# Engineered Raman Lasing in Photonic Integrated Chalcogenide Microresonators

Yufei Huang  Guangdong Provincial Key Laboratory of Optoelectronic Information
Processing Chips and Systems, School of Electrical and Information Technology,
Sun Yat-sen University, Guangzhou 510275, China  these authors contributed
equally to this work  Di Xia  Guangdong Provincial Key Laboratory of
Optoelectronic Information Processing Chips and Systems, School of Electrical
and Information Technology, Sun Yat-sen University, Guangzhou 510275, China
these authors contributed equally to this work  Pingyang Zeng  Guangdong
Provincial Key Laboratory of Optoelectronic Information Processing Chips and
Systems, School of Electrical and Information Technology, Sun Yat-sen
University, Guangzhou 510275, China  Jiaxin Zhao  Guangdong Provincial Key
Laboratory of Optoelectronic Information Processing Chips and Systems, School
of Electrical and Information Technology, Sun Yat-sen University, Guangzhou
510275, China  Zelin Yang  Guangdong Provincial Key Laboratory of
Optoelectronic Information Processing Chips and Systems, School of Electrical
and Information Technology, Sun Yat-sen University, Guangzhou 510275, China
Suwan Sun  Key Laboratory of Specialty Fiber Optics and Optical Access
Networks, Shanghai University, Shanghai 200444, China  Liyang Luo  Guangdong
Provincial Key Laboratory of Optoelectronic Information Processing Chips and
Systems, School of Electrical and Information Technology, Sun Yat-sen
University, Guangzhou 510275, China  Guiying Hu  Guangdong Provincial Key
Laboratory of Optoelectronic Information Processing Chips and Systems, School
of Electrical and Information Technology, Sun Yat-sen University, Guangzhou
510275, China  Dong Liu  Guangdong Provincial Key Laboratory of Optoelectronic
Information Processing Chips and Systems, School of Electrical and Information
Technology, Sun Yat-sen University, Guangzhou 510275, China  Yufei Li
Guangdong Provincial Key Laboratory of Optoelectronic Information Processing
Chips and Systems, School of Electrical and Information Technology, Sun Yat-
sen University, Guangzhou 510275, China  Hairun Guo  Key Laboratory of
Specialty Fiber Optics and Optical Access Networks, Shanghai University,
Shanghai 200444, China  Bin Zhang  Guangdong Provincial Key Laboratory of
Optoelectronic Information Processing Chips and Systems, School of Electrical
and Information Technology, Sun Yat-sen University, Guangzhou 510275, China
Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen
University, Guangzhou 510275, China  Corresponding author:
<EMAIL_ADDRESS><EMAIL_ADDRESS>Zhaohui Li  Guangdong
Provincial Key Laboratory of Optoelectronic Information Processing Chips and
Systems, School of Electrical and Information Technology, Sun Yat-sen
University, Guangzhou 510275, China  Key Laboratory of Optoelectronic
Materials and Technologies, Sun Yat-sen University, Guangzhou 510275, China
Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai,
519000, China  Corresponding author<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Chalcogenide glass (ChG) is an attractive material for integrated nonlinear
photonics due to its wide transparency and high nonlinearity, and its
capability of being directly deposited and patterned on Silicon wafer
substrates. It has a singular Raman effect among amorphous materials. Yet, the
Raman lasing performance in high quality and chip integrated ChG
microresonators remains unexplored. Here, we demonstrate an engineered Raman
lasing dynamic based on home developed photonic integrated high-$Q$ ChG
microresonators. With a quality factor above $10^{6}$, we achieve the record-
low lasing threshold 3.25 mW among integrated planar photonic platforms. Both
the single-mode Raman lasers and a broadband Raman-Kerr comb are observed and
characterized, which is dependent on the dispersion of our flexible photonic
platform and engineered via tuning the waveguide geometric size. The
tunability of such a chip-scale Raman laser is also demonstrated through
tuning the pump wavelength and tuning the operating temperature on the chip.
This allows for the access of single-mode lasing at arbitrary wavelengths in
the range 1615-1755 nm. Our results may contribute to the understanding of
rich Raman and Kerr nonlinear interactions in dissipative and nonlinear
microresonators, and on application aspect, may pave a way to chip-scale
efficient Raman lasers that is highly desired in spectroscopic applications in
the infrared.

††journal: optica

##  1 Introduction

Stimulated Raman scattering (SRS) is well known as an effective means to
extend the spectral coverage of conventional semiconductor and rare-earth-
doped laser sources [1, 2, 3, 4], in which a long-wavelength signal (i.e. the
Stokes radiation) can be generated from the initial pump wave, with a
frequency offset equal to the molecular vibrational frequency underlying the
material [5, 6]. Potential applications of Raman lasing include optical
amplification, spectroscopic sensing, archaeology, and clinical diagnosis [5,
7, 8].

