1. Introduction

Light emission by stimulated Raman scattering (SRS) has been proposed as an attractive solution for the problematic area of laser and amplifier in silicon photonics technology. Detrimental two-photon absorption (TPA) and subsequently induced free-carrier absorption (FCA) hugely limit the conversion efficiency and elevate the lasing threshold despite silicon’s superior Raman gain [1,2]. Although the use of reverse-biased p-n junction can effectively suppress these losses by sweeping out the free carriers, the methodology is far from satisfying due to its huge excess energy consumption and complicated design [3]. On the other hand, chalcogenide glasses are well known for their high Kerr nonlinearity and Raman gain, large refractive index for optical confinement and transparency far into infrared region. TPA is small with negligible FCA loss in chalcogenide glasses, benefited from their large band-gap energy (E_g~1.78eV) and low carrier mobility [4]. These properties make chalcogenide an ideal platform for integrated nonlinear optics, leading to the recent demonstrations of devices based on cross-phase modulation [5], four-wave mixing [6] and SRS [7].

Among the chalcogenide glasses, As₂Se₃ is particularly appealing for SRS-based application with its largest reported Raman gain [8]. Raman shift for As₂Se₃ and silicon is 7THz [9] and 15.6THz [2] respectively, making As₂Se₃ a more energy efficient material choice than silicon for Raman application with its larger Stokes photon energy. Over the past decades, Raman gain of As₂Se₃ chalcogenide glass has been characterized [9,10] and investigated in fiber laser both theoretically [11] and experimentally [7]. Chalcogenide are traditionally not considered for optical interconnects due to the fact that silicon possesses a slightly larger Raman gain and tighter optical confinement. In this paper, we show by theoretical investigation that As₂Se₃ waveguide Raman laser out-performs silicon Raman laser in spite of these drawbacks. As₂Se₃ waveguide Raman laser displays many desirable laser characteristics in term of ultra-high conversion efficiency, low threshold and wide linear operation region. By comparison through a defined figure-of-merit (FOM) factor, we clearly illustrate that As₂Se₃ waveguide Raman laser is more energy efficient than its silicon counterpart. The significance of various losses and optimization of laser performance through device miniaturization and end-facet reflectivity are also discussed.

2. Theoretical model

Figure 1(a) presents a typical cross-sectional diagram of the As₂Se₃ rib waveguide used, with the same dimensions as the silicon waveguide discuss in [2] for the ease of comparison. Such waveguide has been demonstrated experimentally using complementary metal-oxide-semiconductor (CMOS) technology on SiO₂ substrates [12]. Mode solving with commercial software Rsoft FemSIM yields an effective area A_eff = 1.97µm² and 1.7µm² for As₂Se₃ and silicon waveguide respectively. The simulated fundamental TE₀ mode field pattern for the As₂Se₃ waveguide is shown in Fig. 1(b). The cavity consists of an As₂Se₃ waveguide of length L, closed at two ends with coatings to form a Fabry-Perot cavity as illustrated in Fig. 1(c). Electric field (E) are normalized such that power P = |E|². E_inc and E_out stand for incident pump and output Stokes field respectively. The axis along the length of the waveguide is denoted as z-axis, with the positive direction pointing towards the right. Superscripts ‘f’, ‘b’ represent the forward and backward propagating waves, while subscripts ‘p’ and ‘s’ stand for pump and Stokes respectively. R_front is the reflectivity of the mirror at z = 0, R_back is that at z = L.

 

Fig. 1 Schematic diagrams of As₂Se₃ waveguide Raman laser, (a) waveguide cross-section dimensions, (b) simulated mode field pattern of the fundamental TE₀ mode (A_eff = 1.97µm2) and (c) cavity structure.

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In our earlier work, a theoretical model based on counter-propagating waves has been developed for waveguide silicon Raman laser [13]. The same model can be applied to As₂Se₃ waveguide by removing the FCA term as depicted in Eq. (1) below. This model is similar to that used in mid-infrared chalcogenide fiber laser by assuming continuous wave (CW)-operation and negligible higher order Stokes waves [11]. We differ in the inclusion of TPA terms and resolving of power into counter-propagating electric field amplitudes to account for cavity enhancement effect. In Eq. (1), g_r is Raman gain coefficient, λ is wavelength, α is linear propagation loss and β is TPA coefficient. The steady state operation of waveguide Raman laser can thus be simulated by numerically solving Eq. (1), subjecting to appropriate boundary conditions as shown in Eq. (2). Ideal coupling condition is assumed such that transmission coefficient T = 1-R. We noted here that the validity of this model can be extended to other nonlinear materials such as Ge_11.5As₂₄Se_64.5 [14].

