1. Introduction

Nowadays, optical parametric oscillators (OPOs) have been established as broadly tunable, coherent light sources for numerous applications, for instance in spectroscopy [1,2], LIDAR [3], or trace gas sensing [4]. Unlike conventional light sources, where the wavelength tuning range is limited to tens of nanometers, determined by the electronic transitions of the dopant ions or the semiconductor’s transitions of the gain medium, the gain bandwidth of OPOs is defined by a phase-matching condition, greatly exceeding the limited bandwidth of conventional lasers and allowing for adjustment by dispersion engineering [5,6].

Depending on the selection of the nonlinear parametric gain medium, OPOs could be designed as crystal-based, fiber-based or arising waveguide-based systems [7–10]. In contrast to crystal-based OPOs utilizing $\chi ^2$ nonlinear frequency conversion [7], fiber-based OPOs (FOPOs), exploiting the $\chi ^3$ nonlinear process of four-wave mixing (FWM), provide additional advantages in terms of compactness, robustness, and high beam quality, which are of significant interest for various spectroscopic and imaging applications, such as coherent anti-Stokes Raman scattering (CARS) [11–13].

Integrated waveguides are a prominent alternative to nonlinear fibers due to smaller footprint and higher nonlinearity, which enable to further reduce the size as well as the required pump power of OPO systems. Recently, chip-based OPOs exploiting FWM in microresonators have been demonstrated and resulted in a continuous-wave (cw) output power up to 21mW with a wide frequency separation of 77 THz between the pump and signal/idler beams [14,15]. However, this large frequency separation (> 2568 cm$^{-1}$) as well as the limited cw output power are not optimal for the generation of CARS signals, particularly in the preferred fingerprint regime (< 1800 cm$^{-1}$) [16]. In this regard, synchronously pumped waveguide-based OPOs (WOPOs) show a great potential as tunable, integrated light sources for CARS as well as on-chip biological sensing applications [17–19]. In particular, silicon waveguides, with about five orders of magnitude larger nonlinearity than in photonic crystal fiber (PCF) [13,20–22], have been experimentally used as parametric gain media in OPO systems, implemented with a fiber feedback cavity at repetition rates below 100 MHz [10,20]. However, silicon waveguides suffer from their fundamental limitations of two-photon absorption (TPA) and TPA-induced free-carrier absorption at telecommunication wavelengths, which hinder on-chip integration of such WOPOs at low repetition rates due to high propagation loss [23,24].

In contrast, stoichiometric Si$_3$N$_4$ waveguides with an ultra-low propagation loss [25] have become popular in the field of nonlinear optics for the generation of FWM [26,27], self-phase modulation [28], and supercontinua [29–31]. For instance, a proof-of-concept WOPO exploiting FWM in a Si$_3$N$_4$ waveguide at 1 MHz repetition rate has been recently demonstrated and indicated the feasibility of integrated Si$_3$N$_4$ WOPOs on a chip at lowest repetition rate of 66 MHz [32]. However, the conversion efficiency of such a WOPO was limited to only about −21.5 dB, due to the high cavity loss. Towards further integration and potential applications of Si$_3$N$_4$ WOPOs in the fields of spectroscopy and imaging, it is important to increase the efficiency as well as the output wavelength tunability of such light sources.

