1. Introduction

Chalcogenide glasses (ChGs) are considered a top contender for integrated photonics due to their exceptional nonlinear optical properties and wide transparency window [1–16]. When combined with the advanced lithographic techniques that enable small-volume confinement (wavelength scale), the nonlinearity can be significantly enhanced, enabling the realization of nonlinear signal processing with reduced device length and lower optical power requirements [3,15]. To illustrate this point, the amorphous binary ChG—arsenic trisulfide (As₂S₃)—is a well-established candidate for harnessing various nonlinear optical effects in photonic integrated circuits (PICs) because it combines low loss, typically 0.2 dB/cm [17], low two-photon absorption (TPA), high nonlinearity, $n$₂ one hundred times that of silica, a record of 20 dB Raman gain [18], and 52 dB Brillouin gain [19]. Successful demonstrations using this platform include supercontinuum generation in the near- and mid-infrared window [4,13], the development of Brillouin-based light storage [9], microwave photonic sources and filters [3,5,6], as well as seamless heterogeneous integration with other CMOS-compatible platforms [7,10]. Alternative ChG's compositions, such as GeSbS, have recently emerged as an attractive platform due to the arsenic-free nature and higher glass transition temperature $T$_g of 300 °C, which enables the deposition of high-quality silica cladding [20]. Efficient Brillouin laser and Kerr frequency combs have been demonstrated in this ternary sulfide ChG platform [11,21,22].

While it is evident that sulfide-based ChGs are promising materials for PICs, research into ChGs with larger linear refractive index ${n_0}$ is of great interest to further reduce device size and operational power, as the nonlinear index ${n_2}$ of a material typically scales with ${n_0}$, according to Miller’s law [23]. Furthermore, in our recent work, we also demonstrated using numerical simulations that ChGs with larger $ {n_0}$ and comparable mechanical properties with As₂S₃ can greatly improve the confinement of the guided acoustic waves (GAWs) required to induce forward intermodal Brillouin scattering (FIBS) [24]. With a larger $n$₀, the acoustic wavevector ${k_{AC}}\; $ that is proportional to the effective index difference between the optical fundamental and higher order modes $({n_{\textrm{eff}}^0 - n_{\textrm{eff}}^1} )$, can be further increased through engineering the waveguide dimension, thereby resulting in an acoustic wavelength further below the cut-off wavelength such that the acoustic mode of interest can be confined. Observing this FIBS process serves as a crucial prerequisite for achieving a broadband optical isolator in a non-suspended waveguide structure. Additionally, FIBS also enables the generation of a less dissipative fundamental flexural acoustic mode, resulting in a smaller Brillouin shift that is typically accompanied by a higher phonon lifetime and hence narrower linewidth. These characteristics hold the potential for enhancing the performance of microwave devices and acousto-optic modulators [25].

It becomes apparent that the selenide ChG family, in particular arsenic triselenide (As₂Se₃) with $n$₀ = 2.84 offers significant advantages due to its high refractive index, particularly when combined with the increased nonlinear index—four times that of As₂S₃ [26] and the increased Brillouin gain coefficient; ${g_\textrm{B}}$ scales as the eighth-power with the refractive index (${g_\textrm{B}} \propto n_0^8$) [15,27], so a three-fold improvement in gain is anticipated in the selenide platform if other factors such as opto-acoustic overlap integral, elasto-optic coefficient, material density, frequency shift and linewidth are constant. It is worth noting that a marginal two-fold gain improvement has been reported where the experimental ${g_\textrm{B}}$ values for both As₂Se₃ and As₂S₃ fibers are 6.75 ${\times} $ 10⁻⁹ m/W and 3.90 ${\times} $ 10⁻⁹ m/W, respectively [28]. Low-loss As₂Se₃ planar waveguides have been fabricated [12,29,30] and their photosensitivity beyond and near the bandgap energy has been explored for waveguide direct writing [31] and grating inscription [29]. Stimulated Brillouin scattering (SBS) in As₂Se₃ optical fibers has been studied [32–35], but has not yet been reported for integrated planar waveguides.

