# Brillouin nonlinearity characterizations of a high refractive index silicon
oxynitride platform

Kaixuan Ye  1 Akshay Keloth  1 Yvan Klaver  1 Alessio Baldazzi  2 Gioele
Piccoli  3 Matteo Sanna  2 Lorenzo Pavesi  2 Mher Ghulinyan  3 and David
Marpaung1  1Nonlinear Nanophotonics Group, MESA+ Institute of Nanotechnology,
University of Twente, Enschede, Netherlands
2Department of Physics, University of Trento, Trento, Italy
3Sensors and Devices, Fondazione Bruno Kessler, Trento, Italy
<EMAIL_ADDRESS>
###### Abstract

Silicon oxynitride (SiON) is a low-loss and versatile material for linear and
nonlinear photonics applications. Controlling the oxygen-to-nitrogen (O/N)
ratio in SiON provides an effective way to engineer its optical and mechanical
properties, making it a great platform for the investigation of on-chip
optomechanical interactions, especially the stimulated Brillouin scattering
(SBS). Here we report the Brillouin nonlinearity characterization of a SiON
platform with a specific O/N ratio (characterized by a refractive index of
$n=1.65$). First, we introduce this particular SiON platform with fabrication
details. Subsequently, we discuss various techniques for the on-chip Brillouin
nonlinearity characterizations. In particular, we focus on the intensity-
modulated pump-probe lock-in amplifier technique, which enables ultra-
sensitive characterization. Finally, we analyze the Brillouin nonlinearities
of this SiON platform and compare them with other SiON platforms. This work
underscores the potential of SiON for on-chip Brillouin-based applications.
Moreover, it paves the way for Brillouin nonlinearity characterization across
various material platforms.

††journal: opticajournal††articletype: Research Article

##  1 Introduction

Silicon oxynitride (SiON), an amorphous material with a refractive index
between silicon oxide ($n=1.45$) and silicon nitride ($n=2.0$), emerges as a
promising integrated platform for both linear and nonlinear photonic
applications [1]. It has a broad transparency window spanning from visible
spectrum [2] to near-infrared range [3]. Additionally, it features optical
waveguides with low propagation losses [4], negligible multi-photon
absorption, and low tensile stress in films up to a few micrometers thick [5].

By manipulating the oxygen to nitrogen (O/N) stoichiometric ratio in SiON, its
optical properties, including both the refractive index $n$ and the Kerr
nonlinear index $n_{2}$, can be continuously tuned. In the low refractive
index regime (silica-like), these SiON waveguides exhibit reduced propagation
losses, making them advantageous for applications in biosensing [6] and
passive photonic circuits, such as ultra-high-Q cavities [7], taper designs
[8], filters and interferometers [9]. Conversely, SiON waveguides with high
refractive index (nitride-like) exhibit a more pronounced Kerr effect, making
them highly useful in optical frequency comb-based applications [10, 11] and
in on-chip entangled photon-pair generation schemes [1].

Adjusting the O/N ratio in SiON not only modifies its optical properties but
also affects its mechanical properties. The tunability in both optical and
mechanical properties makes SiON an interesting material for the investigation
of optomechanical interactions, especially the stimulated Brillouin scattering
(SBS). SiON waveguides with different O/N ratios exhibit distinct Brillouin
nonlinearities. In [12], SiON waveguides with a relatively low refractive
index ($n=1.51$), show a Brillouin gain coefficient of 0.32 m-1W-1 at 14.48
GHz. Very recently, SiON waveguides with high refractive index ($n=1.70$) have
also been explored [13], showing a Brillouin gain coefficient of 0.09 m-1W-1
at 16 GHz.

