1. Introduction

Developments in nonlinear phenomena in integrated photonic platforms have created remarkable advancements for on-chip optical signal processing [1,2] and spectroscopy [3,4]. Integrated waveguides not only provide high mode confinement but also the ability of dispersion engineering [5,6], which is crucial in order to design devices capable of both broadband and efficient light conversion. Among the various nonlinear interactions, four-wave-mixing (FWM) has been utilized in a wide range of applications such as wavelength conversion [7,8], optical frequency comb generation [9,10] and optical sampling [11,12].

Various material platforms have been investigated for on-chip FWM, such as silicon (Si) [7], Hydex [13], silicon nitride, chalcogenide glasses [14] and III-V semiconductors [15]. Si and chalcogenides offer some of the highest intrinsic third-order nonlinearity but the former suffers from high nonlinear losses at telecommunication wavelengths while the latter is not CMOS fabrication compatible and still lacks reliability. Despite its weak nonlinearity, low loss fabrication of Hydex allows for the integration of meter-long high quality waveguides. However, Hydex, similar to silica (SiO$_{2}$), has a transparency window limited to 2 µm, such that ultrabroadband conversion is not feasible. Very promising results were recently obtained in III-V [15,16], but high performance devices such as low-loss and dispersion engineered structures are still difficult to fabricate reliably. Stoichiometric silicon nitride (Si$_{3}$N$_{4}$) has over the years appeared as a popular candidate material, with its properties often praised: CMOS-fabrication compatibility, low linear losses reaching few dB/m level, relatively high nonlinearity, and large bandgap allowing transparent operation from the visible to mid-infrared without suffering from two-photon absorption and free carrier absorption. While in the last decades there has been significant work related to FWM in Si$_{3}$N$_{4}$ waveguides, combined broadband and efficient continuous wave (CW) FWM has still eluded the platform and better performances were obtained in seemingly less suited platforms. Very recently, improved performance and even parametric gain were observed in long Si$_{3}$N$_{4}$ waveguides thanks to their ultra-low attenuation and ability to withstand high optical powers [17–19]. This however comes to a tradeoff with bandwidth, especially if low power operation is required, as often the case in CW regime: while efficiency can be improved by increasing the interaction length, it leads to a reduction of the bandwidth for a constant pump power [20]. As such distant FWM to the mid-infrared could only be obtained with pulsed operation (fs-pulse pumping) [21].

In this work, we demonstrate polarization selective broadband CW wavelength conversion in low-loss Si$_{3}$N$_{4}$ waveguides. Leveraging mature fabrication and dispersion engineering on transverse electric (TE) and transverse magnetic (TM) polarizations, we show selective broadband conversion in the telecommunication band and thulium amplification band (near 2 µm ) in 0.5 m long waveguides with low pump power in the tens of mW. Moreover, phase-matching based on higher-order dispersion terms can yield far-detuned and tunable idler formation in either the O-band or the mid-infrared (around 2.5 µm) with low-power CW pumping.

2. Waveguides and experimental procedures

We studied the performance of three Si$_{3}$N$_{4}$ waveguides with different cross-sections. All are fabricated based on the Damascene process [22], fully cladded with SiO$_{2}$ and folded in spirals (see Fig. 1(d) inset). The three waveguides are 0.5 m long with nominal width $\times$ height dimensions of 2.1 µm $\times$ 0.745 µm, 2.0 µm $\times$ 0.760 µm, and 2.3 µm $\times$ 0.755 µm. Their group velocity dispersion (GVD) is plotted in Fig. 1(a) for TE and TM polarizations. In Fig. 1(b) and (c), we show a close up of the GVD in the telecom and 2 µm band, respectively. For all waveguides, we see that TM mode presents a zero dispersion wavelength (ZDW) in the telecom L-band, while TE mode has a ZDW in the thulium amplification band. Such dispersion characteristics should allow for broadband operation in the telecommunication band for TM pumping, and in the thulium band for TE pumping.

