# Efficient Raman lasing and Raman-Kerr interaction in an integrated silicon
carbide platform

Jingwei Li1  Ruixuan Wang1  Adnan A. Afridi2  Yaoqin Lu2  Xiaodong Shi2
Wenhan Sun1  Haiyan Ou2  and Qing Li1  1Department of Electrical and Computer
Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA  2 DTU
Electro, Technical University of Denmark, DK-2800 KGS. Lyngby, Denmark  \+
These authors contributed equally to this work<EMAIL_ADDRESS>
# Supplementary Material

Jingwei Li1  Ruixuan Wang1  Adnan A. Afridi2  Yaoqin Lu2  Xiaodong Shi2
Wenhan Sun1  Haiyan Ou2  and Qing Li1  1Department of Electrical and Computer
Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA  2 DTU
Electro, Technical University of Denmark, DK-2800 KGS. Lyngby, Denmark  \+
These authors contributed equally to this work<EMAIL_ADDRESS>
###### Abstract

Implementing stimulated Raman scattering in a low-loss microresonator could
lead to Raman lasing. Here, we report the demonstration of an efficient Raman
laser with $>50\%$ power efficiency in an integrated silicon carbide platform
for the first time. By fine tuning the free spectral range (FSR) of
43-$\mu$m-radius silicon carbide microresonators, the Stokes resonance
corresponding to the dominant Raman shift of $777\ \text{cm}^{-1}$ ($23.3$
THz) is aligned to the center of the Raman gain spectrum, resulting in a low
power threshold of $2.5$ mW. The peak Raman gain coefficient is estimated to
be ($0.75\pm 0.15)\ \text{cm}/\text{GW}$ in the 1550 nm band, with an
approximate full width at half maximum of ($120\pm 30$) GHz. In addition, the
microresonator is designed to exhibit normal dispersion at the pump wavelength
near 1550 nm while possessing anomalous dispersion at the first Stokes near
1760 nm. At high enough input powers, a Kerr microcomb is generated by the
Stokes signal acting as the secondary pump, which then mixes with the pump
laser through four-wave mixing to attain a wider spectral coverage.
Furthermore, cascaded Raman lasing and occurrence of multiple Raman shifts,
including $204\ \text{cm}^{-1}$ ($6.1$ THz) and $266\ \text{cm}^{-1}$ ($8.0$
THz) transitions, are also observed. Finally, we show that the Stokes Raman
could also help broaden the spectrum in a Kerr microcomb which has anomalous
dispersion at the pump wavelength. Our example of a 100-GHz-FSR microcomb has
a wavelength span from 1200 nm to 1900 nm with 300 mW on-chip power.

††journal: osajournal††articletype: article

##  1 Introduction

The ubiquitous Raman effect, in which the incident photons experience
inelastic scattering from the optical phonons of the matter, plays an
important role in a range of applications such as material analysis [1],
sensing [2], optical communication [3, 4, 5, 6, 7], and quantum information
processing [8]. By implementing the stimulated Raman scattering in a low-loss
microresonator, efficient Raman lasing can be achieved when the internal Raman
gain exceeds the round-trip loss, thereby extending the wavelength range of
conventional laser sources. This scheme has been demonstrated in silicon and
silica microresonators with sub-mW power threshold and up to $45\%$ power
efficiency [9, 6]. In the past decade, Raman lasing was also explored in wide-
bandgap integrated photonic platforms such as diamond [10], aluminum nitride
[11], and lithium niobate [12]. While these materials exhibit well-defined
Raman peaks due to their crystalline structure, the reported power threshold
is typically on the order of 10 mW or higher with an external power efficiency
of less than $50\%$ (see Table 1).

Recently, silicon carbide (SiC) emerged as a promising photonic and quantum
material due to its unique properties, including strong Kerr nonlinearity (up
to four times of silicon nitride) and hosting of various intrinsic and
extrinsic color centers with appealing quantum properties [13, 14, 15]. These
features, combined with the demonstration of the low-loss SiC-on-insulator
(SiCOI) platform [16, 17, 18], have resulted in a range of competitive device
applications, including Kerr microcombs [19, 20, 21], gigahertz-level electro-
optic modulators [22], as well as single and entangled photon sources [23, 24,
25]. In 4H-SiC, the dominant Raman transition is around 777 $\text{cm}^{-1}$
(Fig. 1(b)) [26], which in terms of frequency shift ($\approx 23.3$ THz) is
only second to that in diamond (see Table 1). To date, only Raman lasing
corresponding to a frequency shift of $6.1$ THz (204 $\text{cm}^{-1}$) was
reported in 4H-SiC, though the realized power efficiency was well below $1\%$
[18].

