Octave-spanning dissipative Kerr soliton frequency combs in Si₃N₄ microresonators

1. INTRODUCTION

Optical frequency combs with coherent optical bandwidths of one octave or more are required for many applications, such as precision spectroscopy [1], optical frequency synthesis [2], or astrophysical spectrometer calibration [3]. Conventionally, these spectra are synthesized by nonlinear spectral broadening of a pulsed laser [1]. However, ensuring coherent spectral broadening, a smooth spectral envelope, and sufficient power in the spectral ends for a given pulse source can be challenging, in particular, for high-repetition-rate pulse sources. Kerr frequency combs [4] have emerged as an alternative scheme, which enables compact form factors, high repetition rates, and broadband optical frequency combs, which are even amenable to wafer-scale integration with additional electrical or optical functionality. The spectral bandwidth of Kerr frequency combs, being independent of a specific material gain and primarily determined by the resonator’s group velocity dispersion (GVD), has reached octave span shortly after the principle’s first demonstration [5,6], although in the high-noise operation regime [7]. Only recently has the observation of dissipative Kerr soliton (DKS) formation in microresonators enabled the controlled excitation of fully coherent Kerr frequency combs [8].

When operated in the single-soliton state, DKS frequency combs feature high coherence across their bandwidths and a smooth spectral envelope, which can be numerically predicted with high accuracy using the Lugiato–Lefever equation or in the frequency domain via coupled-mode approaches [8–10]. Furthermore, higher-order GVD causes soliton Cherenkov radiation, an oscillatory tail in the temporal soliton pulse profile, corresponding to a dispersive wave (DW) in the spectral domain, which extends the spectral comb bandwidth into the normal GVD regime [11]. Soliton Cherenkov radiation in microresonators is a fully coherent process and has, e.g., allowed self-referencing and stabilization without additional spectral broadening via the $2f–3f$ method [12]. These properties have made DKS states the preferred operational low-noise states [7,13,14] of Kerr frequency comb generation with a growing number of applications having been demonstrated, including, e.g., terabit coherent communications [15], dual-comb spectroscopy [16,17], and low-noise microwave generation [18]. So far, DKS formation has been observed in a variety of resonator platforms [8,18–23] among which planar silicon nitride (${\mathrm{Si}}_3{\mathrm{N}}_4$) waveguide resonators have gained significant attention. Allowing CMOS-compatible wafer-scale fabrication and exhibiting low linear and nonlinear optical losses in the telecom wavelength region, ${\mathrm{Si}}_3{\mathrm{N}}_4$ microresonators bear realistic potential for applications [24]. The accurate control of waveguide dimensions during microfabrication is a prerequisite to precise GVD engineering and thus tailoring of the Kerr frequency comb bandwidth [10]. Dual-dispersive-wave emission, which extends the spectral bandwidth to both sides, is attractive for low-power octave-spanning DKS generation, but is particularly challenging to realize as it requires control of higher-order GVD. Most microresonators used for DKS generation to date, except those in references [19,25], did not have specifically engineered GVD, resulting in a limited spectral bandwidth, well below one octave.

Here we present ${\mathrm{Si}}_3{\mathrm{N}}_4$ microresonators with a free spectral range (FSR) of 1 THz, which allow DKS frequency comb generation with bandwidths exceeding one octave. The wide FSR reduces the total power requirements to cover a bandwidth of one octave and benefits the nonlinear conversion efficiency in the DKS state [26]. Such microresonators are thus also of interest for wavelength regions where no high-power pump sources exist. We use the recently developed photonic Damascene process [27] for wafer-scale fabrication of such high-$Q$ microresonator devices with high yield. Figure 1(a) shows a scanning electron microscope (SEM) picture of the microresonator device including a straight bus waveguide. For small microresonator radii ($r\approx 23\mathrm{\mu m}$), the coupling section forms a relatively large fraction of the total circumference and can cause parasitic loss. Thus, void-free fabrication of narrow coupling gaps, as provided by the photonic Damascene process, is important. Moreover, the cross section of the bus waveguide needs to be engineered for high-ideality coupling [28]. The fundamental mode families of the microresonator devices used in this work have a typical internal linewidth of ${\kappa }_0/2\pi =150\mathrm{MHz}$ and thus a loaded finesse of $\mathcal{F}\approx {10}^4$ at critical coupling. As shown in Supplement 1, the wavelength dependency of the coupling rate ${\kappa }_{\mathrm{ex}}$ is significant over the operation bandwidth of the devices, causing increased coupling rate at longer wavelengths.