In order to address these open issues, we present in the following a highly efficient and widely tunable Si$_3$N$_4$ WOPO exploiting degenerate FWM at 40 MHz repetition rate. The WOPO was implemented with a polarization-maintaining fiber (PMF) to provide optical feedback and was synchronously pumped with a mode-locked fiber laser at 1.03 $\mu$m center wavelength with an adjustable duration of the emitted pulses between 0.37 ps and 2.4 ps. In the WOPO, a 10 mm long Si$_3$N$_4$ waveguide as nonlinear parametric gain medium was used, equipped with inverted tapers to enable an efficient input coupling of around 70 % to the waveguide, thus, allowing a high external pump-to-idler conversion of up to 17.2 %. The output idler wavelength was dispersively tunable by adjusting the cavity length [10,20,32]. Meanwhile, the continuous tuning of the idler pulse wavelength was highly extended compared to other Si$_3$N$_4$ WOPOs [32] by using a PMF instead of a combination of single-mode fiber (SMF) and polarization controller, which enabled to further reduce the cavity loss arising from the limited bandwidth of the effective wave plate induced by the polarization controller. Combined with an established fiber-based ultrafast pump source, our Si$_3$N$_4$-based WOPO represents an efficient and versatile light source for further bio-chemical applications such as CARS [18] and lab-on-a-chip devices due to the compatibility of microfluidic channels within Si$_3$N$_4$ [17,33].

In the first part (Sec. 2), the experimental setup of the Si$_3$N$_4$ WOPO and the numerically calculated nonlinear parametric gain in the Si$_3$N$_4$ waveguide are presented. In Section 3, the impact of the pump pulse duration on the WOPO operation characteristics, e.g., oscillation threshold, output energy and spectral output bandwidth is discussed. In the end, targeting to the potential spectroscopic and imaging applications for, e.g., CARS, we compared our WOPO with other WOPOs and a waveguide-based optical parametric amplifier via an application-specific figure-of-merit in Section 4.

2. Experimental setup

The experimental setup of the WOPO, shown in Fig. 1(a), comprised a Si$_3$N$_4$ waveguide as the nonlinear parametric gain medium and a fiber to form a feedback cavity for parametric oscillation. The working principle of such synchronously pumped OPOs was explained in Ref. [32]. The waveguide was pumped by a mode-locked fiber laser with 40 MHz repetition rate at 1.03 $\mu$m wavelength. To investigate the influence of the pump pulse parameters on the characteristics of the WOPO output, a Fourier filter (not shown) was inserted between the pump laser and the WOPO to adjust the pump pulse duration between 0.37 ps and 2.4 ps. A combination of a half-wave plate and a polarizing beam splitter was used to adjust the pump power and select the p-polarized part to excite the fundamental TE mode of the waveguide. An aspheric lens (AL, NA = 0.68, $f$ = 3.1 mm) was used to couple the pump beam into a 10 mm long, 800 nm high, and 1350 nm wide silica-cladded Si$_3$N$_4$ waveguide to generate signal and idler sidebands via degenerate FWM.

 

Fig. 1. (a) Schematic experimental setup. DM: dichroic mirror, AL: aspheric lens, OAPM: off-axis parabolic mirror, L: spherical lens, OSA: optical spectrum analyzer, QWP: quarter-wave plate, HWP: half-wave plate, PMF: polarization-maintaining fiber, PBS: polarizing beam splitter. Left-bottom: Schematic waveguide geometry. w: waveguide width, h: waveguide height. (b) Calculated group velocity dispersion parameter $\beta _{2}$ for TE mode of Si$_3$N$_4$ waveguide (h = 800 nm and w = 1350 nm, blue curve) and PMF fiber (green curve) as a function of wavelength. (c) Calculated FWM gain of the Si$_3$N$_4$ waveguide for a pump peak power of 200 W at 1.03 $\mu$m wavelength.

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For mode propagation and phase-matching, the effective refractive index of the waveguide was calculated for a wide range of wavelengths from 0.7 $\mu$m to 2 $\mu$m using a full vectorial finite-element solver (Fimmwave, Photon Design). Concerning pulse propagation, the waveguide group velocity dispersion parameter (GVD parameter $\beta _{2}$) for the fundamental TE mode showed a value of −8.73 fs$^2$/mm at a pump wavelength of 1.03 $\mu$m (blue curve in Fig. 1(b)). Based on the total waveguide dispersion, the parametric gain for a pump peak power of 200 W and at 1.03 $\mu$m wavelength was calculated as a function of wavelength in Fig.1 (c). Additionally, to increase the input coupling efficiency, the waveguide was designed with inverted tapers both on input and output facets by the manufacturer. The small cross-section of the waveguide facet provided a larger effective mode field diameter of the waveguide, thus, effectively reducing the input coupling loss due to the lower mode mismatch between the incident pump mode and the fundamental TE mode of the waveguide [34]. The inverted tapers resulted in an increase of the coupling efficiency from 20 % [32] to 70 $\pm$ 3 % at 1.03 $\mu$m wavelength, as calculated by the transmission measurements (from 12.88 % [32] up to 48 $\pm$ 3 %) and considering the estimated propagation loss of the Si$_3$N$_4$ waveguide (from 0.53 dB/cm [32] down to 0.2 dB/cm at 1.03 $\mu$m).