In this work, we report the demonstration of an efficient Raman laser in an
integrated 4H-SiCOI platform for the first time. To attain a high Raman
efficiency, we work with over-coupled SiC microresonators with normal
dispersion around the pump wavelength (Fig. 1(c)). To lower the power
threshold, we fabricate SiC microrings with a nominal ring radius of 43
$\mu$m, which is varied by a step of 40 nm to align the Stokes resonance to
the center of the Raman gain spectrum. In such compact microresonators, the
fundamental transverse-electric mode has an intrinsic quality factor ($Q$)
around $3.5$ million and a loaded $Q$ around $1.0$ million at 1550 nm (Fig.
1(d)). At an approximate input power of 10 mW, a strong Raman signal is
observed at a frequency shift of $23.3$ THz away from the pump, displaying an
estimated power efficiency of $51\%$ (Fig. 1(e)). When further increasing the
pump power, a Kerr microcomb resulting from the anomalous dispersion near the
Stokes is produced, which then mixes with the pump laser through four-wave
mixing to reach an even broader spectrum. A detailed study of the Raman-Kerr
interaction is carried out, revealing rich physics for such a compact
nonlinear system.

Figure 1: (a) Energy diagram of the Stokes Raman process: $\omega_{p}$, $\omega_{s}$ and $\Omega_{R}$ represent the frequencies of the pump, Stokes, and Raman shift, respectively. (b) Raman spectroscopic data of an undoped, semi-insulating 4H-silicon carbide (SiC) wafer; (c) Experimental schematic: an amplified continuous-wave (CW) pump is coupled to the 4H-SiC chip through lensed fibers, whose forward (FW) and backward (BW) transmission and optical spectrum are recorded; (d) Representative linear transmission of the fundamental transverse-electric (TE00) mode in a $43$-$\mu$m-radius microring at 1550 nm; and (e) Optical spectrum of the forward transmission for an approximate on-chip pump power of 10 mW (the red dashed line is the recorded power in OSA when tuning the pump laser off resonance). EDFA: erbium-doped fiber amplifier; PD: photodetector; DAQ: data acquisition; and OSA: optical spectrum analyzer. References | Materials | Dominant Raman | Gain coeff. | Threshold | Power
---|---|---|---|---|---
shift (THz) | ($\text{cm}/\text{GW}$) | (mW) | efficiency ($\%$)
Latawiec et.al. (2015) [10] | Diamond | $\approx 40$ | 2.5 | 85 | $<1$
Liu et.al.(2017) [11] | AlN | $\approx 19$ | $0.25-0.45$ | 8 | $10-15$
Yu et.al. (2020)[12] | LN | $\approx 7.5$ | 1.3 | 20 | $\approx 42$
This work | 4H-SiC |  $\approx$ 23.3 | $\mathbf{0.75\pm 0.15}$ | 2.5 | 51
Table 1: Comparison of Raman lasing in crystalline, wide-bandgap integrated
photonic platforms. Note that we have converted the “slope efficiency” defined
in some references to the absolute power efficiency, which denotes the power
ratio between the Raman signal and the pump.

##  2 Efficient Raman lasing and Raman gain coefficient measurement

Figure 2: (a) Illustration of the Stokes Raman process in a microresonator;
(b) Experimentally measured Raman shift (solid circles) and a linear fit
(dashed line) as a function of the microring outer radius (ring width fixed at
$2.5\ \mu$m). (c) Superimposed optical spectra near the $777\ \text{cm}^{-1}$
Stokes signal at the Raman threshold power of 2.5 mW and maximum efficiency of
10 mW. The latter also results in optical parametric oscillation with the
Stokes acting as the secondary pump (other spikes are the amplified
spontaneous emission from EDFA transferred to the Stokes region through four-
wave mixing); (d) Extracted Raman gain coefficients (markers with error bars)
corresponding to different Raman shifts. The red solid line is a Gaussian fit
with its full width at half maximum (FWHM) estimated to be ($120\pm 30$) GHz.
(e) Superimposed Stokes corresponding to the Raman shift of $776.7\
\text{cm}^{-1}$ by varying the pump resonance in the 1529-1572 nm range for a
fixed on-chip power of 10 mW.