 

Fig. 1. Octave-spanning dissipative Kerr soliton frequency comb generation in a dispersion-engineered ${\mathrm{Si}}_3{\mathrm{N}}_4$ microresonator. (a) SEM image of a ${\mathrm{Si}}_3{\mathrm{N}}_4$ microresonator with a 1 THz FSR during fabrication. The waveguide structures are highlighted in blue. (b) Simulated temporal intracavity power profile of an octave-spanning DKS frequency comb excited with 75 mW pump power for $\kappa /2\pi =200\mathrm{MHz}$ using the Lugiato–Lefever equation. The two DWs form an overlapping trailing and leading wave pattern. (c) The corresponding spectral intracavity power distribution (blue) and the integrated dispersion profile $D_{\text{int}}/2\pi (\mathrm{red})$ engineered for DW emission around 1 μm and 2 μm wavelengths.

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While a high microresonator finesse is beneficial to lowering the power threshold of Kerr comb generation, the microresonator GVD mostly determines the power requirements to reach a certain spectral bandwidth. Microresonator GVD is conveniently expressed in its integrated form around a central pump frequency ${\omega }_0$, using the relative mode numbers ${\mu }_{\mathrm{r}}=\mu -{\mu }_0$:

We design the microresonator waveguide cross section based on finite-element method (FEM) simulations of the resonator’s ${\mathrm{TE}}_{00}$ mode family dispersion. DW formation is engineered to occur around wavelengths of 1 μm and 2 μm spanning an octave bandwidth around the pump laser at 1.3 μm or 1.55 μm. Supplement 1 shows a comparison of octave-spanning DKS generation for both pump wavelengths. Full-3D finite-difference time-domain simulations are employed to engineer the bus waveguide cross section for high-ideality coupling to the ${\mathrm{TE}}_{00}$ mode family [28]. Next, we simulate the octave-spanning DKS generation using a Lugiato–Lefever model [9,30] for a critically coupled ${\mathrm{Si}}_3{\mathrm{N}}_4$ microresonator with a linewidth of $\kappa /2\pi =200\mathrm{MHz}$ driven by a pump laser of 75 mW power. Figures 1(b) and 1(c) show, respectively, the intracavity field and spectral envelope of the simulated single-DKS state. As can be seen, the two DWs are present in the temporal intracavity field as trailing and following wave patterns, which fill the complete cavity. Furthermore, close examination reveals that the position of the higher-frequency DW is slightly offset from the linear phase-matching point, indicating the approximative nature of the criterion $D_{\mathrm{int}}(\mu )=0$.

In the following text, we first discuss the challenges of precise waveguide dimension control using the photonic Damascene process. Leveraging optimized fabrication procedures, we achieve control over the DW positions resulting in octave-spanning comb generation based on 1.3 μm and 1.55 μm pump lasers. The coherence of the generated Kerr frequency combs is studied and a response measurement is used to unambiguously identify DKS formation. Finally, we study octave-spanning single DKS formation for 1.3 μm and 1.55 μm pump wavelengths featuring the broadest Kerr soliton frequency comb generated to date, exceeding 200 THz in bandwidth.