Unlike bulk amorphous ChGs, the thin film deposited using vapor deposition technique have stability issues associated with the exposure to heat and light [36], as well as the oxidation at the film surface regardless of the temperature and light condition [37]. The as-deposited films (e.g. As₂S₃ and As₂Se₃) can encounter an irreversible polymerization when heated at glass transition temperature (${T_\textrm{g}}$ = 180 °C [38]) or illuminated with near bandgap light [36]. Moreover, significant photostructural changes can also occur in well-annealed evaporated film when exposed to visible light, inducing a red shift of the optical absorption edge, known as photodarkening effect [39]. Interesting facts associated with this photodarkening process is that: (1) it is attributed to a relatively low material’s bandgap energy (∼ 2 eV) and low coordination number of chalcogen atoms [39]; (2) it can be reverted via annealing below ${T_\textrm{g}}$; (3) it extends beyond the exposure to near bandgap light and encompasses the effect of more intense sub-bandgap light at around 1550 nm [40]. While the multi-photon absorption mechanisms in these ChGs are not fully understood yet, it is speculated that the major cause would be defect absorption arising from the formation of the homopolar bonds such as As-As, Se-Se, S-S, etc., and under- or over-coordinated atoms [41].

On the one hand, the photodarkening effect is useful for modifying the refractive index but at the same time compromises the stability. A notable benefit is that Bragg grating can be inscribed using TPA in ChG fibers [42,43] and these 1550 nm-induced grating stopbands can also be utilized to manipulate the Brillouin response in ChG planar waveguides [8]. Nevertheless, the reversible nature of photodarkening poses challenges for effectively utilizing and controlling ChG devices. Examples include the significant temporal drift of resonant wavelength can be observed in the ChG resonator settings [44] and the unstable spectra (power fluctuation) observed in four-wave mixing experiment [12]. Consequently, when studying the nonlinear effects of ChGs that involve high power injection, it becomes crucial to consider the photosensitivity at 1550 nm. This consideration is necessary to address the potential impact of photodarkening and ensure accurate characterization of ChG behavior under such conditions.

In this work, we characterize and study both the 1550 nm photosensitivity and SBS in As₂Se₃ planar waveguides for the first time. We conducted an initial investigation into the photodarkening effect in these waveguides by subjecting them to intense 1550 nm light. The resulting photo-induced refractive index change was confirmed through the formation of Bragg gratings in a short waveguide, facilitated by high Fresnel reflection from the chip facet. The grating was written using a sub-bandgap Hill approach that has a reversible photodarkening characteristic, with the grating response gradually fading away over the course of a few days. Furthermore, our SBS measurements reveal significant findings: a Brillouin gain coefficient ${g_\textrm{B}}$ of 7.14 ${\times} $ 10⁻¹⁰ m/W and a frequency shift ${v_\textrm{B}}$ of 7.8 GHz. Additionally, at an input power of 144 mW, the Brillouin linewidth $\mathrm{\Delta }{v_\textrm{B}}$ is measured to be 60 MHz, which is four times broader when compared to As₂Se₃ fibers. We also demonstrate that the optical loss-attributed non-uniform sub-bandgap photodarkening effect in As₂Se₃ waveguides plays a crucial role in explaining the underlying mechanisms of the observed phenomena of gain reduction and linewidth broadening in the SBS response. The following section details the design, fabrication, and the loss characterization of the As₂Se₃ waveguide designed to be mode coupling-free. Section 3 focuses on the inscription of Bragg gratings, while Section 4 covers the measurement of SBS in the As₂Se₃ waveguide.

2. Design, fabrication and loss characterization

Stimulated Brillouin scattering (SBS) stands as one of the strongest third-order nonlinear processes, emerging from the intricate interplay between photons and acoustic phonons. According to the principle of conservation of energy and momentum, the excited phonon within the SBS process carries a frequency $\mathrm{\Omega }$ and a wavevector ${\beta _a}$ that corresponds to the difference between the respective characteristics of the two optical modes (${\omega _1} - {\omega _2})$ and (${\beta _1} - {\beta _2})$, where ${\omega _m}$ and ${\beta _m}$ are the frequency and wavevector of the optical mode m. The key to achieving simultaneous optical and acoustic confinement as well as substantial Brillouin gain lies in the combination of a high-index, soft chalcogenide core with low-index, low-loss rigid claddings. Ideally, SiO₂ presents itself as the optimal cladding material for the As₂Se₃ waveguide. Nonetheless, due to the comparatively low glass transition temperature (approximately 180 °C) of As₂Se₃, the subsequent deposition temperature for SiO₂ is constrained to remain below this threshold. At such temperatures, the deposited SiO₂ tends to adopt a porous nature, thereby giving rise to appreciable optical propagation loss.