As illustrated in Fig. 2(a), the effective Raman gain and frequency shift are
both determined by the relative position of the Stokes resonance within the
Raman gain profile. Hence, our design efforts are focused on aligning the
Stokes resonance to the peak Raman gain for a low power threshold and
achieving over coupling for a high Raman efficiency. In the literature, most
of the existing experiments relied upon either random frequency matching [11,
10] or using a microresonator whose FSR is smaller than the Raman gain
bandwidth [12], both of which would result in an inflated power threshold.
Here, we adopt a different approach by employing a compact microresonator
(nominal radius near $43\ \mu$m with a corresponding FSR around 400 GHz) and
varying its radius from $43\ \mu$m to $43.76\ \mu$m in 40 nm increments (20
microrings in total). A straightforward calculation predicts an incremental
frequency shift of $-21.7$ GHz ($\approx\frac{-0.04}{43}\times 23.3$ THz) for
the $777\ \text{cm}^{-1}$ Stokes resonance in each 40 nm increase of the ring
radius. A total of 20 microrings therefore is able to cover the whole FSR,
ensuring that there is at least one microring within $21.7$ GHz of the peak
Raman gain.

To obtain strong coupling at the pump and Stokes resonances, we resort to the
straight coupling scheme, where a 900-nm-wide straight waveguide is
evanescently coupled to the 43-$\mu$m-radius SiC microring with a 200 nm gap.
The linear transmission measurement as shown in Fig. 1(d) confirms that a
coupling $Q$ of $1.4$ million (versus an intrinsic $Q$ of $3.5$ million) is
attained near the pump wavelength of 1550 nm. The coupling $Q$ of the $777\
\text{cm}^{-1}$ Stokes resonance is expected to be smaller, which is typical
for straight waveguide coupling due to increased modal overlap at longer
wavelengths. In fact, numerical simulation points to a coupling $Q$ of $0.6$
million near 1760 nm (see Supplementary). This would lead to a loaded $Q$
around $0.5$ million of the Stokes resonance if the intrinsic $Q$ is the same
as 1550 nm.

With the optimized design, we proceed to fabricate the devices using the
standard nanofabrication process which is described in detail in Ref. 19.
Briefly, we begin with a 4H-SiCOI chip with 700 nm SiC on top of 2 $\mu$m
oxide (NGK Insulators, LTD.). The pattern is first defined using e-beam
lithography and subsequently transferred to the SiC layer using plasma etching
for an etch depth around 575 nm, leaving an approximate 125 nm of pedestal
layer (i.e., unetched SiC). After cleaning, $2\ \mu$m oxide clad is deposited
on the 4H-SiC layer to encapsulate the devices. Next, we characterize the
Raman chip using the experimental schematic described in Fig. 1(c), where both
forward and backward transmissions are measured. The fiber-to-chip coupling is
achieved by implementing inverse tapers on the SiC chip, whose coupling loss
is estimated to be $3$-$4$ dB per facet (see Supplementary for more
information). The overall fiber-to-fiber insertion loss of this chip, however,
is typically around $10$-$14$ dB, as this chip suffers from relatively strong
charging effects in e-beam lithography that left small unexposed areas
(cracks) in random places of waveguides and microresonators (see Supplementary
for details). When appearing in waveguides, each crack introduces an
approximate 2 dB additional loss. The presence of the charging-induced crack
in a microring, on the other hand, will render the device useless since there
is typically no resonance due to extremely low intrinsic $Q$s.

Figure 2(b) summarizes the measured Raman shifts for 13 microrings with
different radii (the missing data points are caused by the charging effects
appearing in the corresponding microrings except for the ring radius of $43.6\
\mu$m, which is discussed in Fig. 4(b)), most of which follow the predicted
linear frequency shift with the increased ring radius. The Raman shifts of the
last two data points, corresponding to radii of $43.72\ \mu$m and $43.76\
\mu$m, are one FSR higher than the predicted trend. This can be understood as
when the Stokes resonance is gradually moved toward the pump (by reducing the
FSR), its adjacent resonance with a lower azimuthal order becomes closer to
the center of the Raman gain and lases instead.