In this study, we report the Brillouin nonlinearity characterization of SiON
waveguides with a different material composition, i.e., with a refractive
index $n=1.65$. This characterization is enabled by the ultra-sensitive
intensity-modulated pump-probe lock-in amplifier setup. We analyze the
influence of various experimental settings, including modulation depth,
modulation frequency, DC bias points, and detection frequency on the
measurement results. With the optimized configurations, we successfully
determined the Brillouin nonlinearity of the SiON waveguides under test,
showing a Brillouin gain coefficient of 0.75 m-1W-1 with a Brillouin frequency
shift of 17.15 GHz. Our results complement previous characterizations of SiON
waveguides with different refractive indexes. Moreover, the analysis of the
intensity-modulated pump-probe lock-in amplifier setup extends beyond SiON,
facilitating the Brillouin nonlinearity characterization across diverse
material platforms.

##  2 SiON platform

Figure 1: (a) SEM image (with false color overlaid on the waveguide area)
showing the cross section of the sample; (b) Microscope image of the top view
of the sample; (c) Measured insertion loss of SiON waveguides in different
lengths.

The fabrication procedure of the SiON platform investigated in this work is
described as follows. We start the fabrication process by growing a 3 $\mu$m
silicon oxide layer with wet thermal oxidation on a silicon wafer. To complete
the bottom cladding, an additional 1 $\mu$m Tetraethyl Orthosilicate (TEOS)
oxide was deposited using low-pressure chemical vapor deposition (LPCVD). The
whole stack was annealed at 1050$\degree$C for a couple of hours to improve
the cladding quality. The core SiON layer was deposited with a low-temperature
plasma-enhanced chemical vapor deposition (PECVD) machine using silane,
ammonia, and nitrous oxide precursor gases. An i-line stepper lithography was
used to pattern the waveguides and to transfer them to the SiON layer using
reactive ion etching (RIE). The so-made waveguides were treated at a
temperature of 1050$\degree$C for 90 minutes in N2 atmosphere to release the
H2 bonds to improve the optical properties. The waveguides were capped by a 50
nm thick LPCVD Si3N4 film to reduce the sidewall roughness thus improving the
propagation loss. Finally, the waveguides were covered with 1150 nm thick
borophosphosilicate glass (BPSG) via LPCVD and re-flowed at 925$\degree$C for
partial planarization. Images of the fabricated device cross-section and the
chip are shown in Fig. 1 (a) and (b), respectively.

We used a cut-back method to measure the coupling and propagation loss of the
waveguides. Lensed fiber with 2 $\mu$m spot size is used to couple light into
waveguide spirals of different lengths. The coupling loss is 2.7 and 2.9
dB/facet for 1.3 $\mu$m and 2.2 $\mu$m wide waveguides respectively.
Additionally, the measured propagation losses are 0.76 dB/cm and 0.83 dB/cm
respectively, as shown in Fig. 1 (c).

##  3 Brillouin nonlinearity characterization

Accurate Brillouin nonlinearity characterization of SiON waveguides requires
an ultra-sensitive setup, given the relatively small SBS gain. For
justification, consider 1 W pump power launched into a 10 cm SiON waveguide.
Taking into account a propagation loss of $\alpha=0.8$ dB/cm and a coupling
loss of 3 dB/facet, the estimated SBS gain from the waveguide is in the range
of 0.1 dB, a magnitude easily susceptible to noise fluctuations.

Thus far, various techniques have been developed to measure on-chip Brillouin
gain. In [14, 13, 15], a single-pump setup is applied, as shown in Fig. 2 (a).
The thermally-generated Brillouin scattering signal is mixed with a local
oscillator (derived from the same laser as the pump) for heterodyne detection
with a radio-frequency spectrum analyzer (RFSA). Although straightforward,
this configuration often demands high pump power to initiate the SBS process.

Figure 2: Simplified on-chip Brillouin nonlinearity characterization setups
and typical responses. (a) Single-pump RFSA-based heterodyne measurement; (b)
Pump-probe sideband-sweeping VNA measurement; (c) Double-intensity-modulated
pump-probe lock-in amplifier measurement; (d) Triple-intensity-modulated pump-
probe lock-in amplifier measurement. Typical responses in the right panel only
serve for illustration purposes and do not represent the real measurement
results. RFSA: radio-frequency spectrum analyzer; VNA: vector-network
analyzer.