Figure 1:  Chip-scale chalcogenide microresonators. (a) A schematic ChG
microresonator and a sketch of the energy level system of the Raman effect.
(b) Measured Raman spectrum of ChG film with a thickness of 0.8 $\mu$m. (c)
Illustration of the single-mode and cascaded Raman laser in the microresonator
with FWM phase matching (cf. Eq. 3, 4). (d) The Raman-Kerr comb state in the
presence of FWM phase mismatch. (e) The SEM image of a GeSbS microresonator,
together with the image on the coupling region. The cross-section of the GeSbS
waveguide is 2.4 $\mu$m × 0.8 $\mu$m, and a radius of 100 $\mu$m. The
microring has a 1.3 $\mu$m wide bus waveguide and a 35° pulley-style coupler
with a critical coupling gap of ca. 550 nm. Simulated field distribution at
(f) the pump wave and (g) the first Stokes wave, respectively. The microring
can support good spatial overlap between the pump and Stokes mode. (h)
Measured transmission spectra and (i) Resonance of fundamental TE modes of the
microring without an Erbium-doped fiber amplifier (EDFA).

Recent development has been on photonic integrated platforms, where Raman
lasers with high compactness and low energy consumption are enabled [9, 10,
11, 12]. Indeed, photonic integrated Raman lasers have been experimentally
demonstrated in silicon racetrack resonators [1, 9, 10], silicon photonic
crystals [2], on-chip diamond resonators [11], photonic aluminum nitride (AlN)
microresonators [12], lithium niobate microresonators (LN) [13] and silica
microcavities [14]. Yet, these platforms intrinsically have shortcomings that
limit the performance of the Raman lasing. For instance, silicon has severe
two-photon absorption (TPA) and free-carrier absorption (FCA), and silica
suffers from a much weaker Raman gain coefficient than silicon [1, 2, 7, 9].
On fabrication aspect, diamond, LN and crystalline AlN need to be co-
integrated on a Silicon substrate either by the “wafer bonding” or carefully
controlled crystal growth processes, which is non-trivial to implement [11,
12, 13]. Moreover, the Raman gain in crystalline materials is always narrow-
band, which requires precise control on the crystal orientation as well as on
the cut. Control on the cavity resonant frequency is also required to align
with the Raman mode.

Among amorphous materials, chalcogenide glass (ChG) has a singular Raman and
Kerr nonlinearity while being resistant to TPA and FCA [15, 16, 17, 18, 19,
20]. It has a wide transparency from the visible to the footprint infrared
region (up to ca. 25 $\mu$m) and has a tailorable nonlinearity by adjusting
the alloy composition [21, 22, 23]. Such properties have led to ultra-
broadband and efficient supercontinuum generation in ChG based optical fibers
and waveguides [21, 22, 24], and strong SRS within a wide wavelength range up
to the mid-infrared (above 4 $\mu$m) has been demonstrated [3, 8, 25, 26]. Of
particular interest is photonic chip integrated ChG devices [27], which could
largely boost the performance of SRS and the Raman lasing. Indeed, ChG can
adhere to the Silicon wafer substrate by thermal evaporation at a low glass
transition temperature ($T_{g}$, less than $300^{\circ}\mathrm{C}$), free from
the bonding or surface modification processes [16, 28, 29, 30, 31]. Being
amorphous, the material Raman gain becomes broadband, which enables a flexible
design on the free spectral range (FSR) of integrated microresonators [11,
12]. To date, single-mode Raman lasing has been implemented in ChG
microspheres [32, 33]. Yet, there remain challenges in the implementation of
high-quality and chip integrated ChG microresonators. Usually, ChG films
prepared with Arsenic (As)-based components are prone to oxidation and
photorefraction. The on-chip ChG-based devices also suffer from laser-induced
damage when being exposed to a pump power of tens mW [34, 35]. Regarding the
quality of ChG microresonators, the reported $Q$-factors to date remain
insufficient to support high-efficient nonlinear interactions as well as the
SRS [36].