2. PRECISION DISPERSION ENGINEERING USING THE PHOTONIC DAMASCENE PROCESS

Dispersion engineering for octave-spanning Kerr frequency comb generation requires stringent waveguide width and height control of the order of 10 nm, which is challenging to meet. As detailed below via simulations (shown in Fig. 3), especially the position of the DW features is very sensitive to variations of the waveguide dimensions. Although DKS frequency comb generators have been fabricated using conventional subtractive processing, several challenges arise for the fabrication of high-confinement ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides for nonlinear applications. In particular, these are cracking of the highly stressed ${\mathrm{Si}}_3{\mathrm{N}}_4$ thin film and void formation at the microresonator coupling gap [27]. The recently reported photonic Damascene process, employed in the present work, solves these problems by depositing the ${\mathrm{Si}}_3{\mathrm{N}}_4$ thin film on a prestructured substrate and subsequent removal of the excess material using chemical mechanical planarization (CMP). A dense filler pattern surrounding the waveguide structures effectively lowers the thin film’s tensile stress and enables crack-free fabrication even for micrometer-thick waveguides. Moreover, the filler pattern helps to control and unify the material removal rate across the wafer during CMP.

Although the level of control on the waveguide width is similar for the Damascene and subtractive processing schemes (both relying on the precision of lithography and etching processes), the waveguide height control is substantially eased in the subtractive fabrication scheme: a typical thin-film deposition non-uniformity of 3% across a $4^{\prime \prime }$ wafer results in a maximal 25 nm height deviation for 800 nm thick ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides. For the Damascene process, the variation of the final waveguide thickness depends on the uniformity of the dry etch process used to structure the waveguide trenches and, most importantly, on the uniformity of the CMP process. While optical interferometry can give precise local information on the removal rate during CMP, especially the wafer bow and the local loading lead to height variations [see Fig. 2(a)]. This reduces the yield of devices with dimensions within the tolerance range for octave-spanning Kerr comb generation and causes uncontrolled spectral positions of the DWs.

 

Fig. 2. Origins of non-uniform planarization in the photonic Damascene process. (a) Schematic representation of wafer bow and local loading causing non-uniformity during CMP. (b) Measurement of wafer bow evolution during planarization for a 525 μm thick $4^{\prime \prime }$ wafer with an $\sim 1\mathrm{\mu m}$ thick ${\mathrm{Si}}_3{\mathrm{N}}_4$ thin film. (c) Photograph of a $4^{\prime \prime }$ wafer after planarization showing non-uniformity through colored interference patterns. (d) Optical microscope image of a 1 THz FSR microresonator surrounded by a ”checkerboard” filler pattern. The ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides are highlighted in blue. (e) SEM image of a non-uniformly planarized bus waveguide (indicated in blue). The neighboring filler pattern patches have different loading and thus cause more ${\mathrm{Si}}_3{\mathrm{N}}_4$ (dark-shaded areas) to remain over the bus waveguide in certain areas. (f) Cross section of the bus waveguide used to couple light in a microresonator with a 1 THz FSR. The dimensions ($0.5\mathrm{\mu m}\times 0.67\mathrm{\mu m}$) are chosen to provide high-ideality coupling to the microresonator’s fundamental ${\mathrm{TE}}_{00}$ mode family. (g) Optical microscope image of waveguide structures surrounded by an optimized filler pattern.