To alleviate the requirement on the pump power, pump-probe techniques are more
often applied for the on-chip Brillouin nonlinearity characterization [16, 17,
18, 19, 12, 20, 21, 22], as shown in Fig. 2 (b)-(d). The pump is usually put
at a fixed frequency. Meanwhile, the probe frequency is swept across the
Brillouin frequency shift region, either by electro-optical modulation or by
controlling the current or temperature of the laser. Fig. 2 (b) shows the
simplified schematic of the pump-probe setup based on the vector network
analyzer (VNA). By sweeping the RF frequency applied to the modulator, the
sideband of the probe will scan across the Brillouin frequency shift region of
the waveguide. The sideband and carrier of the probe will beat at the
photodiode (PD), and the Brillouin gain profile can be obtained [23, 24]. This
method enables accurate Brillouin frequency shift measurement. Nevertheless,
fluctuations in the VNA would deteriorate the signal-to-noise (SNR) ratio,
making it difficult for accurate readout when the SBS gain is small.

To enhance the SNR of the detected signal, pump-probe setups based on the
lock-in amplifier have also been developed [19, 20, 12, 17]. The lock-in
amplifier selectively detects signals pertaining to the SBS process, as a
result, the sensitivity of this technique would be significantly higher than
the above-mentioned techniques. Fig. 2 (c) shows the simplified schematic of
the double-intensity-modulated pump-probe lock-in amplifier setup for the
Brillouin nonlinearity characterization (the operating principles and the
detailed setup will be included in later subsections). While it is effective
in most cases [19, 20, 12], for samples with high Kerr nonlinearity or strong
reflection at the facets, the oscillation in the noise floor would still
obscure the signal of interest. To suppress the oscillation, a triple-
intensity-modulated pump-probe lock-in amplifier setup, as shown in Fig. 2
(d), was also developed.

In this work, we characterized the Brillouin nonlinearity of the SiON
waveguides with the intensity-modulated pump-probe lock-in amplifier
technique. In the following subsections, we start by describing the operating
principles of the double-intensity modulation setup. Subsequently, influences
of various experimental parameters are investigated in detail. We provide
guidelines for the optimized experimental configurations and justify the
conditions when the triple-intensity modulation setup is necessary. In the
end, we introduce the triple-intensity modulation setup applied in this work.

###  3.1 Intensity-modulated pump-probe lock-in amplifier technique

Figure 3: (a) Schematic of the double-intensity-modulated lock-in amplifier
setup; (b) Configurations of the pump, probe, and the optical bandpass filter;
(c) The measured SBS signal from the lock-in amplifier. The fiber peak signal
is clearly visible at the Brillouin frequency shift of 10.8 GHz, while the SBS
signal from the waveguide is obscured within the fluctuating noise floor.

Fig. 3 (a) shows the schematic and the optical spectrum of the double-
intensity-modulated pump-probe lock-in amplifier setup. The pump (1560.67 nm)
and probe (frequency downshifted from the pump by tens of GHz) are coupled
into the waveguide from opposite directions. The pump frequency is fixed while
the probe frequency is swept by changing the current of the laser. Both the
pump and probe are intensity-modulated with RF signals at slightly different
frequencies, $\Omega_{RF1}$ (10 GHz) and $\Omega_{RF2}$ (10 GHz + 75 kHz). To
achieve sufficient SBS gain, the pump is amplified with a high-power erbium-
doped fiber amplifier (EDFA1). In the meantime, the probe is also amplified by
EDFA2 to compensate for insertion losses and ensure adequate optical power at
the photodiode. Two circulators (Cir1 and Cir2) are placed after the EDFAs to
separate the transmitted probe from the pump and safeguard the probe laser
against residual pump light. Additionally, polarization controllers (PC1 and
PC2) are added to align the polarization of the pump and the probe. The
transmitted probe, together with the reflected pump, comes out from Port 3 of
Cir1. A bandpass filter is deployed to filter out the reflected pump and
solely transmit the probe signal to the photodiode. Subsequently, the output
of the photodiode is connected to a lock-in amplifier that detects signals at
frequency $|\Omega_{RF1}-\Omega_{RF2}|$ (75 kHz).