The output from the waveguide was collected and collimated with an off-axis parabolic mirror (OAPM, $f$ = 6.35 mm) to reduce chromatic aberration. The total transmission of the waveguide section at the pump wavelength was determined to −3.18 $\pm$ 0.27 dB (48 $\pm$ 3 %) by taking the ratio between the power of the incident pump in front of the AL and the transmitted power behind the OAPM. The output coupling loss of 1.41 dB mainly resulted from the Fresnel loss (0.19 dB) and the truncation loss at the OAPM (1.22 dB).

In order to collect the signal sideband for feedback, a dichroic mirror (DM2) was inserted behind the waveguide output to enable the broadband signal pulses to be transmitted and coupled into a 4.5 m long polarization-maintaining fiber (PMF, $\beta _2$ = 31 fs$^2$/mm at 900 nm, green curve in Fig. 1(b)) with a signal coupling efficiency of −3.28 dB (47%) at 900 nm, while the idler sideband was reflected as the WOPO output for detection. Moreover, an additional quarter-wave plate (QWP) and a HWP were used to align the polarization of the transmitted signal pulses with the polarization of the pump pulses for maximal feedback. The total cavity length (fiber section and free-space section) was selected to match the repetition rate of the pump pulse for synchronous pumping. The feedback signal pulses were temporally stretched inside the PMF and, then, temporally and spatially overlapped with the next pump pulse at the dichroic mirror (DM1) to stimulate the FWM process in the following round trip through the waveguide. The fiber cavity provided a group delay dispersion (GDD) of 0.14 ps$^{2}$ at 900 nm wavelength, which allowed for dispersive tuning of the signal wavelength by adjusting the free-space delay ($\Delta$t), and thus simultaneously tuning also the central idler wavelength [32,35]. We note that the parametric amplification in the fiber cavity was negligible, because the nonlinear parameter of the PMF fiber was approximately three orders of magnitude smaller than that of the Si$_3$N$_4$ waveguide as well as the peak power of the feedback signal pulse was limited [10].