In this work, we overcome the above challenges by developing a photonic
integrated high-$Q$ ChG microresonator platform and demonstrate a highly
efficient chip-scale Raman lasing at the telecommunication $L$ band. The
integrated microresonators are based on environment-friendly Ge25Sb10S65
(GeSbS), which has strong Kerr nonlinearity, high Raman gain, high damage
threshold and superior thermal stability [37, 38, 39]. The intrinsic
$Q$-factor of our microresonators is as high as $2.2\times 10^{6}$, and the
threshold power for the Raman lasing is as low as 3.25 mW. We demonstrate both
the single-mode and the cascaded Raman lasing, together with a broadband
Raman-Kerr comb [40], by engineering the dispersion and the four-wave-mixing
(FWM) phase matching condition underlying the microresonator. The tunability
of the Raman laser is also demonstrated to cover a wavelength range over 140
nm. Our work marks, to the best of our knowledge, the first observation of
engineered and widely tunable Raman lasers in photonic chip integrated
platforms, which may contribute not only to the fundamental physics of Raman
lasing in dissipative Kerr resonators, but also to spectroscopic applications
by e.g. supporting a hyperspectral imaging.

##  2 Device fabrication and characterization

The photonic integrated ChG waveguides and microresonators are fabricated
based on an improved subtractive nano-fabrication process that allows for
stable and high-quality ChG microresonators [18, 38]. Initially, GeSbS glass
is synthesized from high purity elements, including 6N Germanium (Ge), 6N
Antimony (Sb) and 6N Sulfur (S), by the conventional melt-quenching technique
[24, 39], which is further purified by our home developed physical and
chemical purification technique [24]. The high purity GeSbS is then deposited
on a Silicon wafer with a 3-$\mu$m SiO2 layer via thermal evaporation, forming
a film of 0.8-$\mu$m thickness. Next, the film is patterned by electron-beam
lithography. Afterwards, the pattern is etched in an inductively coupled
plasma reactive ion etcher (ICP-RIE) with CHF3 gas. At last, a 3-$\mu$m layer
of silica is deposited on the device via inductively coupled plasma chemical
vapour deposition (ICP-CVD) as the cladding. Regarding this work, the ChG
waveguides and the microresonators have a fixed height of 0.8 $\mu$m, and the
width is flexibly tailored in the range 1.6-2.4 $\mu$m, which allows for
dispersion engineering as well as engineered Raman lasing.

##  3 Results and Discussions

###  3.1 ChG Microresonator Characterization

A schematic of the GeSbS-based microring resonator is shown in Fig. 5(a). The
Raman gain spectrum of the GeSbS film was experimentally measured by Raman
spectrometer, (see Fig. 5 (b)), which shows a broadband spectral profile
compared with that of crystalline materials [41]. In particular, the main
Raman gain is centered at the frequency offset of 340 cm-1 ($\sim$10.2 THz),
with a linewidth of ca. 1.73 THz (estimated by a single-Lorentzian fit of the
gain profile) [42]. A complete analysis of all vibrational modes underlying
the gain spectrum is presented in the supplementary information (SI). The
normalized Raman peak gain is ca. 6.0 (extracted with
$\int_{0}^{\infty}h_{R}(t)dt=1$, where $h_{R}(t)$ is the temporal Raman
response function). The nonlinear coefficiency (_n 2_ ) of GeSbS is ca.
$2.0\times 10^{-18}$ m2/W [37]. A typical SEM picture of the fabricated GeSbS
microresonators is presented in Fig. 5(e), together with the picture of the
magnified coupling region. For the purpose of Raman lasing, the GeSbS
waveguide is designed to support normal cavity dispersion. This will suppress
nonlinear parametric oscillations usually evoked by the spontaneous Kerr
nonlinearity in the anomalous dispersion regime [40]. As such, engineering the
waveguide geometry (i.e. changing the core width and height) will mainly
contribute to tuning the FWM phase-matching condition among the pump wave and
the Raman-induced Stokes / anti-Stokes waves. Consequently, there are mainly
two types of the Raman lasing: single-mode and cascaded Raman lasers in the
FWM phase-matching condition, and a relative broadband Raman-Kerr comb in the
presence of phase mismatch, see Fig. 5(c,d). In a microresonator with the FSR
of $\sim$200 GHz, a typical resonance linewidth of $\sim$150 MHz was measured
in the regime of the critical coupling, see Fig. 5(i). This indicates a high
intrinsic $Q$-factor ($Q_{i}$) >$2.2\times 10^{6}$. In exploring the Raman
lasing dynamic, the GeSbS microresonator is deliberately designed to support
under coupled pump modes and over coupled Stokes modes, such that the
conversion efficiency is effectively elevated at the transmitted port of the
microresonator [43].

###  3.2 Low-threshold single-mode Raman laser

We characterized the Raman lasing in the fabricated GeSbS microresonators. In
the experiment, an amplified continuous wave (CW) tunable laser is coupled to
the resonator. The insertion loss of fiber-to-chip coupling is $\sim$2.5
dB/facet for the fundamental TE mode. At the output, the optical signal is
monitored by an optical spectral analyzer (OSA), in which the generated Raman
lasing is quantitatively noted (cf. SI for a detailed experimental setup).