In response to this challenge, our approach encompasses the implementation of alumina (AlOx) coating, accomplished through the 130 $^\circ $C low-temperature atomic layer deposition (ALD) process. This not only serves the purpose of protection but also enhances the confinement of acoustic waves within the As₂Se₃ rib waveguide [10]. The inclusion of an ultra-thin layer of 2 nm AlOx also facilitates the subsequent spin-coating of a low-loss silica-index polymer (known as ZPU polymer). This polymer, applied as an upper-cladding material plays an important role in protecting the As₂Se₃ from oxidation and aging effects.

The proposed As₂Se₃ waveguide structure is depicted in Fig. 1(a). Notably, the SU-8 polymer is employed to prevent chemical attack from the alkaline developer utilized in the UV lithography process [45]. In the past, As₂Se₃ planar waveguides have been fabricated by both wet- and dry-etching approaches [12,30]. While the former reported a low propagation loss (0.26 dB/cm) in a 4 µm wide ∼10% shallow-etched waveguide [30], the etch is isotropic and not suitable for higher aspect ratio waveguides, thus limiting the design flexibility and practicality for on-chip waveguide components. Here we employ the latter method to fabricate a shallow-etched rib waveguide as shown in Fig. 1(a). By reducing the etch depth, the sidewall-roughness induced scattering loss can be minimized, leading to an improvement in the effective Brillouin interaction length.

 

Fig. 1. (a) The schematic diagram of the shallow etched As₂Se₃ rib waveguide structure. (b-c) Modeled effective refractive index ${n_{\textrm{eff}}}$ for four lowest order optical modes TE₁₁, TM₁₁, TE₂₁, and TE₃₁ as a function of width w at (b) $t$ = 1000 nm and (c) $t$ = 700 nm where the electric field profiles for the different mode families are illustrated above the plots. Note that the electric field profiles of the four mode types shown above the plots are corresponding to a waveguide dimension of $w$ = 2600 nm, $t$ = 700 nm and $e$ = 0.33 t.

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We set the etch depth $e $ to 33% of the film thickness t and employed finite element method (FEM) modeling to calculate the waveguide modal dispersion for various combinations of waveguide width w and film thickness t. When choosing an appropriate width w, a trade-off between optoacoustic overlap (a key metric for Brillouin gain) and sidewall roughness-induced scattering loss must be considered. In general, a smaller w enhances optoacoustic overlap but also increases scattering loss. In our study, we chose a w range of 2–3 $\mathrm{\mu}$m, ensuring a computed Brillouin gain coefficient $g$_B above 1000 W^-1m^-1. Here the ${g_\textrm{B}}$ is computed via an open-source Numerical Brillouin Analysis Tool (NumBAT) based on the finite element (FEM) approach [46]. It is imperative to underscore that, owing to the absence of comprehensive elastic property data of ZPU polymer, the simulation was performed using an air cladded As₂Se₃ waveguide structure. Although the simulated ${g_B}$ values may not precisely reflect the Brillouin response of the fabricated structure, they offer a useful estimate for preliminary assessment.

Within the study range of w, we aimed to maximize the difference in effective refractive index $\mathrm{\Delta }{n_{\textrm{eff}}}$ between the fundamental and higher-order optical spatial modes, in particular the TM₁₁ and TE₂₁ modes to mitigate mode coupling and enable low propagation loss in the two orthogonal polarization axes. Referring to Fig. 1(b-c), it can be observed that reducing film thickness t from 1000 nm to 700 nm decreases the TM₁₁-TE₂₁ mode coupling, albeit at the cost of a slightly lower optical confinement. Based on simulation and modeling results, we selected As₂Se₃ waveguides with a w of 2.6 µm, t of 700 nm, and ∼33% etch depth. This structure provides a high opto-acoustic overlap, minimizes sidewall roughness-induced scattering loss, and reduces mode coupling between the first few orders of the supported optical modes.