The optical spectrum configurations of the pump, probe, and bandpass filter
are presented in Fig. 3 (b). The pump frequency is fixed at the stopband of
the bandpass filter, while the probe frequency is scanned within the passband
of the filter. At each probe frequency, the lock-in amplifier collects the
beating signal, which pertains to the SBS process. Having the probe frequency
scanned across the Brillouin frequency shift region of both the fiber and the
waveguide, the Brillouin gain profiles of both the fiber and the waveguide
under test can be obtained.

In the experiment, the sweep speed of the probe must be slower than the time
constant of the lowpass filter inside the lock-in amplifier for accurate data
acquisition. Additionally, the step frequency of the sweeping needs to be
sufficiently small to resolve the linewidth of the SBS responses of both the
fiber and the waveguide.

In an ideal scenario, the lock-in amplifier measurement would display distinct
SBS responses from both the fiber and the waveguide. Leveraging the well-
studied properties of the single-mode fiber, the fiber peak in the experiment
can serve as a reference for both locating the Brillouin frequency shift and
calculating the Brillouin gain coefficient of the waveguide. Given the fiber
peak and the waveguide peak reading from the lock-in amplifier is $V_{\rm
fiber}$ and $V_{\rm wg}$, respectively, the Brillouin gain coefficient of the
waveguide can be calculated as below [19]:

$g_{\rm{B},\rm{wg}}=\frac{V_{\rm{wg}}}{V_{\rm{fiber}}}\frac{g_{\rm{B},\rm{fiber}}L_{\rm{eff,fiber}}P_{\rm{pump,fiber}}}{L_{\rm{eff,wg}}P_{\rm{pump,wg}}}$
(1)

While Eq. (1) provides a direct approach for estimating the Brillouin gain
coefficient of the waveguide, it lacks consideration for the influence of
experimental settings on measurement outcomes. Illustrated in Fig. 3 (c), sub-
optimal experimental configurations would lead to oscillations in the noise
floor, obscuring the SBS response of the waveguide even when the SBS response
of the fiber is evident. This complication hinders the accurate estimation of
the Brillouin gain coefficient of the waveguide using Eq. (1).

###  3.2 SBS process in the intensity-modulated pump-probe lock-in amplifier
setup

To investigate the influences of various experimental settings, it is
imperative to derive the SBS process with relevant parameters included.
Assuming the pump is coupled from $z=0$ and probe is coupled from $z=L$, the
SBS process in the waveguide is governed by [25]:

$\displaystyle-\frac{dP_{pr}}{dz}$ $\displaystyle=g_{B}P_{p}P_{pr}-\alpha
P_{pr}$ (2) $\displaystyle\frac{dP_{p}}{dz}$
$\displaystyle=-g_{B}P_{p}P_{pr}-\alpha P_{p},$

where $P_{pr}$ and $P_{P}$ is the intensity-modulated pump and probe signal,
$g_{B}$ is the Brillouin gain coefficient, and $\alpha$ denotes the
propagation loss.