At a low pumping power, the threshold for the Raman lasing is identified. In
this condition, only single-mode Raman lasers are observed, see Fig. 6(a).
When the microresonator is pumped at 1550 nm with the power of 3.5 mW, a
significant Stokes laser is monitored at 1637 nm, in the transmitted port of
the resonator. The frequency offset is $\sim$10.3 THz, which is close to the
central peak of the Raman gain. In addition, a weak anti-Stokes laser is also
monitored at the blue side of the pump with a similar frequency offset.
Moreover, the transmitted power of this single-mode Stokes wave is traced as a
function of the pump power, in which a threshold power of $\sim$3.25 mW can be
identified [Fig. 6(b)]. Above the threshold, the Stokes wave is enhanced when
the pump power is increased. The external slope efficiency is extracted to be
13.86$\%$. We can further deduce the Raman gain coefficient (gR) of GeSbS
material, which is ca. $7.37\times 10^{-12}$ m/W (a value over 100 times
higher than that in silica.)

Figure 2: Raman threshold power. (a) Measured optical spectra of the first
Stokes wave at around 1637 nm, with the on-chip pump power estimated to be
$\sim$3.5 mW. (b) The power trace of the first Stokes wave as a function of
the pump power.The slope efficiency is $\sim$13.86$\%$ and the threshold power
is ca. 3.25 mW. Figure 3: Engneered Raman lasing dynamics. (a) Schematic of
the degenerate FWM between the pump wave, the first and the second Stokes
waves. (b) Calculated dispersion parameter $D_{2}$ of the microresonators,
with different waveguide widths (1.7 $\mu$m and 2.4 $\mu$m). The $Q$ factors
of the 1.7-$\mu$m microresonator is $Q_{i}=0.93\times 10^{6}$,
$Q_{L}=0.8\times 10^{6}$, $Q_{c}=5.8\times 10^{6}$. (c) Calculated phase
mismatch for the degenerate FWM process ($\Delta\nu^{1}$). (d, e) The measured
Raman spectra in the 1.7-$\mu$m microresonator, by narrowly tuning the laser
frequency (i.e. changing the laser-cavity detuning). This operation is
equivalent to the change on the cavity coupling power. The pump power is
$\sim$35 mW (corresponding intracavity power intensity is 345.1 mW/cm2). The
first Stokes and second Stokes lasing with Raman shifts of $\sim$10.22 THz and
$\sim$10.24 THz are generated almost simultaneously, implying similar
threshold power. (f, g) The measured Raman spectra of the microring with 2.4
$\mu$m width by changing the detuning. The pump power is $\sim$20 mW
(corresponding intracavity power intensity is 273.7 mW/cm2). Numerical
simulations in both dispersion conditions of the microresonators with the
width of (h) 1.7 $\mu$m and (i) 2.4 $\mu$m.

###  3.3 Engineered Raman Lasing at high pump power

In the presence of a strong pump wave, the Raman lasing dynamic is enriched.
Given that the nonlinear parametric oscillations are effectively suppressed
(in the condition of overall normal cavity dispersion), dispersion engineering
within a certain range would mainly alter the potential phase matching
condition for the SRS as well as for the Raman lasing. In particular, with
respect to the generation of the second Stokes wave, there are FWM processes
along with the Raman effect. One is the degenerate FWM process involving the
pump wave, the first and the second Stokes waves. In this case, the pump
energy is converted to the first Stokes wave because of the accompanied SRS
effect, followed by the conversion between the first and the second Stokes
waves. This would lead to a strong second Stokes wave that may surpass the
anti-Stokes wave in the power. The other is the non-degenerate FWM process
involving the pump wave, the first and the second Stokes waves and the anti-
Stokes wave. In microresonators, the phase mismatches ($\Delta\nu$) of these
FWM processes are reflected by the difference of resonant frequencies of
related modes [30], i.e.:

$\Delta\nu^{1}=2\omega_{s,1}-\omega_{0}-\omega_{s,2}$ (1)
$\Delta\nu^{2}=\omega_{0}+\omega_{s,1}-\omega_{as,1}-\omega_{s,2}$ (2)

where $\omega_{0}$ indicates the resonant frequency of the pumped mode,
$\omega_{s,1}$, $\omega_{s,2}$ are resonant frequencies of modes that support
the first and the second Stokes waves, respectively, $\omega_{as,1}$ is the
resonant frequency of the anti-Stokes mode.