Among all the working microresonators, the one with the $43.36\ \mu$m radius
exhibits the lowest Raman threshold of $2.5$ mW with a measured Raman shift of
$776.7\ \text{cm}^{-1}$ (Fig. 2(c)). For each Raman shift, we estimate the
corresponding Raman gain coefficient $g_{R}$ based on the knowledge of the
power threshold $P_{\text{th, Raman}}$ [3]:

$P_{\text{th,
Raman}}\approx\frac{\pi^{2}n_{\text{SiC}}^{2}V_{\text{eff}}}{\lambda_{p}\lambda_{s}g_{R}}\cdot\frac{Q_{c,p}}{Q_{l,p}^{2}}\cdot\frac{1}{Q_{l,s}},$
(1)

where $n_{\text{SiC}}$ is the refractive index of SiC ($n_{\text{SiC}}\approx
2.6$); $V_{\text{eff}}$ is the effective mode volume ($V_{\text{eff}}\approx
270\ {\mu m}^{3}$ for 43-$\mu$m-radius SiC microrings); $\lambda_{p}$ and
$\lambda_{s}$ denote the wavelengths of the pump and Stokes, respectively;
$Q_{c,p}$ and $Q_{l,p}$ are the coupling $Q$ and loaded $Q$ of the pump
resonance, respectively; and $Q_{l,s}$ is the loaded $Q$ of the Stokes
resonance. In Eq. 1, the only parameter that cannot be directly measured is
$Q_{l,s}$, which is due to a lack of a tunable laser source near the Stokes
resonance. However, as explained earlier, we can infer the coupling $Q$ at the
Stokes resonance based on the measured coupling $Q$ at 1550 nm, while assuming
that the intrinsic $Q$ at the Stokes resonance is the same as the pump. Take
the pump resonance shown in Fig. 1(d) (which corresponds to the microring with
the lowest power threshold) for example, its coupling $Q$ and loaded $Q$ at
1760 nm are approximated to be $0.6$ million and $0.5$ million, respectively.
These numbers can be corroborated using the fact that when the Stokes power is
large enough, optical parametric oscillation (OPO) is observed near the Stokes
resonance because of its anomalous dispersion (Fig. 2(c)). (Note that the OPO
pairs are generated 5 FSRs away from the Stokes while the rest peaks observed
in Fig. 2(c) are the transferred noise from the EDFA.) The OPO threshold with
the Stokes serving as the secondary pump is given by [20]:

$P_{\text{OPO}}\approx\frac{\pi
n_{g}^{2}V_{\text{eff}}}{4\lambda_{s}n_{2}}\cdot\frac{Q_{c,s}}{Q_{l,s}^{3}},$
(2)

where $n_{g}$ ($n_{g}\approx 2.7$) is the group index and $n_{2}$ is the Kerr
nonlinear index of 4H-SiC ($n_{2}\approx 9.1\times
10^{-19}\text{m}^{2}/\text{W}$ for the TE polarization) [14]. The computed
power threshold of $5.0$ mW is consistent with the experimental data shown in
Fig. 2(c) (the on-chip Stokes power corresponding to 10 mW input is
approximately $10\times 51\%=5.1$ mW). Hence, recording the OPO threshold
power for each Raman shift provides an effective calibration for the
estimation of the Raman gain coefficient. In Fig. 2(d), we plot the extracted
Raman gain coefficient as a function of the corresponding Raman shift, where a
Gaussian fit reveals a full width at half maximum (FWHM) around $(4\pm 1)\
\text{cm}^{-1}$, or $(120\pm 30)$ GHz.

In addition to the efficient Raman lasing, the Stokes is expected to shift in
sync with the pump resonance to maintain a fixed Raman shift. Figure 2(e)
shows one such example for the microring with radius of $43.36\ \mu$m, where
we sequentially select pump resonances from 1529 nm to 1572 nm (limited by the
EDFA range) for a fixed on-chip power of 10 mW and superimpose the resultant
Stokes generated from 1735 nm to 1792 nm. The non-uniformity in the Stokes
power is mainly attributed to the slight variations in the input power and
resonant properties of different azimuthal orders. Nevertheless, the result
displayed in Fig. 2(e) demonstrates the ease of wavelength tuning for the
Raman lasing process, which is important for many practical applications.

##  3 Raman-Kerr interaction and comb generation

Figure 3: (a) Inferred on-chip Stokes power of the $776.7\ \text{cm}^{-1}$
Raman shift for the forward and backward transmission after accounting for
coupling losses; (b) Stokes efficiency by normalizing the on-chip Stokes power
by the pump power; (c) and (d) Measured optical spectra for the forward and
backward transmission at three different pump powers.