The arsenic triselenide rib waveguide was fabricated using the same approach as its sulfide counterpart [10]. First, a 700 nm arsenic triselenide film was deposited on a 5 µm thick thermal oxide substrate at room temperature using the thermal evaporation technique. The as-deposited film was coated with a 150 nm thick SU-8 polymer to avoid chemical attack from the alkaline developer used in the UV lithography process [45]. After resist patterning, inductively coupled plasma-reactive ion etching (ICP-RIE) with an argon-trifluoromethane gas mixture was performed to etch the exposed As₂Se₃ [47]. Under the specified conditions (RF bias power = 30 W, induction power = 300 W, CHF₃ flow rate = 20 sccm, gas pressure = 10 mTorr, substrate temperature = 20$^\circ $C), the etch rate of As₂Se₃ was measured to be 200 nm/min. Then the waveguides were coated with a 2 nm aluminum oxide AlOx layer to protect the sidewall of the As₂Se₃ waveguides from oxidation. Finally, the waveguides were cladded with a silica-index polymer (ZPU) after resist removal.

The fabricated chips consist of multiple waveguides with varying lengths: 2 cm, 8 cm, 15 cm, and 24 cm. Loss characterization was conducted by butt-coupling light into the waveguides with different lengths using lens-tip fibers with a Gaussian spot size of 2.5 µm. Through cut-back measurement, the coupling loss and propagation loss were determined to be 5.5 dB/facet and 1 dB/cm, respectively. The experimental coupling loss is slightly higher than the simulated loss attributed to the sum of mode overlap loss (3.3 dB/facet) and Fresnel reflection (1.1 dB/facet). However, the propagation loss result is comparable to the best achievable dry-etched As₂Se₃ with similar dimensions [12].

3. 1550 nm photosensitivity in As₂Se₃ planar waveguide

We conducted a Bragg grating inscription experiment based on the Hill approach [48] to investigate the 1550 nm photosensitivity of the As₂Se₃ waveguide. The experimental setup is depicted in Fig. 2(a). By launching 100 mW level optical power into the waveguide, the interference between a high-power forward and a backward optical wave that is reflected from the chip facet (Fresnel reflection ${\approx} $ 23%) can cause an index modulation along the waveguide due to the photorefractive effect.

 

Fig. 2. (a) Schematic diagram of the grating inscription setup used to measure transmission and reflection. PC: polarization controller; C: circulator; PM: optical power meter; BPF: bandpass filter; EDFA: Erbium-doped fiber amplifier. (b) Time evolution of the grating growth process with a writing laser power ${P_i}$ = 30 mW. (c-e) Grating inscription in four different 2 cm waveguide channels with different laser writing wavelengths. (c) Illustration of the writing laser profile at different wavelengths for each channel ch 1, 2, 3 and 4. (d) Transmission spectrum and (e) reflection spectrum of the grating for each channel.

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The experimental setup consists of two main parts: a laser source for writing the grating and an optical network analyzer (ONA) for measuring the transmission and reflection spectrum of the device under test (Fig. 2(a)). The laser source is amplified using an Erbium-doped fiber amplifier (EDFA), and the amplified spontaneous emission noise is then filtered by a bandpass filter (BPF). To ensure that the optical TE mode is coupled into the waveguide, the polarization controllers (PC2 and PC1) are adjusted to maximize the readings of the optical power meters (PM1 and PM2). The ONA captures both the TE- polarized transmitted and reflected light from the chip via circulators (C2 and C1) for monitoring the growth of the grating over time, and after the writing laser is turned off.

The initial step of experiment involved gradually increasing the input power of a continuous wave (CW) laser to a 2 cm long straight waveguide until a grating response was observed. While gradually increasing the input power, no gratings were observed during the initial 10 minutes of writing when the $P$_i remained below 20 mW. However, within less than 30 seconds of reaching a power of 100 mW, a distinct dip in the transmission spectrum became evident on the PM2 reading. This power level corresponds to a writing laser power ${P_\textrm{i}}$ = 30 mW or an intensity of 0.25 GW/cm² at the beginning of the waveguide, taking into account a coupling loss of 5.5 dB per facet and an effective mode area of 1.21 µm².

Figure 2(b) illustrates the evolution of the grating during the 6-minute writing process. It is worth noting from the figure that the 2.5 dB power modulation across the entire wavelength range is attributed to the Fabry-Perot effect, resulting from the reflection at the chip facet. It can be seen that a 15 dB transmission dip and a grating bandwidth of 0.025 nm can be obtained with a writing time of 6 minutes. Further, gratings were written into four different channels with different laser wavelengths as illustrated in Fig. 2(c). Their corresponding transmission and reflection spectra are shown in Fig. 2(d) and Fig. 2(e), respectively. Overall, the good alignment between the Bragg wavelengths and the writing laser wavelengths indicates precise control over the resonant wavelengths of these gratings.