The intensity-modulated pump and probe are influenced by the DC bias and the
modulation depth, which can be expressed as:

$\displaystyle P_{p}\approx\frac{P_{p0}}{2}\left[1-{\rm
cos}\phi_{B1}J_{0}(m_{1})+2{\rm sin}\phi_{B1}J_{1}(m_{1}){\rm
cos}(\Omega_{RF1}t)\right]$ (3a) $\displaystyle
P_{pr}\approx\frac{P_{pr0}}{2}\left[1-{\rm cos}\phi_{B2}J_{0}(m_{2})+2{\rm
sin}\phi_{B2}J_{1}(m_{2}){\rm cos}(\Omega_{RF2}t)\right]$ (3b)

where $P_{p0}$ and $P_{pr0}$ denote the average power of the pump and probe.
The term $\phi_{B}=\frac{\pi V_{bias}}{V_{\pi,DC}}$ signifies the phase shift
induced by the DC bias, while $m=\frac{\pi V_{RF}}{V_{\pi,RF}}$ represents the
modulation depth of the intensity modulator. The symbols $J_{0}$ and $J_{1}$
correspond to the zero- and first-order Bessel function applied to the
modulation depth, i.e., $J=J(m)$.

The amplified probe can be calculated by applying expressions in (3b) into
(2). While the differential equations in (2) cannot be solved analytically,
assuming the SBS gain is small and dropping the DC terms in (3b), the
transmitted probe power can be approximated as:

$\displaystyle P_{pr(z=0)}$ $\displaystyle\approx P_{pr0}{\rm
sin}\phi_{B2}J_{1}(m_{2}){\rm cos}(\Omega_{RF2}t)e^{-\alpha L}\ \times$ (4)
$\displaystyle\left[1+g_{B}P_{p0}{\rm
sin}\phi_{B1}J_{1}(m_{1})\int^{L}_{0}{\rm cos}\left(\frac{2\pi}{\lambda_{\rm
RF1}}z-\Omega_{RF1}t\right)e^{-\alpha z}dz\right]$

where $\lambda_{\rm RF1}=\frac{2\pi c}{n_{g}\Omega_{RF1}}$ is the wavelength
of the envelop of the intensity-modulated pump.

The second term in (4) describes the SBS signal while considering the
influence of various factors, including propagation loss, DC bias points,
modulation depths, and modulation frequencies. This expression converges to a
similar but simplified form as presented in [17] assuming that both intensity
modulators are biased at the quadrature point, the modulation frequencies are
low, and the propagation loss is negligible. However, it is crucial to note
that these assumptions are generally not applicable in real scenarios, and all
these parameters would influence the detected signal in the experiments.

###  3.3 Influences of DC bias voltages and modulation depths

Figure 4: (a) The DC part and the modulation part of the optical power at
different DC bias points, which contribute to the noise floor and the signal
in the lock-in amplifier measurement, respectively; (b) Measured noise floor
at the lock-in amplifier at various bias voltages.

The influence of the DC bias voltages and modulation depths can be
investigated with (3b) and (4). As shown in (4), only the beating between the
AC terms in (3b) will be detected by the lock-in amplifier. The DC terms in
(3b), which represents the average optical power, primarily contributes to the
noise received at the photodiode [26]. Fig. 4 (a) depicts the AC and DC terms
in (3b) at various bias angles. With a constant bias, increasing the
modulation depth, i.e., increasing the RF power, would increase the signal
strength. Conversely, tuning the bias angle affects both the signal strength
and the average optical power. At the quadrature bias angle
($\Phi_{B}=0.5\pi$), the AC term is the highest, however, it also leads to a
high DC term. Shifting the DC bias towards the null point ($\Phi_{B}=0$) would
reduce both the signal and the noise strength. Nevertheless, the DC term drops
quicker than the AC term, which potentially leads to a higher SNR.

The optimized configuration of the bias voltage applied to the intensity
modulators is a trade-off between the signal strength and the noise floor
level. To keep the noise floor low while maintaining the signal strength, the
DC bias point in the experiments should be kept between 0 and $0.5\pi$, which
is similar to the low-biasing technique widely used in the microwave photonics
field [27]. Fig. 4 (b) shows the measured noise floor at the lock-in amplifier
at various bias voltages. In the experiments, we put the bias voltage between
2.0 and 2.5 V for the best SNR. However, notice that the drifting of the
modulator might result in different optimized bias voltage.