3. Experimental results

3.1 Stimulated FWM

In order to investigate operation in the stimulated FWM regime, the WOPO was pumped with pulses of 0.75 ps pulse duration and 0.6 nJ pulse energy. With the feedback blocked, the pump generated a broadband idler sideband (Fig. 2(a), blue curve) at around 1.15 $\mu$m wavelength with a bandwidth of 100 nm via degenerate spontaneous FWM. In contrast, when unblocking the feedback, a 57 dB amplification of peak power spectral density(PSD) was observed at the idler wavelength of 1.13 $\mu$m, indicating stimulated FWM(Fig. 2(a), red curve). In contrast to other work, also using a 10 mm Si$_3$N$_4$ waveguide as parametric gain medium[36], up to 25 dB enhancement was reached by parametric amplification. The reduced PSD of the pump pulses in the output spectra of the WOPO (Fig. 2(a)) resulted from a filtering effect of the used dichroic mirror (DM2 in Fig. 1(a)). Moreover, the stimulated FWM spectrum showed additional peaks due to cascaded FWM, e.g. at 1.25 $\mu$m and 1.41 $\mu$m wavelength (red curve, in Fig. 2(a)). To clearly present the idler energy change with the increase of the pump pulse energy, the idler energy was extracted by integrating only the PSD across the idler bandwidth from the WOPO output spectra for pump energies from 0 to 2 nJ, then, the according idler energy was re-scaled to account for the coupling loss into the optical spectrum analyzer (OSA). After the WOPO reached its oscillation threshold at 0.44 nJ, the idler pulse energy increased nearly linearly with the pump energy (Fig. 2(b). Consequently, the background due to spontaneous FWM in the output spectrum (yellow solid curve, Fig. 2 (a)) also increased and filled in the space between the distinct peaks. This background was preserved when the feedback was blocked (yellow dashed curve, Fig. 2 (a)), and was identified as the result of modulation instability (MI) induced supercontiuum generation (SCG) [37,38]. Within the SCG regime, the idler energy decreased due to back conversion and pumping the cascaded FWM [19,39]. The maximum output energy of the WOPO was obtained at the highest pump pulse energy in the regime of stimulated FWM (red shaded area, Fig. 2(b)). As the FWM gain is proportional to the pump peak power [40], one way to increase the output energy of the current WOPO is to pump the waveguide with pulses of longer duration and higher energy. Due to the lower pump peak power at longer pump duration, the WOPO can potentially be operated in the stimulated FWM region even at a pump energy higher than 1.4 nJ, so that the idler energy continues to increase linearly with the pump energy, since the onset of SCG is also shifted to a higher energy level with longer pulses.

 

Fig. 2. (a) Experimental power spectral density (PSD) of spontaneous (blue), stimulated (red) FWM at a pump pulse energy of 0.6 nJ and a pump pulse duration of 0.75 ps. Additionally, the output spectra for 2 nJ pump energy with (SCG, yellow solid curve) and without feedback (SCG, yellow dashed curve) were included. The reduced PSD peak of the pump pulses resulted from a filtering effect of the used dichroic mirror. (b) Idler pulse energy versus pump pulse energy at 0.75 ps pump pulse duration. A linear fit was added to guide the eye.

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3.2 Pump dependence of WOPO

In the following, we investigated the impact of the pump pulse duration on the WOPO operation characteristics, e.g., oscillation threshold, output energy and spectral output bandwidth, by pumping the WOPO at different pump pulse durations between 0.75 ps and 2.4 ps. Even shorter pump pulse duration down to 0.37 ps could be applied, however, then, a significant spectral broadening by SCG dominated the nonlinear dynamics due to high pump peak power beyond 0.7 nJ pump energy, similar as shown in Fig. 2(a). Additionally, at a maximum pump pulse duration of 2.4 ps, the available pump energy was restricted to 1.5 nJ owing to the transmission loss of the Fourier filter, limiting the available output energy of the WOPO. Based on the different applications of the WOPO, where different output pulse parameters are required, the optimal pump pulse parameters can be determined by these investigations on pump dependence.

First, in order to determine the necessary pump energy to drive the WOPO at different pump pulse durations, the WOPO output energy behind the DM2 (see Fig.1(a)) was measured as a function of pump energy for different pump pulse durations with a powermeter (see Fig. 3(a)), where the oscillation threshold value was estimated from a linear fit. The measured oscillation threshold versus pump pulse duration is plotted in Fig. 3(b), indicating a lowest value of 0.44 nJ at a pump pulse duration of 0.75 ps. The oscillation threshold scaled linearly with pump pulse duration, which can be explained by the direct proportionality between pump peak power and FWM gain at threshold, where the FWM gain, generated inside the waveguide, was able to compensate for the approximately constant cavity loss [40].

 

Fig. 3. (a) WOPO output energy vs. pump pulse energy for three different pump pulse durations 0.75 ps (blue), 1.5 ps (green), and 2 ps (red). The oscillation threshold of the WOPO was estimated from a linear fit. (b) Comparison of oscillation threshold (blue crosses) as a function of the pump pulse duration with a linear fit (dashed). Error bars indicate two-times standard deviation ($\pm$ 6%) of the input coupling efficiency.