 

Fig. 1. (a) Simulated GVD for the three waveguides under test, and for TE and TM modes; (b) Zoom of the GVD in the telecom band. TM mode shows a ZDW; (c) zoom of the GVD in the 2 µm band. TE mode shows a ZDW. (d) Experimental setup. PC: polarization controller, WDM: wavelength division multiplexer, LF: lensed fiber, PBS: polarization beam splitter, PD: photodetector, OSA: Optical spectrum analyzer. Inset: picture of the SiN chips with long spiral waveguides; (e) Example of superimposed experimental FWM spectra between a 1.6 µm pump and a tunable C/L band signal for TM polarization in the 2.1 µm $\times$ 0.745 µm waveguide.

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The experimental setup is shown in Fig. 1(d) and consists of a pump-probe architecture. Different sets of sources, combining telecommunication lasers tunable in the C/L bands and 2 µm lasers, including a fixed wavelength semiconductor source and a home-made tunable thulium fiber laser (TDFL). Apart from the TDFL, the pump and signal seeds are amplified before being combined using either a WDM or a power coupler, and coupled into the waveguide with a lensed fiber. We estimate the input coupling loss around 6 dB for telecom wavelength and 5 dB for 2 µm. The output light is collected with a lens and collimated back to a fiber to measure the spectrum on an optical spectrum analyzer (OSA). Depending on the wavelength range to monitor, either the Yokogawa AQ6376 (1500 to 3400 nm) or AQ6375B (1200 to 2400 nm) is used. The polarizations of both beams are controlled and continuously monitored at the output of the waveguide using a polarization beam splitter. The FWM idler wave at frequency $\omega _i$ satisfies the energy conservation $2\omega _{p} = \omega _{s} + \omega _{i}$, with $\omega _p$ and $\omega _s$ the pump and signal frequency, respectively. The conversion efficiency of the FWM process, defined as ${\textrm{CE}} = {\textrm{P}_{\rm i}}/{\textrm{P}_{\rm s}}$ with $\textrm{P}_{\textrm{i}}$ and $\textrm{P}_{\textrm{s}}$ the output idler and signal powers, respectively, is estimated based on the measured spectra as illustrated in Fig. 1(e).

3. Broadband wavelength conversion

We first investigated the potential of broadband conversion by leveraging pumping near the ZDW. To achieve broadband FWM, phase matching condition needs to be continuously ensured for large detuning between the fixed pump wavelength and the signal. The phase mismatch can be expressed as $\kappa = \Delta \beta + 2\gamma P_P$. Here $\Delta \beta = \beta _s + \beta _i - 2\beta _P$ is the linear phase mismatch with $\beta _s$, $\beta _i$, and $\beta _P$ the signal, idler and pump propagation constants, respectively. The nonlinear contribution is proportional to the pump power $P_P$ and the waveguide nonlinear parameter $\gamma = \frac {2\pi \textrm{n}_2}{\lambda \textrm{A}_{\textrm{eff}}}$, with n$_2$ the nonlinear parameter and A$_{\textrm{eff}}$ the effective mode area. The CE is then given by (with $\alpha$ the linear loss):

We estimated the FWM performance of the 0.5 m long waveguides by plotting the theoretical CE contour maps for different pump and signal wavelengths. The $\gamma$ used is based on the extracted wavelength dependent A$_{\textrm{eff}}$ extracted from COMSOL simulations and for a n$_2$ = 2.4x10$^{-19}$ m$^2$/W [23]. The loss was measured to be 5.5 dB/m at 1550 nm. Examples of such maps are shown in Fig. 2(a) and (c) for the 2.1 µm $\times$ 0.745 µm waveguide pumped in the telecommunication band and for a 50 mW of pump power. For TE pumping (Fig. 2(a)), a narrow band FWM is expected since the pump is far from the ZDW as seen in Fig. 1(b). In addition, owing to the relatively flat dispersion over the entire telecom band, we do not expect to see any significant bandwidth variations with pump wavelength. A completely different behavior is predicted for the same waveguide for TM (Fig. 2(c)). A much broader and flat operation can be obtained when pumping slightly detuned from the theoretical 1603 nm ZDW, exploiting the merger of the main phased-matched region around the pump with the higher-order phase-matched lobes, as will be explained in detail in the following section.