###  3.4 Influences of modulation frequencies and detected frequency

Figure 5: (a) Interaction between the intensity-modulated pump and probe when
the waveguide length $L$ is much shorter than the modulation envelop
$\lambda_{\rm RF1}$. (b) Brillouin gain from the waveguide when $\lambda_{\rm
RF1}$ is much larger than the waveguide length $L$ or $\lambda_{\rm RF1}$ is
smaller or comparable to $L$. (c) Detected signal strength at the lock-in
amplifier in these two situation.

The modulation frequencies of the pump and probe would influence the strength
of the detected signal at the lock-in amplifier. Fig. 5(a) illustrates the
interaction between the intensity-modulated pump and probe inside the
waveguide. The optical wavelength (in the range of micrometers) is much
shorter than the waveguide (in the range of centimeters). However, the
envelope of the pump $\lambda_{\rm RF1}$, which is determined by the
modulation frequency, might have a wavelength that is comparable to the
waveguide length. As a result, the modulation frequency of the pump might
influence the total SBS gain.

Two extreme scenarios are considered in Fig. 5 (b). When $\lambda_{\rm RF1}$
is much longer than the length of the waveguide $L$, i.e., when the modulation
frequency is low enough, the pump strength inside the waveguide would be
different at any given time, depending on the phase of the pump envelopes. In
other words, the SBS gain from the waveguide will oscillate at the modulation
frequency. Conversely, when $\lambda_{\rm RF1}$ is comparable to or even
shorter than the spiral length, the pump power inside the waveguide would be
almost constant, leading to a diminished amplitude in the SBS gain
oscillation. The influence of the modulation frequency on the SBS gain is also
reflected in the integration term in (4).

Since the lock-in amplifier detects the signal at the beating frequency of the
pump and probe, lower SBS gain oscillation amplitude would lead to a lower
amplitude in the detected signal, as shown in Fig. 5 (c). Consequently, from
the signal strength point of view, a relatively lower modulation frequency is
preferred in the experiment.

Furthermore, an inappropriate modulation frequency may lead to a potentially
inaccurate evaluation of the Brillouin gain coefficient. Typically, the
Brillouin gain coefficient of the waveguide is determined by comparing the SBS
signal from the fiber and waveguide peak. Taking into account the influence of
the modulation frequency, the Brillouin gain coefficient can be calculated as:

$g_{\rm{B},\rm{wg}}=\frac{V_{\rm{wg}}}{V_{\rm{fiber}}}\frac{g_{\rm{B},\rm{fiber}}P_{\rm{pump,fiber}}\int_{0}^{L_{\rm
fiber}}{\rm cos}\left(\frac{2\pi}{\lambda_{\rm
RF1}}z\right)dz}{P_{\rm{pump,wg}}\int_{0}^{L_{\rm wg}}{\rm
cos}\left(\frac{2\pi}{\lambda_{\rm RF1}}z\right)e^{-\alpha z}dz}$ (5)

When the modulation frequency $\Omega_{\rm RF1}$ is too high (in the order of
tens of GHz), i.e., the wavelength of the envelope $\lambda_{\rm RF1}$ is
comparable to the waveguide length, the detected SBS signals from both the
fiber and the waveguide would be small, and the SNR of the measured signal
would be poor. When $\lambda_{\rm RF1}$ is larger than the length of the
waveguide but not the fiber, only the fiber peak would be diminished, and the
calculation based on (1) would overestimate the Brillouin gain coefficient of
the waveguide. When $\lambda_{\rm RF1}$ is substantially larger than the
length of both the waveguide and the fiber, the expression in (5) converges to
(1), and the detected signals will also be the strongest.