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Second, to estimate the potential for increasing the idler energy, the maximum idler energy as a function of pump pulse duration plotted in Fig. 4(a), where the maximum idler energy was determined right before transition into the SCG regime, as shown in Fig. 2(b). For a pump pulse duration between 0.75 ps and 2 ps, the idler energy increased linearly. Similar like the linear increase of the oscillation threshold of the WOPO, this linear trend can be explained by the fact that the spectral broadening towards SCG appeared at an approximately constant pump peak power. At pump pulse durations above 2 ps, the maximum idler energy decreased, which resulted from insufficient pump pulse energy, due to the losses introduced by the used Fourier filter (see Fig. 4(a), red crosses). Nevertheless, up to 387 pJ of idler energy were extracted out of the WOPO at 2 ps pump pulse duration and 2.25 nJ pump pulse energy, corresponding to an external pump-to-idler conversion efficiency of −7.64 dB (17.2%). The internal pump-to-idler conversion efficiency was estimated by waveguide transmission measurements to −4.46 dB (35.8%), where the pump depletion reached its maximum of 74% (Fig. 4(b)). It can be seen that the internal pump-to-idler conversion efficiency was more than half of the pump depletion. The higher pump-to-sideband conversion efficiency may result from the power transitions among pump, idler, signal and cascaded FWM pulses [41]. The high conversion efficiency in this work resulted from the efficient input coupling as well as the ultra-low propagation loss of the Si$_3$N$_4$ waveguide [10,20,32]. Meanwhile, at 2 ps pump pulse duration, up to 64 dB enhanced peak PSD was obtained for the idler output (Fig. 4 (c)). As the spectrum of idler sideband was shaped as a Gaussian function, the idler pulse duration was estimated from the intensity autocorrelation measurement (IAC, Fig. 4(d)) to 1.1 ps. In contrast to other works on WOPOs with an external pump-to-one-sideband conversion efficiency up to −14.52 dB, [10,20,32], our WOPO exhibited a more than 6.9 dB improvement of the conversion efficiency, which resulted from the efficient input coupling due to the use of an inverted tapered waveguide as well as the ultra-low propagation loss of Si$_3$N$_4$ compared to silicon.

 

Fig. 4. (a) Maximum idler energy (blue crosses) as a function of pump pulse duration with a linear fit (dashed). Idler energy at above 2 ps pump pulse duration (red crosses) decreased due to insufficient pump energy. Error bars indicate two-times standard deviation ($\pm$ 6%) of the input coupling efficiency. (b) Residual pump energy at waveguide output versus input pump energy when the feedback was blocked (blue dots) and unblocked (red dots) at a pump pulse duration of 2 ps. (c) Output spectra of WOPO when the feedback was blocked (blue) and unblocked (red) at a pump pulse duration of 2 ps and 1.15 nJ pump energy, indicating a 64 dB enhancement of peak PSD. The reduced PSD peak of the pump pulses resulted from a filtering effect of the used dichroic mirror. (d) Measured intensity autocorrelation trace of the idler pulse with a full width at half maximum of 1.5 ps.

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Third, to investigate the influence of the pump bandwidth on the idler bandwidth, the full width at half maximum spectral bandwidths of the idler pulses were measured from the output spectra of the WOPO at a fixed pump pulse energy of 1 nJ and for different pump pulse durations. As can be seen in Fig. 5(a), the idler bandwidth broadened for shorter pump pulse durations. This can be explained by the broader pump spectra for shorter pump pulse duration at fixed pump energy. The spectral bandwidth values (Fig. 5(b)) decreased with the increase of pump pulse duration, corresponding to the decreasing pump spectral bandwidth and followed a hyperbolic fit as expected from the time-bandwidth product. Towards potential applications of WOPO light sources, by only adjusting the pump pulse duration, the idler pulse could be either broadband for ultra-short pulse generation [42], i.e., 10.25 nm at 0.75 ps pump pulse duration, or narrowband, i.e., 2.9 nm for 2.4 ps pump pulse duration, e.g., for spectroscopic and imaging applications [9,39].