As we further increase the pump power, the Stokes signal saturates to a level
of 6-8 mW on chip for the forward transmission (Fig. 3(a)). Hence, the maximum
Stokes efficiency is achieved when the input power is around 10 mW, beyond
which it begins to decrease with increased powers (Fig. 3(b)). This is not
surprising since when the Stokes power is above the OPO threshold (around 5
mW), it can act as a secondary pump for the Kerr microcomb generation due to
the anomalous dispersion around the Stokes resonance (see Supplementary). In
addition, the Raman process in general would result in clockwise (backward)
and counter-clockwise (forward) Stokes inside the microresonator [12], which
might have slightly different power thresholds. To understand the interactive
dynamics between Raman and the pump laser, we plot the optical spectra
corresponding to the forward and backward transmissions at three
representative powers in Fig. 3(c). As can be seen, a primary comb with
multiple-FSR-separation is first generated near the Stokes resonance at a pump
power of 20 mW (which can be compared to Fig. 2(c) to support the OPO
identification). These comb lines are also transferred to the pump region due
to a non-degenerate four-wave mixing process (so-called four-wave mixing Bragg
scattering): $\omega_{\textmd{comb near pump}}=\omega_{\textmd{comb near
Stokes}}+\omega_{p}-\omega_{s}$ [27]. In fact, the small peaks near the Stokes
resonance are the transferred noise from the EDFA (amplified spontaneous
emission) based on the same principle: $\omega_{\textmd{noise near
Stokes}}=\omega_{\textmd{noise near pump}}+\omega_{s}-\omega_{p}$. The
backward spectrum at 20 mW consists of the reflection of the pump and the
backward-propagating Stokes comb generated inside the microring. As we
increase the pump power to 80 mW, we begin to see major differences in the
forward and backward optical spectra: the backward spectrum contains a filled
Kerr microcomb (termed as Raman-Kerr comb for simplicity) that is well
separated from the 1550 nm pump, while the forward spectrum consists of
additional combs lines between the pump and the Stokes resonance. Such
difference can be understood as the forward optical spectrum consists of the
counter-clockwise Raman-Kerr comb and the pump laser, both of which propagate
in the same direction inside the microresonator and hence interact with each
other through four-wave mixing. In contrast, the backward spectrum consists of
the reflected portion of the pump and the clockwise Raman-Kerr comb without
them mixing with each other inside the microresonator. Finally, as the pump
power is increased to 200 mW, both the forward and backward spectra are
significantly widened, though the forward spectral coverage is modestly wider,
spanning from 1400 nm to 2100 nm.

Figure 4: (a) Cascaded Raman shifts of $777.3\text{cm}^{-1}$ from the
microring with outer radius of $43.32\ \mu$m at an input power of 200 mW. (b)
The blue solid line is the Raman-Kerr comb from the microring with outer
radius of $43.6\ \mu$m when pumped at the TE00 resonance near $1549.5$ nm. The
red solid line corresponds to pumping at the next resonance near $1552.9$ nm,
whose spectrum consists of two cascaded Raman shifts, one near $266\
\text{cm}^{-1}$ and the other near $781.8\ \text{cm}^{-1}$, without Kerr comb.
The insets show the zoom-in spectra near the two Raman shifts, suggesting that
the Stokes are likely formed by a different mode family (TM).

In addition to Stokes-induced Kerr microcomb, we also observe cascaded Raman
generation in a few microrings, pointing to even more complicated interactions
between the Raman and Kerr effects [5, 18]. For example, Fig. 4(a) shows that
there are two cascaded $777.3\ \text{cm}^{-1}$ Stokes in the microring with a
radius of $43.32\ \mu$m, each generating a Kerr microcomb in the adjacent
region. Moreover, while the $777\ \text{cm}^{-1}$ Stokes dominates over other
Raman transitions in most of the microring resonators, we also observe
different Raman shifts in certain geometries. For example, in the microring
with a radius of $43.6\ \mu$m radius, when pumping the TE00 resonance near
$1549.5$ nm, a regular Raman-Kerr comb is observed in the forward transmission
(blue solid line in Fig. 4(b)). However, when we tune the pump laser to the
$1552.9$ nm resonance, only two cascaded Raman shifts are observed in the
spectrum, one corresponding to $266\ \text{cm}^{-1}$ and the other
corresponding to $781.8\ \text{cm}^{-1}$ (red solid line in Fig. 4(b)). An
inspection of the optical spectrum near the two Stokes (see the two insets in
Fig. 4(b)) suggests that the two Stokes are not from the TE00 mode family.
Instead, they are likely the TM00 modes of the microring that happen to be
accidentally frequency matched to the TE00 pump for the observed Raman
transitions. This may explain why the $266\ \text{cm}^{-1}$ Raman transition
is often absent in the bulk-wafer measurement (see Fig. 1(b)) [26].