Clearly, the FWM phase-matching condition can be altered by tailoring the
dispersion of the microresonator, which is implemented _via_ tuning the core
width of the GeSbS waveguides. In our experiments, we designed mainly two
types of GeSbS microresonators, with a difference in the cavity dispersion
[see Fig. 7(b)]. In detail, in microresonators with a waveguide width of 1.7
$\mu$m, the calculated cavity dispersion indicates that both of the phase
mismatch values $\Delta\nu^{1}$ and $\Delta\nu^{2}$ are close to zero, while
with a width of 2.4 $\mu$m, the phase mismatch is large [see Fig. 7(c) and
Fig. S-3].

As a result, distinguished Raman lasing dynamics are observed. In the case of
small phase mismatch, the FWM processes will be dominant, leading to single-
mode and cascaded Raman lasing when the pump power is increased [Fig. 7(d,
e)]. In contrast, in the case of large phase mismatch, a remarkable broadband
comb spectrum is observed mainly around the pump wave and the first Stokes
wave [see Fig. 7(g, h)]. This is understood that when the energy conversion to
the second Stokes wave is suppressed as being largely phase mismatched, the
accumulated phase in the first Stokes wave would surpass the FSR of the
resonator and start to convert energy to the neighboured resonant modes. As a
consequence, the spontaneous Kerr nonlinear process is triggered, which leads
to the generation of “sub-Kerr-combs” around the first Stokes wave and around
the pump wave. The FWM phase-matching conditions at different pump wavelengths
are also estimated, cf. the SI, in which the phase mismatch value
($\Delta\nu^{1}$) is slightly decreased with an increase in the pump
wavelength. As such, a smooth transition from the single-mode cascaded Raman
lasing to the Raman-Kerr comb state is observed, cf. the Raman lasing spectra
presented in Fig. S-4.

Indeed, such a Raman-Kerr comb has been previously reported in whispering
gallery mode crystalline resonators, which was also attributed to the cavity
dispersion effect [44]. However, due to the fact that performing dispersion
engineering in such resonators is difficult, the pump frequency has to be
carefully selected to meet the required dispersion condition. In this context,
our work may contribute to providing a flexible photonic platform that allows
for engineered Raman lasing performance.

We also performed numerical simulations in both dispersion conditions
underlying the two microresonator structures (i.e. the waveguide width of 1.7
$\mu$m and 2.4 $\mu$m). The simulation is based on the _Lugiato-Lefever_
equation with the complete form of the Raman response included [44]. As a
result, both the cascaded Raman lasing and the Raman-Kerr comb are observed by
simulations, which show good agreement with experiment results. In addition,
simulations also indicate that the cascaded Raman lasing represents a stable
state in the cavity, while the Raman-Kerr comb is a non-stable state.

###  3.4 Tunability of Raman Laser

We next demonstrated the tunability of the Raman Lasers in the FWM phase-
matching condition, which is by means of tuning the pump wave or by tuning the
operating temperature on the photonic chip. As a result, by consecutively
couple the pump wave into the resonant modes of the microresonator, both the
first and the second Stokes waves are shifted accordingly, see Fig. 8(a, b).
The tested tuning range for the first Stokes wave is 1615-1658 nm and that for
the second Stokes wave is 1720-1755 nm, while the pump wavelength is tuned
within the telecommunication $C$-band (1540-1565 nm).

Moreover, the Raman laser can also be continuously tuned by tuning the
temperature. It is observed that with an increase in the temperature, the
first Stokes wave is red shifted, see Fig. 8(c,d). By tuning the temperature
of $\sim$40 ${}^{\circ}\mathrm{C}$, the first stokes wave is continuously
swept over one FSR (ca. 220 GHz) of the microresonator.

Therefore, with a combination of both the pump laser and the temperature
tuning schemes, single-mode Raman lasing at an arbitrary wavelength in the
range 1615-1755 nm is accessible. In principle, such a tunability on the Raman
lasing is unlimited since the Stokes wave is only coupled to the pump wave
with a fixed frequency offset. Yet, at the moment, we are limited by the
operational bandwidth of our laser sources as well as the optical fiber
amplifiers. On another aspect, the FWM phase-matching condition should always
be carefully controlled as it may drift over the wavelength and becomes
detrimental to the laser tunability.

Figure 4: Tunability of the Raman laser. Discrete tuning of (a) first Stokes
and (b) second Stokes pumped at $C$-band boosted by an EDFA. (c) The pump
frequency is tuned within a thermally red-shifted resonance. The output power
is normalized to the peak emission at each pump wavelength. (d) Individually
measured first Stokes wavelengths of the microring resonator corresponding to
the different temperatures. Continuous tuning of the Stokes wavelength over
$\sim$220 GHz (more than 1-FSR).