3. Simulation results and discussions

Results for silicon Raman laser are obtained using model and parameters described in our earlier work [13]. It will be used as a benchmark for comparison for the proposed As₂Se₃ waveguide Raman laser in this paper. Simulation parameters for As₂Se₃ waveguide are set as L = 4.8cm, α_p = α_s = 0.25dB/cm, β = 0.25cm/GW and g_r = 5.1cm/GW [8] according to experimental characterization. This Raman gain value is measured using continuous-wave (CW) pump [8], which is more appropriate for our proposed device than that measured in [9] with a pulsed pump. Pump wavelength (λ_p) is set at 1550nm to take advantages of the high power Erbium doped fiber amplifier (EDFA) in this range [2]. Stokes wavelength (λ_s) is expected at 1608nm. We start with analyzing the single-pass Raman gain of silicon and As₂Se₃ waveguide by setting all reflectivities to 0, as shown in Fig. 2 . No net gain is observed in normal silicon waveguide. When a reversed bias of 25V is applied to sweep out free carrier, a net gain occurs and saturates around 6dB, in good agreement with experimental measurement [2]. Raman gain of As₂Se₃ waveguide is similar to that of the reversed-bias silicon waveguide in low pump power region, but out-performs silicon beyond 1.5W pumping. It should be noted that this value can be hugely reduced when waveguide length or cavity losses are optimized. No gain saturation is observed, with a 16dB gain observed at 4W pumping. We believe the negligible FCA loss and low TPA loss account for this improvement. Furthermore, bandwidth of As₂Se₃ stimulated Raman gain is 2 THz [9], much wider than the 105GHz of silicon. Such wide bandwidth will enable on-chip amplification of ultra-high speed signals up to Tera-bit/s that is not achievable by silicon. As₂Se₃ waveguide thus provides a promising platform for amplification, without the need for extra voltage supply.

 

Fig. 2 Single-pass Raman gain for As₂Se₃ and silicon waveguide under normal (τ_eff = 23ns) and 25V biased (τ_eff = 1ns) operation [2].

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We proceed to investigate and compare both waveguide Raman lasers by setting the front facet reflectivity as R_front,p = R_front,s = 30%. The back facet is covered with broadband high reflectivity coating (90%), following the same reflectivity as in the silicon Raman laser experiment [2]. No lasing is observed for normal silicon waveguide due to the absence of net gain. We thus focus on analyzing key Raman laser performance parameters of As₂Se₃ waveguide and 25V-biased silicon waveguide. For both Raman lasers, conversion efficiency maximizes at 1W pumping as shown in Fig. 3(a) . This is due to the trade-off between cavity enhancement effect and loss increment with respect to the growing intra-cavity power, which represents the most energy-efficient operation point of Raman lasers. One should note that this is well within the optical damage threshold of the material, which can be further enhanced by methodologies such as anti-reflection (AR) coating, better mode matching and improvement of waveguide quality [15]. As₂Se₃ waveguide Raman laser is much greener in terms of energy consumption, highlighted by the maximum conversion efficiency of 31%. This efficiency is around five times better than the 6% efficiency of silicon, even without taking the energy dissipation of 25V bias voltage into account. This could be attributed to the lower TPA and negligible FCA loss in As₂Se₃ waveguide, as well as its larger Stokes photon energy compared to silicon. Considering the large experimental uncertainty in its future exploration [9], we also include the conversion efficiency curve for a smaller Raman gain of 2.2 cm/GW in Fig. 3(a). The device still outperforms its silicon counterpart in high pump power region under such low Raman gain. From the Stokes output curve in Fig. 3(b), the problematic gain reduction and output saturation of silicon Raman laser at high pumping level is also not observed in As₂Se₃ waveguide. A linear operation region up to 1.5W pump power is subsequently obtained. The lasing threshold is another key parameter for integrated laser sources, mainly due to the raise in cost as the pump power increases. We evaluate the lasing threshold by locating the pump power at where the overall gain in cavity reaches unity. It was found to be 299mW and 443mW for As₂Se₃ and silicon respectively. To investigate the influences of various losses in the As₂Se₃ waveguide Raman laser, two special cases are also shown in Fig. 3(b). We explicitly simulate the Stokes output when TPA and linear propagation loss are assumed absence respectively. The results suggest that linear propagating loss improvement will have a greater impact in reducing lasing threshold and enhancing conversion efficiency due to the relatively low TPA loss in As₂Se₃. Impurity absorption and side-wall scattering are the major contributions limiting linear propagation loss [16]; future waveguide fabrication advancement in these areas is thus highly recommended. Despite its relatively smaller Raman gain, As₂Se₃ out-performs silicon as the material candidate for on-chip Raman laser with the negligible FCA loss.