Notably, the impact of the writing laser power (${P_i}$) on the grating response is worth discussing. Due to the presence of 1 dB/cm losses and 23% Fresnel reflection, an incomplete destructive interference arises from the interaction between the incoming and reflected waves with unequal amplitudes. As a result, a finite standing wave ratio (SWR) is generated, defined as (1 + $\Gamma (z )$)/(1 - $\Gamma (z )$) where $\Gamma (z )$ represents the ratio of reflected power to the incoming power at waveguide position z. Our calculations indicate that the SWR at the front facet (z = 0) and back facet (z = 2) are 1.2 and 1.6, respectively. Consequently, this leads to an upper and lower envelope for power modulation, ranging from 1.1 ${P_i}$ to 0.8 ${P_i}$ and 0.9 ${P_i}$ to 0.5 ${P_i}$, respectively. Therefore, employing a higher ${P_i}$ can cause a background dc refractive index change, potentially reducing the grating's index modulation or the visibility of the fringe pattern.

Both the dc and ac index modulations at a specific time, $\mathrm{\Delta }{n_{\textrm{DC}}}(t )$ and $\mathrm{\Delta }{n_{\textrm{AC}}}(t )$, can be estimated using Eq. (1–2) based on coupled mode theory, where ${\lambda _{\textrm{B},\textrm{i}}}$, $\mathrm{\Delta }{\lambda _\textrm{B}}(t )$ and ${\lambda _\textrm{B}}(t )$ represent the initial resonant wavelength, grating bandwidth, and resonant wavelength at time t, respectively.

By substituting the measured values, the estimated $\mathrm{\Delta }{n_{\textrm{DC}}}(t )$ and $\mathrm{\Delta }{n_{\textrm{AC}}}(t )$ at $t$ = 6 min are found to be 2 ${\times} $ 10⁻⁴ and 0.5 ${\times} $ 10⁻⁴, respectively. However, the ac index change in this study is constrained by the single-sided injection of the writing laser. Moreover, when employing a higher ${P_i}$, an additional loss is observed throughout the measured spectrum. In principle, $\mathrm{\Delta }{n_{\textrm{AC}}}$ can be enhanced by either implementing dual-sided injection of the writing laser into the chip or prolonging the exposure time. A previous report demonstrated that $\mathrm{\Delta }{n_{\textrm{AC}}} \approx $ 1 ${\times} $ 10⁻³ can be achieved in an As₂Se₃ microwire with a dual-sided input intensity sum of 0.5 GW/cm² and an exposure time of 20 minutes [42]. The report also indicates the possibility of achieving even higher $\mathrm{\Delta }{n_{\textrm{AC}}}$ with an extended exposure time. However, it should be noted that the SMF-AsSe fiber interface used in their work exhibits low loss (0.5 dB/facet for the sum of mode overlap loss and Fresnel reflection) [49], and the implementation of angle coupling can further mitigate the Fresnel reflection at the interfaces [34]. Therefore, to reproduce a $\mathrm{\Delta }{n_{\textrm{AC}}}$ of 10⁻³ or higher in our current As₂Se₃ setup, mitigation of Fresnel reflection is necessary to enable the implementation of dual-sided injection.

Owing to high birefringence of the waveguide, the grating written along the TE-polarization axis can result in a distinct Bragg resonant wavelength for the TM-polarization axis, as suggested by the classic Bragg equation (Eq. (3)), where ${n_{\textrm{eff}}}$ represents the effective refractive index and $\mathrm{\Lambda }$ denotes the grating period.