Figure 5: (a) Optical spectrum of a SiC microring with a radius of 178 $\mu$m
(corresponding free spectral range around 100 GHz), which consists of the Kerr
comb from the pump itself and two cascaded Raman peaks near $776\
\text{cm}^{-1}$ and $204\ \text{cm}^{-1}$. (b) Zoomed-in spectra near the two
Raman peaks.

So far, we have only discussed the stimulated Raman scattering in SiC
microresonators that exhibit normal dispersion at the pump wavelength, a
preferred configuration to avoid competition between the Raman and Kerr
effects at the same wavelength [28]. It is possible, however, to observe
Stokes appearing in a Kerr microcomb as well. Figure 5 shows one such example
for a 178-$\mu$m-radius SiC microring resonator. The TE00 mode at this
increased radius possesses a weak anomalous dispersion (see Supplementary for
more details). When pumped at 300 mW power, a broad Kerr microcomb spanning
from 1200 nm to 1900 nm is generated along with two cascaded Raman
transitions, with one peak corresponding to $776\text{cm}^{-1}$ and the other
to $204\ \text{cm}^{-1}$. A zoom-in view of the two Raman peaks reveals that
they are from the same mode family.

Finally, we want to comment on the coherence properties of the Raman-Kerr comb
generated in this work. Most of them, with the only exception of the primary
comb in Fig. 3(c), are believed to be in the chaotic state that is not phase-
locked to the pump laser. It is possible, however, to observe a soliton
microcomb with the Stokes serving as the secondary pump or the coexistence of
the Stokes soliton with the Kerr soliton generated by the pump [29, 30]. A
detailed discussion on these aspects of Raman-Kerr interactions is beyond the
scope of this paper and will be left to future works.

##  4 Conclusion

In conclusion, we performed a thorough investigation of the Raman effect in
low-loss 4H-SiC microresonators, resulting in the demonstration of an
efficient Raman laser with $>50\ \%$ power efficiency and a detailed
characterization of the Raman gain coefficient for the dominant $777\
\text{cm}^{-1}$ ($23.3$ THz) Stokes transition, both of which are the first in
an integrated SiC platform (to the best of our knowledge). In addition, our
study of the Stokes-induced Kerr comb and its interplay with the pump laser
revealed the different roles of four-wave mixing in the forward and backward
transmissions as well as the rich interactions between the Raman and Kerr
effects. Finally, we also observed the occurrence of other Raman transitions
such as $204\ \text{cm}^{-1}$ ($6.1$ THz) and $266\ \text{cm}^{-1}$ ($8.0$
THz) along with the $777\ \text{cm}^{-1}$ Stokes, a feature that can be
utilized to broaden the Stokes-induced or pump-induced Kerr microcombs. We
believe that our results fill up the gap in the understanding of the
stimulated Raman process in 4H-SiC microresonators, which could potentially
lead to a myriad of applications including efficient Raman lasers and novel
approaches to generating broadband microcombs.

##  1 Inverse tapers and charging effect

Figure S1: (a) Optical micrograph of a lensed fiber aligned to a polished SiC
facet; (b) The mode profile of the SiC inverse taper with a (bottom) width
around 250 nm. The inset shows the optical micrograph of the taper region
where the pedestal layer is removed by an additional step of lithography; (c)
Optical micrograph highlighting charging-induced cracks (red circles) in
waveguides and microresonators; and (d) Statistically averaged fiber-to-fiber
insertion loss as a function of the number of cracks appearing in waveguides.