 

Fig. 2. (a) Theoretical contour graph of CE (dB) of the 2.1 µm $\times$ 0.745 µm waveguide for TE polarization and telecom band pumping; (b) Experimental CE (dots) and theoretical CE (lines) for TE pumping at 1600 nm and 1605 nm with 75 mW of coupled pump power; (c) Theoretical contour graph of CE (dB) of the 2.1 µm $\times$ 0.745 µm waveguide for TM polarization and telecom band pumping; (d) Experimental CE (dots) and theoretical CE (lines) for TM pumping at 1600, 1605 and 1610 nm with 50 mW of coupled pump power.

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The experimental data is in good agreement with the theoretical prediction. In Fig. 2(b), the TE experimental CEs for two pumping wavelengths (1600 and 1605 nm) are plotted together with the theoretical curves. We estimate the coupled pump power to be 75 mW. The CE quickly drops and no significant difference is observable when changing the pump wavelength. For TM, Fig. 2(d), we see a broadband and flat CE for the 1600 nm pump. When increasing the pump wavelength, the bandwidth starts to decrease as expected. We obtain a slightly lower CE for 1610 nm pumping, due to a decrease in coupled pump power from 50 mW to 40 mW. Owing to experimental limitations, we could not characterize the waveguide with a shorter pump wavelength. However, from Fig. 2(b), pumping below 1600 nm would result in the separation between the main and high-order phase matched lobes, reducing the flatness of the CE spectrum. At the optimal pumping wavelength of 1600 nm, we measure a two-side 3 dB bandwidth of 150 nm, limited by the tuning range of the signal seed.

The waveguides can also provide broadband wavelength conversion in the 2 µm by exploiting TE pumping. For this experiment, the available pump is a 2.004 µm laser diode amplified with a thulium doped fiber amplifier. Based on the 3D CE maps, we identified the 2.0 µm $\times$ 0.760 µm waveguide to have the best potential for flat and broadband conversion given this fixed pump wavelength. The measured spectra at the output of the waveguide for a 200 mW coupled pump power are shown in Fig. 3(a), while the retrieved CE spectrum is plotted in Fig. 3(b). The data is once again in good agreement with the theoretically expected CE and we measure a two-sided 3 dB bandwidth of 120 nm. The idler is efficiently generated up to 2.2 µm, once again limited by the tuning range of our TDFL. A slight discrepancy is measured over the further detuned lobe. As mentioned, this lobe is the result of higher-order dispersion phase matching and is more sensitive to waveguide dimension fluctuations, which will tend to broaden and flatten the peak as routinely observed in optical fibers [24]. A slightly wider CE spectrum could be obtained by red-detuning the pump wavelength, which in our case is limited by the laser diode.

 

Fig. 3. (a) Superimposed experimental FWM spectra in the 2.0 µm $\times$ 0.760 µm waveguide for a 2.004 µm pump and tunable TDFL for TE polarization; (b) Experimental CE (dots) and theoretical CE (lines) for TE pumping at 2004 nm with 200 mW of coupled pump power. Theoretical TM CE is plotted in dotted line.