Through FEM simulation, the ${n_{\textrm{eff}}}$ for the TE- and TM- fundamental modes of the As₂Se₃ waveguide under test were determined as 2.70 and 2.64, respectively, at $\lambda $ = 1550 nm (see Fig. 1(b)). This discrepancy in ${n_{\textrm{eff}}}$, denoted as $\mathrm{\Delta }{n_{\textrm{eff}}}$, corresponds to an approximate $\mathrm{\Delta }{\lambda _\textrm{B}}$ of 30 nm, implying that ${\lambda _{\textrm{B},\; \textrm{TM}}}$ is shifted by 30 nm towards the shorter wavelength end compared to ${\lambda _{\textrm{B},\; \textrm{TE}}}$. To validate the modeled $\mathrm{\Delta }{\lambda _\textrm{B}}$, an additional experiment was conducted. By optimizing the polarization state using PC1, the measured spectra for both TE- and TM-axes were obtained for two different writing laser wavelengths ${\lambda _w}$ of 1550 nm and 1580 nm, as depicted in Fig. 3. The figure reveals that while ${\lambda _{\textrm{B},\; \textrm{TE}}} \approx {\lambda _w}$, a weak grating response with a 30 nm blue shift is observed, consistent with the above-mentioned simulation results, confirming that the dip corresponds to the Bragg condition for the TM fundamental mode.

 

Fig. 3. The transmission spectra for different laser wavelengths and polarization axes: the first and the second column illustrate the spectra for 1550 nm and 1580 nm writing wavelengths respectively; the first and second row show the spectra optimized at TE-axis and TM-axis respectively.

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Degradation in the grating properties has been observed within a few days, despite the waveguides being kept under minimal light conditions. The responses of the four gratings written under the same condition after 5 and 10 days are measured and illustrated in Fig. 4. While the grating lifetime of most gratings can be maintained over 5 days, most of them were being erased after 10 days.

 

Fig. 4. The transmission spectra of the written gratings in their initial state, after 5 days and 10 days for four different channels ch1, ch2, ch3 and ch4.

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4. SBS measurement in the As₂Se₃ planar waveguide

This section details the characterization of the backward SBS response of a 15 cm long As₂Se₃ planar waveguide using pump-probe heterodyne technique. The details and schematic of the measurement setup are depicted in Fig. 5. Both the optical pump and probe waves were divided into two separate paths originating from the same laser source. These waves were then frequency-shifted by $\omega $₀ and $\omega $_RF, respectively, filtered, and entered the chip from opposite ends. The SBS Stokes power with a Brillouin shift $\mathrm{\Omega }$ was extracted from the input end of the pump wave using a circulator and measured using a photodetector connected to an electrical vector network analyzer (VNA). By sweeping the $\omega $_RF using the VNA, we were able to observe the amplification of the modulated sideband of the probe wave when the condition ($\omega $_RF = $\omega $₀ - $\mathrm{\Omega }$) was met.

 

Fig. 5. SBS measurement setup using heterodyne technique. A laser with a carrier frequency ${\omega _c}$ is divided into two paths in a 50:50 ratio. The upper path carries pump waves, while the lower path carries probe waves. The pump wave is modulated by an electro-optic modulator (EOM), generating two sidebands with a frequency shift of ${\omega _0}$. The carrier and lower sideband are then filtered using a bandpass filter (BPF) and amplified by an Erbium doped fiber amplifier (EDFA) before entering the chip from the right-hand side. The probe wave is modulated by a sweeping RF frequency output from a vector network analyzer (VNA), and the lower sideband is filtered by a narrow BPF before entering the chip from the left-hand side. Polarization controllers PC1 and PC2 are used to optimize the polarization state for maximizing the optical output from the EOM while PC3 and PC4 ensure that both pump and probe waves entering the chip are set to TE- polarization state. The carrier and probe beats at photodetector PD, resulting in a microwave beatnote at the ${\omega _{RF}}$ produced by the VNA. Note that optical fibers are indicated by the blue line, while the RF cables are represented by the orange line.

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Figure 6(a) illustrates the Brillouin gain spectra corresponding to different input power $P$_i. It is important to highlight that the choice of input power range, ${P_\textrm{i}}$, was deliberately tailored to prevent the formation of a grating within the 15 cm As₂Se₃ waveguides. When plotting these peak Brillouin gain against input power $P$_i on linear scale axes, as depicted in Fig. 6(b), we can perform exponential fit to the data (the gray dashed lines) and further extract the gain coefficients $g$_B using Eq. (4)

 