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Figure 2(b) shows the bow evolution of a 525 μm thick $4^{\prime \prime }$ wafer during planarization measured using a thin-film stress measurement tool. After deposition, the continuous ${\mathrm{Si}}_3{\mathrm{N}}_4$ film on the wafer backside causes a positive deflection as its tensile stress is higher than the stress on the wafer’s front side, which is reduced by the prestructured surface. The removal of the backside ${\mathrm{Si}}_3{\mathrm{N}}_4$ prior to CMP inverts the bow to more than $-90\mathrm{\mu m}$. The subsequent planarization step removes the excess ${\mathrm{Si}}_3{\mathrm{N}}_4$ on the front side and continuously relaxes the wafer bow. This bow variation leads to non-uniformity with radial symmetry visible as a colored interference ring pattern in Fig. 2(c). Furthermore, local non-uniformity in the central wafer region can also be observed, which originates from different removal rates due to loading variations. Loading here refers to the amount of excess ${\mathrm{Si}}_3{\mathrm{N}}_4$ that is in direct contact with the polishing pad and depends on the local structure density. Such local variations can also occur on much smaller scales. This is exemplified in Fig. 2(e) for an area around a bus waveguide (indicated in blue) after CMP. Depending on the loading of the neighboring filler pattern, more or less ${\mathrm{Si}}_3{\mathrm{N}}_4$ (darker shaded area) remains above the silicon dioxide (${\mathrm{SiO}}_2$) preform (lighter shaded area). Such loading-dependent non-uniformity leads to local variations of the waveguide height, and therefore needs to be minimized. Finally, during landing, when most excess ${\mathrm{Si}}_3{\mathrm{N}}_4$ is removed and mostly the ${\mathrm{SiO}}_2$ preform is in contact with the polishing pad, the material removal rate can drastically change. Thus, the polishing endpoint is hard to predict and the overall mean waveguide height differs from the target value.

Compared with the results presented in Ref. [27], we apply here an optimized planarization process that enables attaining the required precision. First, a thicker wafer substrate (700 μm instead of 525 μm) is used to reduce the amount of initial wafer bow to $-50\mathrm{\mu m}$. Next, an optimized CMP process pressing the wafer significantly stronger to the polishing pad, equalizes the wafer bow and reduces its effects during planarization. The removal rates for ${\mathrm{Si}}_3{\mathrm{N}}_4$ and ${\mathrm{SiO}}_2$ are chosen to be similar, limiting the uncertainty during landing. In order to reduce local loading effects, a novel filler pattern geometry [see Fig. 2(g)] is used, which homogenizes the loading while providing sufficient stress release for crack-free fabrication. The dispersion control achieved using this optimized CMP process is summarized in Fig. 3 by comparing the frequency comb spectra generated in different waveguide geometries to the simulated dispersion. Based on FEM simulations of microresonator GVD shown in Fig. 3(a), the target waveguide height of 0.74 μm was chosen to enable octave-spanning DKS frequency comb generation in the resonator’s ${\mathrm{TE}}_{00}$ mode family for a 1.3 μm pump laser. The simulation predicts DW formation around 1 μm and 2 μm for a 1.425 μm wide, fully ${\mathrm{SiO}}_2$-cladded waveguide with a sidewall angle of 82°. As shown in Fig. 3(a), a waveguide height deviation of only 10 nm causes a shift of the low-frequency DW position by 5 THz (i.e., ca. $\mathrm{\Delta }\lambda =75\mathrm{nm}$ in wavelength). A change in the waveguide width does not strongly influence the position of the low-frequency DW, but changes the position of the high-frequency DW.

 

Fig. 3. Wafer-scale dispersion engineering of octave-spanning Kerr frequency combs. (a) Simulated integrated dispersion $D_{\text{int}}(\nu )/2\pi$ of fully cladded ${\mathrm{Si}}_3{\mathrm{N}}_4$ microresonators with 82° sidewall angle and different widths and heights for generating dual-dispersive-wave DKS states. For a pump wavelength of 1.3 μm, DWs can be excited at positions close to the zero points of the integrated dispersion. (b) High-noise Kerr frequency combs generated in three different samples fabricated on the same wafer at different positions, which are indicated in the inset. The spectral position of the two dispersive waves are indicated by gray arrows. The samples have by design a difference of 50 nm in waveguide width, which enables tuning of the position of the high-frequency DW position, demonstrating the dimension control of the Damascene process.