##  4 Conclusion

In summary, we have presented an engineered Raman lasing in an integrated
GeSbS microring resonator with a high $Q$-factor (above 106). We achieved the
single-mode and the cascaded Raman lasing, together with a broadband Raman-
Kerr comb, by tailoring the dispersion of the microresonator. We also provided
an insightful understanding of the effect of dispersion on the interaction of
the Kerr-Raman effect. Moreover, single-mode Raman lasing at an arbitrary
wavelength in the range 1615-1755 nm is accessible by combining the pump laser
tuning and the temperature tuning schemes. By comparing Raman laser
characteristics based on different material platforms [Table S-1], our ChG-
based Raman microresonator displays a relatively competitive advantages in the
low pumping threshold (ca.3.25 mW) and high slope efficiency (ca. 13.6$\%$).
Further improvement is expected by improving the intrinsic Q-factor and
optimizing the coupling design. Our results pave the way for the generation of
varietal on-chip Raman lasers and Kerr frequency combs covering the NIR to MIR
range based on the ChG photonic platform.

FundingNational Key R$\&$D Program of China under Grant (2019YFA0706301),
National Science Foundation of China (NSFC) (U2001601, 61975242, 61525502,
61435006, 61490715), the Science and Technology Planning Project of Guangdong
Province (2019A1515010774), the Science Foundation of Guangzhou City
(202002030103).

Disclosures The authors declare no conflicts of interest.

See Supplement 1 for supporting content.

##  Appendix A Engineered Raman Lasing in Photonic Integrated Chalcogenide
Microresonators: supplemental document

This document provides supplementary information to “Engineered Raman Lasing
in Photonic Integrated Chalcogenide Microresonators,” including GeSbS Raman
spectroscopy, experimental setup, detailed calculation of frequency mismatch,
numerical simulations and material platforms comparison.

###  A.1 Raman spectroscopy measurement

The Raman spectrum of the GeSbS film deposited on a pure quartz substrate was
measured at room temperature using the Raman Spectrometer (Renishaw inVia
Reflex). The pump wavelength of the laser is 785 nm, see Figure. 5. Lorentz
fitting of the Raman spectra was carried out to distinguish the vibrational
frequencies of the Raman-active phonon. The possible frequencies of molecular
bond vibration modes of GeSbS films are listed in figure [45, 46], and the
corresponding peaks are fitted by dotted lines in Fig.5.The main peak gain is
located at around 330 cm-1 (9.9 THz), corresponding to the vibrational
frequencies of the GeS4/2 bond[47].

Figure 5: Measured Raman Spectra of the GeSbS film and corresponding phonon
modes.

###  A.2 Experimental setup for Raman lasers measurement

The experimental setup for measuring the Raman lasers in GeSbS microrings is
schematically illustrated in Fig. S2, similar to Ref [40]. Briefly, a tunable
continuous wave (CW) laser (Toptica CTL 1550) was used as the pump laser,
which was amplified by an erbium-doped fiber amplifier (EDFA, Amonics
AEDFA-33-B-FA). The polarization of pump light was aligned with fiber
polarization controllers (FPCs) to TE polarization of the waveguide. The
output power was monitored using Oscilloscope to realize the effective
detuning between the pump laser and resonance. The results of Raman lasers
spectra were recorded by two optical signal analyzers (OSA, Yokogawa AQ6370D
with available wavelength range from 0.7$\mu$m to 1.7$\mu$m and a wavelength
resolution of 20pm, and AQ6375B with available wavelength range from 1.2$\mu$m
to 2.4$\mu$m a wavelength resolution of 50 pm) ). The temperature controller
(TEC) is applied to keep thermal stability of the on-chip microrings during
the Raman laser measurement.

Figure 6: Schematically illustrating the experimental setup for Raman lasers
generation. Figure 7: (a)A schematic illustrating the non-degenerate FWM
between the pump,1st Stokes, 2nd Stokes and anti-Stokes modes.(b)Calculated
the frequency mismatch value of non-degenerate FWM for the two microrings with
the width of 1.7 $\mu$m and 2.4 $\mu$m.

###  A.3 Frequency matching for FWM process

Beside the frequency mismatching of degenerated FWM discussed in the main
text, here, we calculated the frequency mismatching values of the non-
degenerate FWM process involving the pump wave, the first and the second
Stokes waves and the anti-Stokes wave, see Fig. 7. In this case, the
calculated cavity dispersion indicates that the phase mismatch values
($\Delta\nu$) in microresonators with a waveguide width of 1.7 $\mu$m is also
close to zero, while the phase mismatch is large in the microring with a width
of 2.4 $\mu$m.