Fig. 6. SBS in As₂Se₃ planar waveguide: (a) Measured Brillouin gain spectrum corresponding to different input pump power $P$_i. (b) Plot of linear Brillouin gain versus input power $P$_i where the gray dashed line represents exponential fitting to the data. (c) Comparison between experimental normalized gain profile at $P$_i = 144 mW with the fitted Lorentzian and Gaussian curves of the same FWHM linewidth. (d) Principle showing the impact of photorefractive effect on the SBS phase-matching condition. White and black dots represent the pump and Stokes modes in the $\omega - \beta $ space while different red arrows of different transparency indicate the SBS phase-matching condition at different position of the waveguide as labelled. (e) Modelled gain spectrum of the As₂Se₃ waveguides with different refractive index $n$₀. Note that the modelled gain spectra (red curves) do not represent the expected linewidth, instead the data represent the gain coefficient ${g_\textrm{B}}$ for the distinct acoustic modes at different frequencies computed using open-source Numerical Brillouin Analysis Tool (NumBAT).

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As illustrated in Fig. 6(a), the Brillouin linewidth $\mathrm{\Delta }{v_\textrm{B}}$ decreases from 80 MHz to 60 MHz when ${P_\textrm{i}}$ is increased from 17 mW to 144 mW. This is consistent with the theoretical model that attributes this phenomenon to the spontaneous nature of SBS initiation [50]. However, these linewidths are more than four times wider compared to that of As₂Se₃ fibers [32]. The broadening of $\mathrm{\Delta }{v_\textrm{B}}$ is associated with the decrease in phonon lifetime, which can be significantly influenced by the composition and temperature of the material. In the case of amorphous materials, viscosity also plays a prominent role in determining the phonon lifetime [51]. It is worth noting that As₂Se₃ fibers possess high gain coefficient and very narrow linewidth (approximately 13 MHz) [32], indicating that material properties are not the cause of linewidth broadening in our case. Surrounding the waveguide with a soft cladding material has also been suggested as a potential cause for linewidth broadening and gain reduction [33–35,52]. However, this explanation does not fully explain the 60 MHz linewidth as As₂S₃ waveguides cladded with a 2 nm AlOx and ZPU polymer can achieve an approximately 30 MHz linewidth under the same fabrication steps [10,15].

Further investigation into the origin of the broad linewidth is carried out by performing the gain profile analysis. We compared the experimental normalized gain profile at $P$_i = 144 mW with fitted Lorentzian and Gaussian curves having the same full width at half maximum (FWHM) linewidth of 60 MHz (see Fig. 6(c)). By focusing on the normalized gain above 0.5, we observed that while the Lorentzian curve exhibited a narrower profile than the experimental data, the Gaussian counterpart showed good agreement. The formation of this Gaussian-like gain profile is likely due to the presence of the photo-thermal effect (spontaneous nature) or non-uniform photo-induced refractive index change (photodarkening or Kerr) along the waveguide [50], caused by high propagation loss (1 dB/cm).

The impact of the non-uniform photo-induced refractive index change $\mathrm{\Delta }n$ on the Brillouin shift can be explained through a dispersion diagram, as illustrated in Fig. 6(d). The white dots, labeled as $l$ = 1, 2, and 3, correspond to the optical pump launched at ${\omega _p}$ with varying mode propagation constants ${\beta _l}$ at different points along the waveguide due to the non-uniform $\mathrm{\Delta }n$. These distinct ${\beta _l}$ values give rise to different phonon frequencies ${\mathrm{\Omega }_l}$ and wavevectors ${\beta _{a,l}}$, influenced by the acoustic mode dispersion denoted by the blue dotted line on the same axes. Consequently, the frequency of the Brillouin Stokes signal (represented by the black dots), defined as $\omega - {\mathrm{\Omega }_l}$, also exhibits position-dependent characteristics. To further verify this concept, we further model the acoustic mode that is responsible for the backward SBS process using finite element method based Numerical Brillouin Analysis Tool (NumBAT) [46] by varying the refractive index of As₂Se₃. Notably, in Fig. 6(e), the simulated Brillouin response does not take into account the prediction of gain linewidth. Instead, the peaks represent distinct acoustic modes that exhibited favorable opto-acousto overlap at the selected $n$₀ values of 2.83, 2.84, and 2.85. The blue dashed line in the figure represents the Gaussian profile depicted in Fig. 6(c). Simulation results indicated that a 20 MHz shift in the Brillouin frequency is achievable with a refractive index change of 0.01.