 

Fig. 5. (a) Output spectra of the WOPO for pump pulse durations from 0.75 ps (blue) to 2.4 ps (purple) at a fixed pump pulse energy of 1 nJ. The reduced PSD peak of the pump pulses resulted from a filtering effect of the used dichroic mirror. (b) Bandwidth of the idler pulses (circles) as a function of pump pulse duration. Hyperbola fit was added to guide the eye. The error bars indicate two-times standard deviation ($\pm$ 6%) of the input coupling efficiency.

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3.3 Wavelength tunability

In order to obtain broadband FWM gain for the wavelength tunability measurement of the idler sideband,the waveguide was pumped with 2 nJ pump pulse energy and 2 ps pump pulse duration. The dispersive tuning of the idler wavelength was achieved by adjusting the cavity length via the free-space delay. In a previous work [32], where an SMF was applied to form a feedback cavity, stimulation of FWM was accomplished with an additional polarization controller to adjust the polarization of the feedback pulses for matching the pump pulse polarization. However, the continuous tuning range of the idler pulse was limited due to the cavity loss introduced by the limited bandwidth of the effective wave plate induced by the polarization controller. Therefore, to avoid a step-by-step re-alignment of this controller during tuning, a PMF was utilized in this WOPO for feedback, which enabled to further reduce the cavity loss by ensuring a parallel polarization of the spontaneously generated signal sidebands and the subsequent pump pulses. This 4.5 m long fiber cavity provided a total GDD of 0.14 ps$^{2}$ at 900 nm, which temporally stretched the broadband signal pulse. The center wavelength of the idler pulse was dispersively tunable across a spectral range of 191 nm, i.e., 42 THz bandwidth from 1.075 $\mu$m to 1.266 $\mu$m, (shown in Fig. 6), which was about 2.2 times broader than the previously reported idler tuning range [32]. Similarly, depending on the application, signal pulses (i.e., 42 THz from to 0.87 $\mu$m to 0.99 $\mu$m) could also be extracted out of the WOPO. Depending on the bandwidth of spontaneous FWM, the tuning range of the idler pulses was limited to the long-wavelength side of 1.266 $\mu$m. Nevertheless, due to the non-degenerate FWM between pump pulses and idler as well as signal pulses, cascaded FWM sidebands could be generated at longer wavelengths, up to 1.6 $\mu$m. However, the output energy of the cascaded FWM pulses was at least 4.1 dB lower than that of the corresponding idler pulses (Fig. 6). Despite this, the utilization of cascaded FWM can be explored depending on the specific application.

 

Fig. 6. Color-coded output spectra of the WOPO as a function of the relative delay between the temporally stretched signal sideband and the subsequent pump pulses of 2 nJ energy and 2 ps duration.

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4. Discussion

In the previous section, a highly efficient and widely tunable synchronously pumped WOPO was demonstrated and investigated in detail. In this section, we like to put our results into context as well as target to potential spectroscopic and imaging applications, e.g., for CARS. For this purpose, we defined a figure-of-merit (FOM) to compare our WOPO with other waveguide-based oscillator and amplifier (WOPA) light sources. The FOM incorporated various parameters being crucial for specifying a WOPO or WOPA suitable for CARS applications. Considering the difference on propagation length and the nonlinear coefficient of different nonlinear media, the corresponding pump parameters within the reference WOPO or WOPA systems have to be taken into account. Therefore, external conversion efficiency was considered for comparison in the FOM, such that a higher external conversion efficiency corresponded to a higher FOM value. Moreover, since the spectral resolution of CARS is highly dependent on the bandwidth of two input pulses, widely tunable and narrowband output pulses are recommended for sufficient spectral resolution [19], the tunability of WOPOs and WOPAs as well as the bandwidth of the output pulses were also included in the FOM. In this regard, a large FOM value was referred to a broader tunability or a narrower output bandwidth. Therefore, the FOM value is given as