 

Fig. 3 (a) Conversion efficiency for As₂Se₃ under different measured g_R [8,9] and silicon; (b) output power for As₂Se₃ and silicon waveguide Raman laser. Stokes output subjected to no TPA (β = 0cm/GW) or linear propagation (α_p = α_s = 0dB/m) loss are also displayed.

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Due to the precious space on chip, footprint size (waveguide length in our case) is a very important consideration in optical interconnect component design. Increment of waveguide length will incur two counter-acting effects: enhancement of Stokes wave from longer interaction length and reduction of Stokes wave due to the increased loss. As waveguide length increases from 5mm, lasing threshold drops because enhancement effect outplays the loss at low pump power around threshold. This scenario reverses after the pump power is fully depleted at around 55mm waveguide length, forming a minimum threshold there at 296mW, as shown in Fig. 4(a) . The same explanation accounts for the variation of maximum conversion efficiency at 1W pumping. The turning point occurs at a shorter waveguide length of 17mm, mainly due to the higher losses incurred at this high pump power. Maximum conversion efficiency achieved is 40%. Miniaturization by waveguide length reduction is thus beneficial in the perspective of conversion efficiency.

 

Fig. 4 Influence of waveguide length (L) on (a) lasing threshold and optimal conversion efficiency; (b) FOM for both As₂Se₃ and silicon waveguide Raman laser.

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To compromise the trade-off between lasing threshold and optimal conversion efficiency, we specifically define a figure of merit (FOM) factor for waveguide Raman laser as the absolute ratio of Stokes output power (1W pumping) to the lasing threshold power. This is illustrated as Eq. (3) below. Maximum FOM value of 1.1 occurs at 30mm waveguide length for As₂Se₃ waveguide Raman laser as shown in Fig. 4(b), which is the optimized operating point in terms of energy consumption with low threshold and high conversion efficiency. This is almost an order of magnitude higher than the maximized FOM value for silicon waveguide Raman laser at 60mm waveguide length, indicating a huge advantage for As₂Se₃ waveguide Raman laser in terms of energy efficiency and devices miniaturization capability.

Further reduction of As₂Se₃ waveguide Raman laser threshold can be achieved by optimizing the end facet reflectivity, as illustrated in Fig. 5(a) . We use the optimized cavity length (L) of 30mm here. Front end-facet reflectivity for pump (R_front,p) is set at 0% to maximize the coupled-in pump power [13]. Lasing threshold reduces when we increase reflectivity for Stokes wave (R_front,s), mainly due to the lower cavity loss incurred. 100mW threshold is achieved when we increases R_front,s to 90%, which is three times better than the 310mW at 30% reflection. The variation of conversion efficiency curve with respect to R_front,s increment displays a parabolic shape, with maximum value of 35% occurring at R_front,s = 24%. Trade-off between Stokes output growth from cavity enhancement and drop in out-coupling ratio accounts for that. As shown in Fig. 5(b), a further FOM factor optimization to 1.4 can be achieved at 60% reflectivity.

 

Fig. 5 Influence of Stokes front end-facet reflectivity on (a) lasing threshold and maximum conversion efficiency, (b) FOM.

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4. Conclusion

In conclusion, we have presented a comprehensive investigation of As₂Se₃ waveguide Raman laser as a promising laser source for optical interconnect using silicon Raman laser as the benchmark. We have numerically demonstrated that As₂Se₃ waveguide is a more energy-efficient integrated platform for amplification and lasing than silicon despite its smaller Raman gain. Seven times efficiency enhancement and 33% threshold reduction are simultaneously achieved, without the need for any external voltage supply. Through comparison with the defined FOM factor for energy efficiency quantification, we further illustrated the advantage of As₂Se₃ waveguide Raman laser in terms of device miniaturization and energy consumption. We also explored the influence of end-facet reflectivity on As₂Se₃ waveguide Raman laser with optical cavity size, in which a minimum 100mW threshold is achieved by employing high reflection cavity.