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The dispersion of different samples is evaluated based on the spectral envelopes of the generated frequency combs. The low values of microresonator GVD (i.e., $D_2/2\pi \sim 20\mathrm{MHz}$), the strong avoided modal crossings, and the bandwidth limitations of our precision diode laser spectroscopy setup [31] did not allow measuring higher-order dispersion terms and thus to extrapolate the DW positions. Figure 4(a) shows the setup used for DKS frequency comb generation. A 1.3 μm external-cavity diode laser (ECDL) is amplified using a tapered semiconductor amplifier (SOA) to a maximum power of 0.75 W. Laser light is coupled into the photonic chip using lensed fibers and inverse tapered waveguides with $\sim 3\mathrm{dB}$ loss per facet. During the laser tuning into the ${\mathrm{TE}}_{00}$ mode family resonance, the transmission through the device as well as the generated comb light are recorded using photodiodes ($f_{3\mathrm{dB}}\approx 1\mathrm{GHz}$). Up to three optical spectrum analyzers (OSAs) are used to capture the generated broadband comb spectra. Figure 3(b) shows octave-spanning high-noise comb states excited in three different microresonator chips. The sample position on the $4^{\prime \prime }$ wafer is provided as an inset. As can be seen, the position variation of the low-frequency DW for the three samples is 5.5 THz around the designed target value of 150 THz. In comparison with the simulations in Fig. 3(a), this indicates a variation of less than $\pm 10\mathrm{nm}$ in waveguide height around the target value of 0.74 μm. Moreover, the width variation allows tuning the position of the high-frequency DW. A waveguide width reduction of 50 nm in the design moves the position of the high-frequency DW by $\sim 25\mathrm{THz}$, in good agreement with the simulations. We measured the quadratic dispersion $D_2/2\pi$ to be (from top to bottom) 7.08 MHz, 14.15 MHz, and 37.2 MHz. These measurements reveal dimensional control sufficient to tune the DW position for devices from large areas of the wafer. The photonic Damascene process with an optimized planarization step thus offers sufficient precision in the control over waveguide dimensions to allow wafer-scale fabrication of microresonators with engineered dispersion properties over a full octave of bandwidth.

 

Fig. 4. Distinction of octave-spanning multisoliton states and non-solitonic states. (a) Schematic of the setup used to generate octave-spanning Kerr combs using 1.3 μm or 1.55 μm pump lasers. In both cases, an arbitrary waveform generator (AFG) provides the voltage ramp to tune the external-cavity diode seed laser (ECDL) into a resonance of the device under test (DUT). Either an EDFA or a SOA is used to amplify the seed laser before coupling onto the photonic chip using lensed fibers. An oscilloscope (OSC) records the transmitted and converted comb light power during the scan. Several OSAs are used to capture the full spectra of the excited comb state. A 1064 nm fiber laser allows the recording of heterodyne beat notes using a fast photodiode and an ESA. The comb state response is measured with a VNA, which drives an EOM and receives part of the transmitted light on a photodiode with a bandwidth of 25 GHz. (b) Highly structured octave-spanning comb state excited by tuning the 1.3 μm pump laser into the step-like feature (which, importantly, does not originate from soliton formation) highlighted in (d) with gray arrows. The red boxes mark comb teeth, which reveal a splitting of $\sim 8\mathrm{GHz}$ upon close examination in (c), demonstrating subcomb formation. (d) Oscilloscope trace of the voltage ramp (blue), the generated comb light (green), and the transmitted light signal (red). (e) Narrow heterodyne beat note of a 1064 nm fiber laser, with the comb tooth marked with a green arrow in (b) of a non-solitonic comb state. (f) Three comb states excited in three different microresonators with the same waveguide dimensions. (g) Response measurements associated with the comb states in (f). The positions of the cavity ($\mathcal{C}$-res.) and the soliton ($\mathcal{S}$-res.) resonance are indicated.