However, applying an excessively low modulation frequency is also discouraged.
Given that EDFA is applied to amplify the intensity-modulated pump and probe,
the amplified spontaneous emission (ASE) from the EDFA will significantly
increase when the modulation frequency is too low, leading to a rise in the
noise floor. In our experiment, we set the the modulation frequencies at 10
MHz and 10.075 MHz for the pump and probe respectively, corresponding to
$\lambda_{\rm RF1}$ of approximately 30 m. This value is much longer than both
the waveguide (3 cm) and the fiber (5 m) lengths while the ASE from the EDFA
remains negligible.

Figure 6: Measured input-referred noise spectrum of the lock-in amplifier
setup.

The selection of the detected signal frequency is mainly related to the
technical noise in the setup. Fig. 6 shows the measured input-referred noise
spectrum of the lock-in amplifier setup. While the noise at low frequencies is
relatively high, the measured noise is close to the white noise floor from 75
kHz. By modulating the pump and the probe signal at slightly different
frequencies (10 MHz and 10 MHz + 75 kHz in our experiment), this configuration
shifts the detected frequency from DC to 75 kHz, significantly reducing the
influences of technical noise at low frequencies.

###  3.5 Influences of the facet reflection and the Kerr effect

For samples with high reflection at the facet, strong oscillation would appear
in the noise floor in the dual-intensity-modulated pump-probe lock-in
amplifier setup. This oscillation is caused by the mixing between the
reflected pump, which is comparable or even higher than the probe, and the
transmitted probe. As shown in Fig. 3(c), the oscillation frequency in the
noise floor is close to the free spectral range (FSR) of the Fabry-Perot (FP)
cavity formed by the two facets of the sample, indicating that the transmitted
spectra of FP cavity is imprinted into the noise floor. Consequently, to
reduce the influence of the oscillation in the noise floor, samples with anti-
reflection coating at the facets are preferred. Moreover, high-rejection
optical bandpass filter can also be introduced to filter out the reflected
pump.

Figure 7: (a) Schematic of the triple-intensity-modulated lock-in amplifier
setup; (b) The optical spectra of the two pumps, the probe, and the optical
bandpass filter; (c) The measured SBS signals from the 3 cm long SiON
waveguide and the 5 m long optical fiber in the setup. The noise floor is
lower compared to the double-intensity modulation setup and the waveguide peak
appears at 17.15 GHz.

The noise floor oscillation is also caused by the Kerr effect in the
waveguide. Due to the Kerr effect, the FSR of the cavity would change as a
function of time:

$\frac{dFSR}{dt}=\frac{dFSR}{dP_{p}}\cdot\frac{dP_{p}}{dt}\approx\frac{2\pi
n_{2}c}{n_{g}^{2}LA_{\rm eff}}\cdot\left[P_{p0}\Omega_{RF1}{\rm
sin}\phi_{B1}J_{1}{\rm sin}(\Omega_{RF1}t)\right]$ (6)

in which $n_{2}$ is nonlinear index, $c$ is the speed of light in vacuum,
$n_{g}$ is group index, $L$ is the waveguide length, and $A_{\rm eff}$ is the
effective optical mode area.

As indicated by (6), the Kerr effect imparts the pump oscillation onto the FSR
of the cavity. This FSR oscillation affects the transmitted probe, giving rise
to spurious signals at the beating frequency $|\Omega_{RF1}-\Omega_{RF2}|$. In
other words, the Kerr effect also contributes to the noise floor oscillation
in the intensity-modulated pump-probe lock-in amplifier setup. To alleviate
the influence of the Kerr effect, the pump variation needs to be reduced,
which can be realized with the triple-intensity-modulated pump-probe
technique.