Compared with other WOPOs using silicon waveguides [20], see Table 1, a similar wavelength tuning range of idler pulses was measured in this current work. However, as Si$_3$N$_4$ is well known as ultra-low loss material in the near IR regime, our Si$_3$N$_4$ WOPO showed an at least 4.9-times improvement in the external conversion efficiency compared to silicon WOPOs and at maximum a 28-times higher FOM value [10,20]. In the Si$_3$N$_4$ WOPO of reference [32], according to an input coupling ratio of only 20 %, the maximum achieved conversion efficiency of −21.5 dB was mainly limited by the waveguide damage threshold due to the need of high pump energy. In contrast, an efficient input coupling ratio of about 70 % was possible now by using inverted tapers, which resulted in a significant increase in the external conversion efficiency of up to −7.64 dB, corresponding to an internal conversion efficiency of −4.46 dB (see Table 1). Furthermore, with the reduced cavity loss by introducing PMF for feedback, the idler tuning range was more than doubled within our dispersive tuning measurement. All these improvements together led to a 157-times higher FOM value for Si$_3$N$_4$ WOPOs.

Table 1. FOM comparison of WOPO and WOPA light sources in different materials. $\eta _{pi}$: external pump-to-idler conversion efficiency, $\delta f_{i}$: idler bandwidth, $\Delta f_{i}$: idler tunability.

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Particularly, to bring our WOPO to applications, we included a Si$_3$N$_4$ WOPA system in our FOM comparison which has been experimentally demonstrated for CARS imaging [19]. Compared to the WOPA, our WOPO offered 6-times higher idler pulse energy with reduced output spectral bandwidth of 3.3 nm (25.8 cm$^{-1}$) instead of 14 nm (95.2 cm$^{-1}$) without the need for an additional seed laser, which eases to improve both signal strength and spectral resolution in CARS imaging. Moreover, the tuning range of the idler wavelength in our WOPO covered 77 % of the fingerprint region (from 406 cm$^{-1}$ to 1800 cm$^{-1}$) of typical Raman spectra [16]. Although, silicon WOPOs seem to be competitive for CARS applications due to their slightly higher FOM values compared to the Si$_3$N$_4$ WOPA, the output energy of silicon WOPOs, limited to 1.52 pJ [10,20], is too low for sufficient CARS signal generation. Finally, the 39-times higher FOM value of our WOPO in comparison to the Si$_3$N$_4$ WOPA is indicating to be a more efficient and compact chip-based light source for spectroscopic and imaging applications.

5. Conclusions

We have demonstrated a highly efficient, wavelength-tunable and synchronously pumped WOPO by using a Si$_3$N$_4$ waveguide with inverted input and output tapers as nonlinear gain medium. At a pump pulse duration of 2 ps and 2.25 nJ pump pulse energy, up to 387 pJ idler energy was measured, corresponding to an external conversion efficiency of up to 17.2 % (−7.64 dB) at 74% pump depletion. Our WOPO achieved an at least 4.9-times improvement of the conversion efficiency compared to other $\chi ^3$ WOPOs [10,20,32]. By adjusting the cavity length, the idler center wavelength was dispersively tunable across 191 nm (42 THz bandwidth) from 1.075 $\mu$m to 1.266 $\mu$m wavelength, which was about 2.2-times broader than the idler tunability reported from previous Si$_3$N$_4$ WOPOs [32]. The improved conversion efficiency, extended idler tunability and narrow idler spectral bandwidth (3.3 nm) indicate that our WOPO is an efficient and compact chip-based light source for applications, like anti-Stokes Raman scattering spectroscopy as well as imaging.

Furthermore, the footprint of the current Si$_3$N$_4$ WOPO could be further reduced by integrating also the feedback loop onto the chip [32], making robust on-chip biomedical imaging and spectroscopy feasible.