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4. Distant wavelength conversion

The phase-matching condition can be satisfied not only around the pump wavelength but also far-detuned owing to the effect of the higher-order dispersion terms when the pump is slightly offset from the ZDW. We can approximate the linear phase mismatch in terms of the GVD and the fourth order dispersion coefficient $\beta _4$ as $\Delta \beta = \beta _2\Delta \omega ^2 + \beta _4\Delta \omega ^4/12$, for a difference between the pump and the signal angular frequencies given by $\Delta \omega$. A higher-order phase-matched lobe, in addition to the main band around the pump, occurs when $\beta _2\beta _4 < 0$ [25]. Relying on the theoretical CE contour plots, we identified far-detuning phase-matched regions of interest for the 2.3 µm $\times$ 0.755 µm waveguide when combining telecom and 2 µm sources, as illustrated in Fig. 4(a) and (d). Once again, polarization switching unlocks two different wavelength regions. For TE polarization, for which the theoretical ZDW is located at 2.017 µm, the TDFL is acting as the pump while the C/L band source tuned between 1538 and 1615 nm acts as the signal. The idler wave is generated around 2.5 µm as shown in Fig. 4(b). Spectra for several pump wavelengths are collected and the extracted CEs as a function of idler wavelengths are plotted in Fig. 4(c). The spectral zone accessible, given our available sources, corresponds to the dashed region highlighted in Fig. 4(a). We see the idler forming between 2.4 and 2.56 µm with a clear increase when higher-order phase matching is satisfied. We are able to measure a CE higher than −40 dB detuned by 1000 nm for a coupled pump power estimated at 200 mW. The experimental trend is in excellent agreement with the theoretical prediction. The same experiment was repeated for TM polarization, with now the telecom source acting as a pump to take advantage of the theoretically predicted ZDW at 1.633 µm. For such configuration, the theory predicts an efficient conversion to an idler around 1.35 µm when coupling a 2 µm signal (Fig. 4(d)). Spectra for several pump wavelength between 1595 and 1615 nm, and the TDFL tuned from 1821 to 1998 nm are collected, such as shown in Fig. 4(e), and the CEs plotted in Fig. 4(f). Once again the experimental data, with the peak of CE due to higher-order dispersion phase matching, is agreeing extremely well with the theoretical prediction, and phase matched idlers tunable between 1340 and 1430 nm can be generated.

 

Fig. 4. Distant idler conversion results for TE polarization in the 2.3 µm $\times$ 0.755 µm waveguide: (a) Theoretical contour graph of CE (dB) for thulium band pumping;(b) spectrum for a 1.950 µm pump and 1.6 µm signal; (c) Experimental contour CE (dB) for various pumps in the thulium and a signal in the C/L-band. Distant idler conversion results for TM polarization in the 2.3 µm $\times$ 0.755 µm waveguide: (d) Theoretical contour graph of CE (dB) for L-band pumping;(e) spectrum for a 1.6 µm pump and 1.95 µm signal; (f) Experimental contour CE (dB) for various pumps in the L-band and a signal in thulium band.

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Finally, we measured the scaling trends for distant wavelength conversion and for narrow-band conversion in the L band. To that end, an optimized WDM has been used in the experimental setup in order to reach the best coupling for two fixed wavelength seeds. For distant conversion, we used 1600 nm and 1950 nm, while 1568 nm and 1570 nm were used for narrow band characterization. Such optimized setup resulted in the possibility to couple more power, in particular for the two fixed telecom signals. The results for distant conversion in TE and TM polarizations are shown in Fig. 5(a) and (b), respectively. From the data, we extract a linear fit with a slope of 2.2 and 1.9 for TE and TM, respectively. The deviation from the expected slope of 2 can have several roots. First, we observed some fluctuations in the output power of the TDFL. Second, the fact that we are covering a very broad wavelength range, leads to some uncertainties in the actual values of signal and idler powers, as would be the case in any platform. On the one hand, we could not fully characterize the linear losses over the entire 1.3 µm - 2.5 µm range. And on the other hand, there could be some differences in coupling losses at the output of the waveguide over such a broad range of wavelengths. Nevertheless, the trend is close to expected, an indication that despite possible variations our waveguides are well suited for broadband operation. The CE as a function of coupled pump power, Fig. 5(c), for the narrow-band case shows a quadratic behavior for both TE and TM cases. Note that a higher CE close of −18 dB was obtained owing to the improved coupled pump power. From this data, we extracted a nonlinear coefficient $\gamma$ at 1570 nm of approximately 0.66 W$^{-1}$m$^{-1}$ for TE and 0.46 W$^{-1}$m$^{-1}$ for TM, in agreement with the theoretically expected values of 0.8 W$^{-1}$m$^{-1}$ for TE and 0.75 W$^{-1}$m$^{-1}$ for TM.