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3. COHERENCE AND SOLITON IDENTIFICATION

For applications of the octave-spanning Kerr comb state, coherence is a key requirement. Common methods to classify the coherence of Kerr comb states are measurements of the low-frequency amplitude noise of the generated comb light, the repetition rate beat note, as well as heterodyne beat notes with reference lasers [7]. Among different low-noise comb states [7,13,14], the DKS state is particularly attractive as it provides high coherence across its entire bandwidth. Soliton Kerr comb states have in particular been identified via characteristic abrupt changes in the transmitted light (”steps”), via the red-detuned nature of the pump laser, as well as the characteristic soliton spectral envelope. Although the spectra contain no direct information on coherence, for microresonators with dominant (positive) quadratic dispersion $D_2$, the single-soliton state exhibits a characteristic spectral ${\mathrm{sech}}^2$ envelope. For broadband Kerr combs, the spectral envelope can exhibit DWs, due to higher-order microresonator dispersion. Although DW features are also present in the high-noise-state spectra, in the DKS state their width reduces with a simultaneous increase in the individual comb tooth power and a shift of the DW maximum [19]. Other spectral signatures of the DKS regime include the soliton Raman self-frequency shift, which leads to a red shift of the soliton’s ${\mathrm{sech}}^2$ envelope with respect to the pump [32]. The Raman self-frequency shift is absent in the high-noise comb state, but can be masked in the DKS state by the soliton recoil due to DW formation. Single-DKS states are usually clearly distinguished from their incoherent counterparts, whereas multi-DKS state identification purely based on the spectral envelope is unreliable. For octave-spanning soliton Kerr combs with THz mode spacing and DW emission due to microresonator GVD and avoided modal crossings [33], sharp spectral features can also be observed for non-solitonic comb states.

In contrast, a recently introduced response measurement technique [34] allows to unambiguously identify DKS comb states, and is applied here for the first time to octave-spanning soliton states. Figure 4(a) shows the setup used to investigate the coherence of comb states generated with a 1.3 μm and a 1.55 μm ECDL. The 1.55 μm ECDL is amplified using an erbium-doped fiber amplifier (EDFA), and in order to perform the response measurement, a phase modulator with a bandwidth of 10 GHz is added before the amplifier. A vector network analyzer (VNA), probing the Kerr comb state’s response, drives the electro-optic phase modulator (EOM) and receives the signal via a photodiode with a bandwidth of 25 GHz. We note that this measurement was only possible using the 1.55 μm pump laser due to lack of an appropriate phase modulator for the 1.3 μm pump path. A heterodyne beat note of the comb with a fiber laser at 1064 nm is recorded using an electrical spectrum analyzer (ESA). All presented Kerr frequency comb states are excited using a simple laser tuning method, applying a linear voltage ramp provided by an arbitrary function generator (AFG) to controllably tune into a comb state [8,34].

DKS formation is accompanied by characteristic step features that occur simultaneously in the generated comb and transmitted light trace [8]. However, in the experiments reported here in Figs. 4(b)–4(d), we found that abrupt changes in the transmitted power do not necessarily originate from soliton formation. Instead, abrupt changes between different non-solitonic comb states, as well as resonance splitting due to waveguide surface roughness or near-by resonances of other mode families, can cause similar features. Figure 4(b) shows the optical spectrum of a comb state generated by tuning the 1.3 μm pump laser with $P_{\mathrm{bus}}=125\mathrm{mW}$ in the bus waveguide into the step feature visible for the generated light trace in Fig. 4(d). We note that the abrupt change in comb state is best visible in the generated light trace, resulting in only a small discontinuity in the transmitted light intensity. The spectrum spans an octave and is highly structured, featuring individual sharp lines at the DW positions. Moreover, the beat note of an individual comb tooth with a fiber laser at 1064 nm [see Fig. 4(e)] shows low-noise characteristics, i.e., $>20\mathrm{dB}$ signal-to-noise ratio in a 100 kHz resolution bandwidth. Based on these measurements, the generated comb state would agree with properties associated with a multisoliton state. However, close examination of the generated spectral lines, shown in Fig. 4(c), reveals that certain comb lines have a splitting of $\sim 8\mathrm{GHz}$, incompatible with a DKS comb state and associated with merging of individual subcombs [7]. Importantly, commonly employed [7,25] low-frequency amplitude noise measurements, and even local heterodyne beat-note measurements, are insufficient discriminators, unless they are performed over a sufficiently wide bandwidth to detect the subcomb spacing (here $\gg 1\mathrm{GHz}$). Indeed, for the measurements above, no noise $<1\mathrm{GHz}$ is observed, which would lead to an erroneous soliton state identification.