Drawing a definitive conclusion on whether a 0.01 index change can be achieved through the grating writing performed in this study proves challenging due to the low SWR resulting from the single-sided injection scheme. However, it is worth noting that such an index change has been observed in the grating writing process of As₂Se₃ microwires [42]. Hence, it is reasonable to assert that the observed linewidth broadening, attributed to the non-uniform photorefractive effect along the waveguide, remains applicable.

5. Discussion and conclusion

In this work, we optimize the design of As₂Se₃ planar waveguide for achieving both mode-coupling free and high SBS gain properties. The losses of the dry-etched waveguides of 1.1 dB/cm are comparable to the lowest reported values found in the literature [12].

We performed Hill grating inscription through the 1550 nm photosensitivity in the As₂Se₃ planar waveguides. These gratings provide narrowband filtering capabilities (∼0.025 nm bandwidth) and can be easily customized based on the resonant wavelength determined by the writing laser source. They also have diverse applications in the field of integrated optics, including the enhancement or suppression of nonlinear processes such as Raman scattering, Brillouin scattering, and four-wave mixing [1,8]. Additionally, they show promise in linear devices, serving functions such as narrowband filtering and temperature sensing.

Stimulated Brillouin scattering (SBS) in the As₂Se₃ platform has also been studied. The Brillouin shift and gain coefficient are measured to be 7.8 GHz and 7.14 ${\times} $10⁻¹⁰ m/W respectively, accompanied by a gain linewidth of approximately 60 MHz at input power of 144 mW. Unlike the fiber case highlighted in the introduction section, the As₂Se₃ planar waveguides in this work do not exhibit a higher ${g_\textrm{B}}$ value as compared with the lower-index As₂S₃ waveguides. Furthermore, despite having the same cladding structure, the linewidth is twice as broad as that of the As₂S₃ waveguides [15]. This discrepancy can be attributed to the non-uniform TPA-induced photodarkening effect along the waveguide due to the 1.1 dB/cm propagation loss. Therefore, the resulting gain spectrum represents the overlap of different SBS spectra originating from distinct phase-matching conditions.

Moreover, it is also important to discuss the performance stability of this platform. Foremost, the reversible photodarkening effect observed limits the lifetime of the 1550 nm-induced gratings and potentially the SBS performance, leading to linewidth broadening and gain reduction, as outlined above. A previous study has demonstrated that by increasing the energy dose or exposure time of near bandgap light, the photodarkening effect can transition from a reversible state to a permanent regime [53]. In principle, a similar effect is anticipated for sub-bandgap light. However, in the current work, the As₂Se₃ chip facets exhibit high Fresnel reflection, thereby restricting the grating writing process to the single-sided injection scheme. In this scheme, increasing the energy dose further can actually decrease the grating visibility due to the low standing wave ratio (SWR) defined earlier. Therefore, in the future, a dual-sided injection approach will be explored to generate a standing wave pattern with an improved power contrast between the antinodes and nodes. To implement this approach, it is crucial to first mitigate Fresnel reflection by leveraging heterogeneous integration technology, such as inverse tapers [10].

Furthermore, by effectively mitigating the Fresnel reflection, it becomes possible to study the SBS response at even higher power levels. This is achievable due to the suppression of grating formation when the chip is pumped from a single side. Preventing the grating formation allows us to capture the temporal evolution of SBS response under a higher pump power to verify the non-uniform photodarkening effect on the SBS linewidth broadening. By subjecting the system to prolonged exposure to elevated power levels, it should be possible to mitigate the non-uniformity of photodarkening, subsequently giving rise to an anticipated narrowing of the linewidth. Finally, it is also essential to optimize the fabrication process flow to further reduce the waveguide loss as this is necessary to minimize the power non-uniformity along the waveguide, ultimately resulting in improved gain and narrower linewidth.

The findings of this study provide valuable insights into the potential and limitations of As₂Se₃ as well as highlight the current challenges. It is evident that reducing the propagation loss of As₂Se₃ and addressing Fresnel reflection are important areas for future improvement. Additionally, there is also a need to investigate the forward intermodal Brillouin scattering in this high-index chalcogenide glass (ChG) platform, as it is expected to exhibit well-confined flexural acoustic waves. This exploration holds promising opportunities for reconfigurable non-reciprocal propagation, acousto-optic modulation and microwave narrowband filtering applications in non-suspended ChG waveguides.