 

Fig. 5. (a) CE as a function of coupled pump power. The pump is at 1950 nm and the signal at 1600 nm for an idler generated near 2494 all in TE. (b) CE as a function of coupled signal power. The pump is at 1600 nm and the signal at 1950 nm for an idler generated near 1356 nm, all in TM. (c) CE as a function of pump power for a signal at 1568 nm and a pump at 1570 nm. Dashed lines are linear fits.

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5. Discussion and conclusion

In this work, we have demonstrated a polarization selective broadband conversion in stoichiometric Si$_{3}$N$_{4}$ waveguides. Broadband conversion can be obtained in the telecommunication band over more than 150 nm for TM polarization and in the 2 µm thulium-amplification band for TE polarization over 120 nm thanks to particular dispersion characteristics of the waveguides resulting in optimized ZDWs. Compared to other CW FWM work carried out in silicon nitride based platforms, our results show a significant bandwidth improvement, despite the use of long waveguides. As we can see from Table 1, previous work used mm long waveguides to reach bandwidth larger than a few nm, as to counterbalance the non-optimized dispersion engineering. In Ref. [26], the high nonlinearity of Si$_7$N$_3$ is leveraged and enables good CW CE of −25 dB over 90 nm with less than 25 mW of pump. However, the platform presents high losses such that increasing the CE, either through increasing the pump power or the length, would be challenging. High pump power can be coupled in the waveguides presented in refs [17,18,20] which are characterized by an extreme low loss. As such more efficient FWM can be obtained in very long waveguides. However, in [20], owing to the reduced height and large width, such waveguides have a low nonlinearity and dispersion engineering is limited, explaining the relatively low CE despite 1 W of coupled pump power, and the narrow conversion bandwidth. Extremely high CW pump power could be coupled in the 2 m long waveguide in [17] resulting in a record 12 dB gain but the bandwidth is small owing to dispersion. The waveguides used in our study can be dispersion engineered while maintaining a loss around 5 dB/m in the telecom and around 7 dB/m in the 2 µm band. In addition, the coupled pump power used in our experiment is low, in the few tens of mW, solely limited by the experimental setup. We expect that the CE can be significantly improved by coupling higher pump power. It is also worth noting that, as for any dispersion engineered waveguides, variations in cross section due to fabrication tolerances can impact the conversion behavior. While fabrication is constantly undergoing significant progress, height fluctuations in the few nm can still occur at the wafer scale [22]. In our study, we saw that such deviation from nominal dimension could result in a spectral shift of the optimal pumping wavelength, however without impacting the overall expected behavior in terms of reach and bandwidth.

Table 1. Comparison of CW FWM in silicon nitride platforms. BW: bandwidth; PIA: phase insensitive amplification; PSA: phase sensitive amplification.

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Together with broadband conversion around the pump wavelength, we also showed the possibility of distant wavelength conversion projecting towards the O-band and the mid-infrared in the same waveguide by leveraging TE and TM polarizations, through higher-order dispersion phase matching. This anchors the potential of the platform for performing simultaneously inside and outside the telecommunication band. We show that idler waves around 1.3 µm and 2.5 µm are generated, following trends predicted theoretically. The idler generation in mid-infrared at such low pump powers indicates that the losses still remain low in this wavelength range and that the reach could be pushed deeper in the mid-infrared by engineering the dimensions of the waveguide.