplicity but without loss of generality, in the simulation, we only include the mode with the strongest Raman response, A(TO)4. The fractional contribution of Raman response to the total nonlinear polarization is denoted by fR. The Raman response is formulated as a convolution product of the Raman response function and the temporal intracavity optical intensity. A standard form of the Raman response function for a single vibrational mode, hR(t), is given by64,66

$${h}_{R}(t)=\left\{\begin{array}{ll}\frac{{\tau }_{1}^{2}+{\tau }_{2}^{2}}{{\tau }_{1}{\tau }_{2}^{2}}\exp \left(-\frac{t}{{\tau }_{2}}\right)\sin \left(\frac{t}{{\tau }_{1}}\right)\quad &,t \, > \, 0\\ 0\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad &,t \, \le \, 0\end{array}\right.,$$
(4)

where τ1 and τ2 are the time constants characterizing the Raman response. Note that the Raman response function is only defined for t > 0 for the reason of causality.

Numerical simulation of the g-LLE is performed using the split-step Fourier method, which involves 4096 modes. The parameters used to simulate the intracavity waveforms in Fig. 3d are: D1/2π = 24.8 GHz, D2/2π = −6.2 kHz, no = 2.0, n2 = 1.8 × 10−19 m2/W, Aeff = 1.135 μm2, ω0/2π = 191.9 THz, κ(μ)/2π  =  ( − 1.3 × 10−9μ4 + 1.0227 × 10−6μ3 + 2.5846 × 10−3μ2  − 0.49141μ + 70.747) MHz, fR = 0.19, τ1 = 8.3 fs, τ2 = 544 fs49,50,67,68. The detuning I is set δω1/2π = 364 MHz and the detuning II is set δω2/2π = 400 MHz.

Laser noise measurement

The phase noise of the pump laser is measured using a delayed self-heterodyne setup. In this configuration, the laser beam is split into two paths: one path is frequency-shifted by 55 MHz via an acousto-optic modulator, while the other is delayed through a 1-km-long optical fiber. The recombined light is photodetected, and the resulting beatnote is analyzed with a phase noise analyzer to extract its single-sideband phase noise, SB(f). The laser’s phase noise, Sϕ(f), is then derived using the following equation54:

$${S}_{\phi }(f)={S}_{B}(f)\frac{1}{4{\sin }^{2}(\pi f{\tau }_{d})}.$$
(5)

Here, τd represents the time delay between the two arms of the interferometer, which is 4.8821 μs in this work. To prevent divergence at offset frequencies where \(\sin (\pi f{\tau }_{d})=0\), a cut-off frequency is introduced as 1/τd. Beyond this threshold, only data points corresponding to offset frequencies of (N + 1/2)/τd, where N is a positive integer, are plotted to ensure the accurate representation of the phase noise data.

The RIN of the pump laser is measured using a non-amplified photodetector (Thorlabs DET01CFC/M) in conjunction with a phase noise analyzer operating in baseband measurement mode. The contribution of the laser’s RIN, SI(f), to the microwave phase noise is quantified by the expression αSI(f)/f2, where α represents the noise transduction factor.