In this work, efficient fiber-to-chip coupling is achieved by aligning a
lensed fiber (with a mode field diameter of $2.5\ \mu$m) to the SiC inverse
taper implemented at the chip facet (Fig. S1(a)). The mode profile of the
inverse taper is provided in Fig. S1(b), which has an estimated coupling loss
of 2 dB by computing its modal overlap with the lensed fiber. Given that the
presence of a pedestal layer hinders the mode expansion and thus reduces the
coupling efficiency, we remove the pedestal layer in the taper region using an
additional step of lithography (see the inset of Fig. S1(b)). That is to say,
in the microring region the SiC is 700 nm thick with 125 nm pedestal, while
the SiC is only around 550 nm thick without pedestal in the taper region. We
then polish the SiC facets so that the tip of the inverse tapers is only a few
microns away from the facet. In our prior experiments, the inverse tapers
would typically fail at high optical input powers due to residues from the
polishing step that caused strong optical absorption [19]. After switching to
a more thorough cleaning process, the inverse tapers can now sustain optical
powers up to several watts without getting burnt.

When writing long waveguides in the e-beam lithography, the charging effect
caused by charge accumulation in insulating substrates becomes more apparent,
resulting in cracks in the writing area as highlighted in Fig. 1S(c). Though a
few mitigating methods including evaporating a thin layer of aluminum on top
of the e-beam resist have been tried, it is still common to get 1-3 cracks in
a 5-mm-long waveguide. For dense patterns consisting of many devices
(including this Raman chip), the charging effect can be even stronger. Fitting
the measured insertion loss as a function of the observed cracks in various
waveguides reveals a positive correlation between the increased losses and the
number of charging-induced cracks. Statistically, each crack introduces an
approximate $1.5$-$2$ dB additional loss. For waveguides that are free of the
charging effect, the total chip insertion loss is only around 6-7 dB,
suggesting a coupling loss around 3 dB for each inverse taper (which is
slightly higher than the 2 dB number obtained from simulation).

##  2 Dispersion of 43-$\mu$m-radius SiC microrings

Figure S2: (a) Simulated dispersion of the 43-$\mu$m-radius SiC microring used
in this work: a ring width of $2.5\ \mu$m exhibits normal dispersion around
1550 nm and anomalous dispersion around 1760 nm (as highlighted by the two red
dots in the figure); and (b) Experimentally measured dispersion by computing
the integrated dispersion $D_{\text{int}}$ as a function of different
azimuthal orders, confirming normal dispersion in the 1550 nm band.
$D_{\text{int}}$ is defined as
$D_{\text{int}}\equiv\omega_{\mu}-\omega_{0}-D_{1}\mu$ where $\mu$ is the
relative azimuthal order to the pump resonance (i.e., $\mu=0$ for the pump
mode), $\omega_{\mu}$ is the corresponding resonance frequency, and $D_{1}$ is
the free spectral range of the resonator.

As discussed in the main text, the 43-$\mu$m-radius SiC microring employed in
this work is designed to exhibit normal dispersion near the pump wavelength
(1550 nm) while possessing anomalous dispersion in the Stokes wavelength
corresponding to the dominant $777\ \text{cm}^{-1}$ Raman shift (1760 nm).
Numerical simulation performed in Fig. S2(a) suggests that this can be
achieved by choosing a ring width of $2.5\ \mu$m with a height of 700 nm and a
pedestal layer of 125 nm. After fabricating these microrings, a linear
dispersion measurement was performed to confirm the normal dispersion in the
1550 nm region (see one example in Fig. S2(b)).

##  3 Waveguide-resonator coupling simulation

Figure S3: (a) Schematic of straight waveguide coupling between a microring
resonator and the access waveguide. The inset shows the mode profile of the
43-$\mu$m-radius SiC microring used in this work, which has a width of $2.5\
\mu$m and a height of $700$ nm (the pedestal layer is 125 nm). (b) Simulated
coupling $Q$ as a function of wavelengths: the access waveguide has a width of
900 nm and a coupling gap of 200 nm.

The straight coupling scheme, as illustrated in Fig. S3(a), is ideal for
achieving over-coupling in both the pump and Stokes resonances. This is
because in this coupling scheme, the modal overlap factor plays a dominant
role (given the short interaction length), which typically results in stronger
coupling at longer wavelengths [27]. This means if we can achieve over-
coupling in the 1550 nm band, the degree of over-coupling at 1760 nm should be
even stronger (see Fig. S2(b) for simulation). Typically, due to the limited
accuracy in the dimensional control from nanofabrication, we have to adjust
the gap by up to 50 nm to match the observed coupling $Q$ with the
experimental data. In this case, there is good agreement between the measured
coupling $Q$ at 1550 nm and the simulation data based on the designed gap (200
nm). Nevertheless, once we match the coupling $Q$ at the pump wavelength
($1.4$ million at 1550 nm), numerical simulation predicts an approximate
coupling $Q$ of 0.6 million at 1760 nm. This number is also verified by
comparing the predicted OPO power threshold with the experimental data (see
main text).