A more reliable method is using the response of the comb state to a phase modulation of the pump laser. It was shown that the phase modulation response function of DKS states consists of two characteristic resonances originating from the circulating soliton pulses ($\mathcal{S}$ resonance) and the cavity response ($\mathcal{C}$ resonance) [34,35]. Furthermore, the measurement allows inferring the effective pump laser detuning within the DKS state, an important quantity determining the soliton properties. Figure 4(f) shows three comb states recorded from three microresonators on the same photonic chip with the same waveguide dimensions but varying bus–resonator distances. Again, the microresonator dispersion was designed for DW emission around 1 μm and 2 μm, here upon pumping with a 1.55 μm laser. The measured quadratic dispersion is $D_2/2\pi =7.2\mathrm{MHz}$ and all microresonators are overcoupled (${\kappa }_{\mathrm{tot}}/2\pi \approx 1\mathrm{GHz}$). The observed asymmetry in DW power agrees well with the simulations shown in Supplement 1. We excite different comb states and analyze their corresponding response functions as shown in Fig. 4(g). State (i) is a high-noise state and the response function exhibits a single peak and a non-zero background noise at high frequencies. State (ii) has a much more structured spectral envelope and a seemingly sharp DW feature compared with state (i). However, the response measurement reveals a fundamentally different response than expected for a DKS state. Also, state (iii) has a strongly structured spectral envelope with similarities to the envelope of state (ii), but its response function shows two overlapping resonances. The lower-frequency $\mathcal{S}$ resonance originates from the circulating soliton pulses and has a reduced amplitude compared with the cavity $\mathcal{C}$ resonance at a higher frequency, whose frequency indicates the detuning. Moreover, the separation of both peaks diminishes upon laser blue detuning and increases for red detuning. We thus identify state (iii) as a multisoliton state. The multisoliton state leads to an increased conversion efficiency compared with the single-soliton case, resulting in negligible residual pump power in the present case. Moreover, we observe a notable shift of the high-frequency DW peak position (indicated by gray arrows).

4. OCTAVE-SPANNING SPECTRA VIA SINGLE SOLITON GENERATION

Once excited, a multisoliton state can often be converted into a single-soliton state by soliton switching upon “backward tuning” of the pump laser [34]. Figure 5 shows two examples of octave-spanning single soliton generation obtained via this technique using 1.3 μm or 1.55 μm pump lasers. We note that not all multisoliton states excited were observed to switch to a lower soliton number upon backward tuning, but some changed into non-solitonic states. Moreover, it is observed that both single-soliton combs are excited in direct vicinity of an avoided modal crossing causing strong local deviations from the characteristic ${\mathrm{sech}}^2$-shaped spectral envelope. The associated local dispersion variations and its negative influence on soliton formation [36] are mitigated by the large cavity linewidths of $\sim 1\mathrm{GHz}$ due to the overcoupled operation of the microresonators (see Supplement 1). We note that a recent work [25] has observed a positive effect of modal crossings on soliton formation, which is explained through an advantageous thermal behavior, as well as DW formation via avoided modal crossings [33].