Moreover, the different phase mismatch values lead to distinguished dynamics
of the Raman lasing when the microresonators are pumped at different waves.
The phase mismatch values of both microrings with the pump waves ranging from
1530 nm to 1560 nm are shown in Fig.8(a, b). Markedly, in the microring with a
width of 1.7 $\mu$m, the $\Delta\nu$ is increasing at shorter pump waves,
leading to the suppressed cascaded Raman lasering. As a result, the
spontaneous Kerr nonlinear process is triggered, which leads to the generation
of “sub-Kerr-combs” around the first and the second Stokes waves when pumped
at 1541.5 nm [Fig. 8(b)], while pumped at 1560.2 nm, the typical cascaded
Raman laser could be observed [Fig. 8(c)]. For the microring with a width of
2.4 $\mu$m, the frequency mismatch values are all large for different pump
waves, see Fig. 8(d), leading to the similar Raman combs when pumped at both
1540.4 nm and 1563.2 nm [Fig. 8(e, f)]. Such phenomena further illustrate the
frequency mismatching of the FWM plays a significant role in the SRS as well
as the Raman lasing in our GeSbS microresonators.

Figure 8: Calculated frequency mismatch values of the degenerate FWM process
between the pump wave, the first and the second Stokes waves for the microring
with a width of (a) 1.7 $\mu$m and (b)2.4 $\mu$m, respectively, at various
pump wavelengths from 1535 nm to 1560 nm. The corresponding first Stokes is
spanning from around 1613 nm to 1650 nm for both microrings. Measured Raman
spectra for the microring with 1.7 $\mu$m width when pumped at (c) 1541.8 nm,
(d) 1563.2 nm with the same pump power of 35 mW, respectively. Measured Raman
spectra for the microring with 2.4 $\mu$m width when pumped at (e) 1540.4 nm,
(f) 1563.2 nm with the same pump power of 20 mW, respectively.

###  A.4 Numerical simulations

The following section introduces the modelling of the Raman-Kerr comb in GeSbS
microresonators. The master equation reads:

$\displaystyle\frac{\partial}{\partial t}A_{\mu}=$
$\displaystyle\left(-\frac{\kappa}{2}-i\delta_{\omega}-iD_{\text{int
}\mu}\right)A_{\mu}+\sqrt{\kappa_{ex}}s_{in}\cdot\delta_{\mu}$ (3)
$\displaystyle-
ig_{\mu}F\left[\left(1-f_{R}\right)|A(t,\theta)|^{2}A(t,\theta)+\right.$
$\displaystyle\phantom{=\;\;}\left.f_{R}\cdot F^{-1}\left[h_{R}(\mu)\cdot
F\left[A^{2}(t,\theta)\right]_{\mu}\right]A(t,\theta)\right]$

where Aμ is the complex amplitude with respect to the resonant mode $\mu$,
which in the Fourier domain reads A(t, $\theta$) ($\theta$ stands for a fast
axis corresponding to the intracavity phase domain $\theta\in[-\pi,\pi)$ and t
is the slow-time frame), $\kappa$ indicates the resonance linewidth that
consists of both the intrinsic loss rate $\kappa_{0}$ and the coupling loss
rate $\kappa_{ex}$, $\delta_{\omega}=\omega_{0}-\omega_{p}$ is the laser-
cavity detuning ($\omega_{0}$ is the angular frequency of the pumped mode and
$\omega_{p}$ is that of the pump wave), Dint,μ is the integrated dispersion
profile, gμ is the coefficient of the nonlinear-induced frequency shift,
hR($\mu$) indicates the normalized Raman spectrum in $\mu$-domain, fR is the
Raman fraction, sin is the external pump field and $\delta_{\omega}$ is the
Kronecker delta function.

Note that without the Raman effects, this equation (also called the coupled
mode equation[48]) in the $\theta$ -domain is known as the Lugiato-Lefever
equation[49]. The Raman spectrum is obtained by the experimental measure of
the Raman gain spectrum
$\left(\operatorname{Im}\left[h_{R}(\omega)\right]\right)$ and by the
normalization on the corresponding temporal response, i.e.
$\int_{0}^{\infty}h_{R}(t)dt=1$, see Fig.9. In particular, the Raman phase
spectrum $\left(\operatorname{Re}\left[h_{B}(\omega)\right]\right)$ can be
calculated from the gain spectrum by using the Cauchy principal value, i.e.:

$\operatorname{Re}\left[h_{R}(\omega)\right]=\frac{1}{\pi}p.v\cdot\int_{-\infty}^{+\infty}\frac{\operatorname{Im}\left[h_{R}\left(\omega^{\prime}\right)\right]}{\omega-\omega^{\prime}}d\omega^{\prime}$
(4)

Figure 9: (a) Measured and retrieved Raman gain spectrum; (b) Normalized
complete Raman spectrum, consisting of both the real part as the Raman phase
spectrum and the imaginary part as the Raman gain spectrum; (c) Normalized
Raman temporal response function.