##  4 Raman power efficiency estimation

Figure S4: Normalized pump transmission of the $43.36$-$\mu$m-radius SiC
microring at different input powers.

The Raman power efficiency around $51\ \%$ is estimated based on the OSA
spectrum shown in Fig. 1(e), which is given by the ratio between the recorded
Stokes power (when the pump is tuned into resonance) and the off-resonance
pump power. This measurement assumes that the Stokes and pump experience the
same out-coupling loss from the SiC chip (the numerical value of the insertion
loss is less important as long as it stays the same between the two
measurements). It is possible, however, that the coupling loss of the 1760 nm
Stokes is slightly higher than that of the 1550 nm pump, as suggested by
preliminary characterization carried out by the DTU team using a
supercontinuum source on a different SiC chip. This would indicate a slightly
higher power efficiency (by $0.5$ dB) if verified. To be conservative, the
reported number here does not adjust for the difference of the insertion loss
between the Stokes and pump.

One may notice that the extinction ratio of the pump resonance shown in Fig.
1(e) ($\approx 14$ dB) is higher than what is suggested by the linear
transmission in Fig. 1(d) ($\approx 7$ dB). This is confirmed by comparing the
pump transmissions at various input powers in Fig. S4. The result is also
consistent with the interpretation of the over-coupled pump resonance in the
linear regime and high Raman conversion efficiency that depletes the pump when
the input power is around 10 mW.

##  5 Additional information on 178-$\mu$m-radius SiC microrings

Figure S5: (a) Representative linear transmission of the fundamental TE00 mode
of the 178-$\mu$m-radius SiC microring studied in Fig. 5 of the main text,
showing an intrinsic $Q$ around $3.5$ million and a coupling $Q$ around 19
million. The microring has a ring width of $3.5\ \mu$m and an access waveguide
with a width of 1450 nm and a pulley coupling length of 30 $\mu$m; (b)
Dispersion measurement confirms anomalous dispersion in the 1550 nm band,
which is also consistent with simulation shown in (c) at 1550 nm; and (c)
Simulated dispersion for the TE00 mode of the 178-$\mu$m-radius SiC microring,
which shows a mode crossing around 1330 nm.

The 178-$\mu$m-radius SiC microring is from a different chip which was
fabricated using a similar process but with different designs. Notably, it has
the same SiC thickness of 700 nm and a pedestal layer of 125 nm. The most
significant difference is that the coupling to the fundamental TE00 mode is
based on the pulley coupling instead of straight coupling [27]. The linear
transmission shown in Fig. S5(a) reveals that the TE00 mode is under-coupled
at 1550 nm, which explains why the Raman signals are much weaker compared to
those observed in 43-$\mu$m-radius SiC microrings. The dispersion
characterization in Fig. S5(b) confirms that the larger-radius-microring
exhibits weak but anomalous dispersion near 1550 nm, which is consistent with
the simulated dispersion (see Fig. S5(c)). For the 700 nm SiC with 125 nm
pedestal, numerical simulation also points to a possible mode crossing between
the TE00 and TM00 mode families around the wavelength of 1300 nm. This may
explain the disappearance of certain comb lines in that region as shown in
Fig. 5(a) in the main text.

Funding This work was supported by NSF (2127499, 2131162). The DTU team would
like to acknowledge the support of the European Union’s Horizon 2020 FET Open
project (SiComb, No. 899679) and the Villum Fonden (Grant No. 50293).

Acknowledgments The CMU team acknowledges use of the Materials
Characterization Facility at Carnegie Mellon University supported by grant
MCF-677785, as well as the equipment support from Dr. Lijun Ma and Dr. Oliver
Slattery at NIST. R. Wang also acknowledges the support of Tan Endowed
Graduate Fellowship from CMU.

Disclosures The authors declare no conflicts of interest.

Data Availability Data underlying the results presented in this paper are not
publicly available at this time but may be obtained from the authors upon
reasonable request.

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