 

Fig. 5. Octave-spanning single soliton generation at 1.55 μm and 1.3 μm pump wavelengths. (a) The same single DKS state shown for two different pump laser powers and cavity detunings. Inset: response measurement of the single DKS states shown in (a) revealing the respective pump laser cavity detuning. The $\mathcal{S}$ and $\mathcal{C}$ resonances are separated by $\sim 2.5\mathrm{GHz}$ and $\sim 5\mathrm{GHz}$, respectively. (b) Single DKS spanning 200 THz in optical bandwidth with a DW at 850 nm excited using a 1.3 μm pump laser. Fits of both states with a spectral ${\mathrm{sech}}^2$ envelope are shown in red. The pump powers in the bus waveguide and fitted spectral bandwidths are noted.

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The soliton spectrum shown in Fig. 5(a) features no DWs, indicating a dominant quadratic factor of the anomalous GVD. Indeed a measurement reveals that $D_2/2\pi =49.7\mathrm{MHz}$, significantly stronger than the values found for the microresonators above, which generate two DWs. The response measurement shown in the inset shows a double-resonance signature and reveals a cavity detuning of $\sim 4.5\mathrm{GHz}$. The pump power is increased to 455 mW in the bus waveguide while maintaining the single-DKS state, which allows a larger soliton existence range and octave bandwidth at a cavity detuning of $\sim 7\mathrm{GHz}$. This cavity detuning is significantly higher than previously published values for ${\mathrm{Si}}_3{\mathrm{N}}_4$ microresonators, indicating a strong nonlinear phase shift due to the high peak intensity of the soliton pulse [34]. The spectral envelope is fitted using a ${\mathrm{sech}}^2$ shape and a 3 dB bandwidth of 24.85 THz is extracted, corresponding to a 12.7 fs pulse. In Fig. 5(b), we present the broadest single-DKS comb state published to date, to the best of our knowledge. The DKS comb spans a total bandwidth of $\sim 200\mathrm{THz}$, more than double the bandwidth in [19] and 1.5 times the bandwidth in [25], using a pump laser at 1.3 μm providing only 245 mW power in the bus waveguide. The fitted 3 dB bandwidth of 19.9 THz is similar to the value of the single-DKS state shown in Fig. 5(a), even though the required pump power is significantly lower. We note that the quadratic dispersion of this sample could not be faithfully determined due to the strong modal crossing close to the pump mode. These results demonstrate the strong influence of dispersion on the power requirements for broadband comb generation and underlines the necessity for precise dispersion control.

5. CONCLUSION

In conclusion, we have demonstrated DKS generation in ${\mathrm{Si}}_3{\mathrm{N}}_4$ microresonators with a FSR of 1 THz and spectral bandwidths exceeding one octave, at both 1.55 μm and 1.3 μm pump wavelengths. The photonic Damascene process with the optimized planarization step allows high yield wafer-scale fabrication of microresonators with precisely controlled DW positions. Our work moreover revealed that for comb states generated in ${\mathrm{Si}}_3{\mathrm{N}}_4$ microresonators, conventional criteria of coherence can fail. We carefully investigated the coherence of the generated comb states and unambiguously identified octave-spanning multi-DKS states based on their unique phase modulation response signatures. Finally, we demonstrated single soliton generation with a record bandwidth of 200 THz generated with only 245 mW of pump power.

Our findings demonstrate the technological readiness of the photonic Damascene process and integrated ${\mathrm{Si}}_3{\mathrm{N}}_4$ frequency comb generators for a wide range of applications. The ability to generate ultrashort pulses also with a 1.3 μm pump laser, as demonstrated here, opens up applications in biological and medical imaging as this wavelength represents a compromise between low tissue scattering and absorption due to water. Moreover, such DKS frequency combs with designed spectral envelopes may in the future enable chip integration and miniaturization of self-referenced frequency combs [37] and dual-comb coherent anti-Stokes Raman scattering [38].

Data availability. The code and data used to produce the plots within this paper are available at [39]. All other data used in this study are available from the corresponding authors upon reasonable request.