In simulations, the laser scan process is modelled. The laser-cavity detuning
is swept over the pumped resonance, and the averaged intracavity power is
traced and is compared with a standard tilted resonance in the absence of
nonlinear parametric processes (namely in the CW mode). Upon this process, the
intracavity power trace starts to deviate from the CW mode when the detuning
is slightly above zero (in the red-detuned regime), see Fig. 10(a), indicating
the generation of light fields at new frequencies. Indeed, in the spectrogram
of the intracavity field, broadband Raman lasing at Stokes / anti-Stokes
frequencies are observed, see Fig. 10(b). By fixing the laser detuning, the
self-evolution of the intracavity field is also modelled, whose power trace
indicates that the broadband Raman lasing is an unstable state, see Fig.
10(c). The transmitted field spectrum is then obtained by averaging a number
of the intracavity field patterns, see Fig. 10(d), which correctly reflects
the nature of the slow spectral measurement in experiments by using an optical
spectral analyzer. Meanwhile, the dynamics of cascaded Raman lasing can be
simulated using this model with a different dispersion parameter of
$D_{2}=-2\pi\times 1.5$ MHz, $D_{3}=-2\pi\times 26$ KHz.

Figure 10: (a) Modelled intracavity power trace upon a laser scan process,
which is compared with a tilted resonance profile in the CW mode. (b) The
evolution of the intracavity field spectrum over the laser detuning, which
indicates broadband Raman lasing at Stokes / anti-Stokes wavelengths. (c) The
power trace of the self-evolving intracavity field, with a fixed detuning
value of $3\kappa$, which implies an unstable filed pattern. (d) Transmitted
spectrum showing a broadband Raman-Kerr comb, which is obtained by averaging a
number $(35,000)$ of intracavity field patterns. In simulations, the second
and the third order dispersion components are $D_{2}=-2\pi\times 5$ MHz,
$D_{3}=-2\pi\times 22$ KHz, respectively, which is effective for the
microresonator with a waveguide width of $2.4\mu\mathrm{m}$. The pump power is
$30\mathrm{\leavevmode\nobreak\ mW}$.

###  A.5 comparison of various material platforms for Raman laser generation

We compared the performance of Raman lasers generated in both non-integrated
and integrated platforms, see 1. Despite the Raman laser in silica microtoroid
shows both ultralow threshold and high conversion efficiency, the non-
integrated feature hinders its practical application with high stability and
compactness. In the integrated platforms, the threshold power of our GeSbS
microring is comparable with the silicon racetrack resonator. The conversion
efficiency is the same order of magnitude compared with silicon racetrack
resonator, AlN microring and LNoI microresonator. We note that the performance
of our GeSbS microring based Raman laser can be further improved by optimizing
the quality factor, coupling coefficient and mode volume, which is of vital
importance to the realization of an ultra-efficient Raman laser and Raman comb
based on ChG microresonators.

Table 1: Performances of various material platforms for Raman laser generation Platform |  $Q_{int}(10^{6})$ |  Threshold power(mW) |  Slope efficiency |  Coupling system | Ref
---|---|---|---|---|---
Silicon photonic crystal |  4 |  0.001 |  8% |  Non-integrated | [2]
Silica microtoroid |  100 |  0.074 |  45% |  Non-integrated | [14]
Si-O-Si monolayer grafted silica microtoroid |  >10 |  0.2 |  40% |  Non-integrated | [5]
PDMS-coated silica microsphere |  >10 |  1.3 |  0.1% |  Non-integrated | [50]
As2S3 microsphere |  >70 |  0.37 |  0.013% |  Non-integrated | [32]
Silicon racetrack resonator |  2 |  1.3 |  1.1% |  Integrated | [51]
Silicon racetrack resonator |  1.38 |  20 |  28% |  Integrated | [51]
AlN microring |  2.3 |  8 |  3.6% |  Integrated | [12]
AlN microring |  1.5 |  34 |  15% |  Integrated | [12]
LNoI microresonator |  1.5 |  20 |  46% |  Integrated | [13]
Diamond microring |  0.44 |  85 |  0.43% |  Integrated | [11]
GeSbS microring |  2.2 |  3.5 |  13.86% |  Integrated | This work

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