###  3.6 Triple-intensity modulation pump-probe lock-in amplifier setup

Fig. 7 (a) shows the schematic of the triple-intensity-modulated pump-probe
lock-in amplifier setup. The core of this setup is the same as the double-
intensity modulation setup, with the addition of an auxiliary Pump 2 (1561.154
nm). Pump 2 is modulated by an RF signal ($\overline{\Omega_{\rm RF1}}$) at
the same frequency but with an inverse phase compared to the RF signal applied
to Pump 1. Pump 1 and Pump 2 are combined with a 50:50 splitter and are sent
through a polarizer before being amplified by EDFA1. This dual-pump
configuration cancels out the pump power fluctuation inside the waveguide, as
shown in the inset of Fig. 7 (a). As indicated by (6), the influence of the
Kerr effect can be minimized consequently. The spectrum configurations of the
two pumps, the probe, and the optical bandpass filter are shown in Fig. 7 (b).
Pump 2 operates at a considerably higher frequency than Pump 1, ensuring the
generated SBS signal from Pump 2 is at the stopband of the filter and would
not influence the determination of the Brillouin frequency shift.

The measurement result with the triple-intensity-modulated pump-probe lock-in
amplifier setup is presented in Fig. 7 (c). The noise floor is much lower
compared to the double-intensity modulation. Moreover, the oscillation in the
noise floor is negligible. The SBS response from the SiON waveguide is clearly
visible at a Brillouin frequency shift of 17.15 GHz with a Brillouin gain
coefficient of 0.75 m-1W-1.

##  4 Discussions

Table 1: Comparison between different SiON platforms

|  Refractive index |  Propagation loss [dB/cm] |  Brillouin gain coefficient [m-1W-1] |  Brillouin frequency shift [GHz] |  Linewidth [MHz]
---|---|---|---|---|---
[12] | 1.51 | 0.25 | 0.32 | 14.48 | 105
[13] | 1.70 | 0.1 | 0.09 | 16 | 350
This work | 1.65 | 0.8 | 0.75 | 17.15 | 177

Table 1 summarizes the Brillouin nonlinearities of the SiON platform in this
work, alongside two additional SiON platforms in the literature [12, 13].
Varied refractive indexes, in other words, different O/N ratios, result in
distinct Brillouin nonlinearities, confirming the tunability of the SBS
responses in SiON. Despite the refractive index of the SiON in this study
falling between those reported in [12] and [13], the Brillouin nonlinearity of
this platform, particularly the Brillouin gain coefficient and Brillouin
frequency shift, deviates from the values presented in [12] and [13]. This
deviation can be attributed to the diverse mechanical properties of SiON.
Considering that the Brillouin nonlinearity is intricately linked to both the
optical and mechanical properties of the material. While optical properties
are primarily dictated by stoichiometry, mechanical properties significantly
depend on the fabrication process [28]. Variations in mechanical properties,
i.e., Young’s modulus, density, and Poisson ratio, can lead to substantial
disparities in Brillouin nonlinearities. Consequently, a comprehensive
exploration of the mechanical properties of SiON is imperative for further
Brillouin nonlinearity characterizations in SiON platforms.

From the characterization perspective, this work discusses various on-chip
Brillouin nonlinearity characterization techniques, with a particular emphasis
on a detailed analysis of the intensity-modulated pump-probe lock-in amplifier
technique. Employing the triple-intensity-modulated pump-probe setup with the
optimal configurations, we successfully detected the SBS responses from SiON
waveguides with a gain below 0.1 dB. This intensity-modulated pump-probe lock-
in amplifier setup proves to be well-suited for Brillouin nonlinearity
characterizations of platforms with comparable SBS gain, such as silicon
nitride, or aluminum oxide. However, for platforms exhibiting substantially
stronger Brillouin nonlinearity, as observed in tellurite-covered silicon
nitride [29], chalcogenide [23], or thin-film lithium niobate [30],
alternative techniques can also be considered.

Funding The authors acknowledge funding from the European Research Council
Consolidator Grant (101043229 TRIFFIC) and Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO) Start Up (740.018.021) and EC within the
Horizon 2020 project EPIQUS (grant 899368).

Disclosures The authors declare no conflicts of interest.

Data Availability Statement The data that support the findings of this study
are available from the corresponding authors upon reasonable request.

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