1. INTRODUCTION

Femtosecond optical parametric oscillators (OPOs) are an important tool across many disciplines. In engineering, environmental monitoring, and the biosciences, the availability of short mid- or far-infrared pulses can be used for remote sensing, molecular spectroscopy, and more complicated pump–probe diagnostics [1–4]. In physics, degenerate OPOs have emerged as a source of nonclassical light [5,6], which may be used for quantum sensing and computation, and as a promising platform for analog computation [7,8]. At this time, commercially available free-space systems are singly resonant, with short-wavelength pump pulses generating broadly tunable signal and idler pulses at longer wavelengths. These systems yield ${\sim}100\;{\rm fs} $ pulse durations and nanojoule pulse energies.

Recent research in OPOs has focused on degenerate operation and the development of monothically integrated devices. Synchronously pumped degenerate OPOs have their generated signal intrinsically phase-locked to the pump and, thus, inherit its frequency stability [9,10]. In this limit, OPOs may operate with conversion efficiencies past the conventional limits imposed by the quantum defect [11,12], and the discovery of stable pulse formation mechanisms such as quadratic bright-dark solitons (also referred to as temporal simultons) has enabled few-cycle operation [13–15]. In practice, degenerate OPOs based on free-space cavities need active length stabilization to operate, which has limited their use outside of optics labs. In contrast, monolithic OPOs operate stably without active cavity length stabilization [16]. The monolithic chip integration of OPOs also promises lower power requirements and greater stability. Fully integrated continuous-wave OPOs have been widely demonstrated using different platforms such as Ti-indiffused periodically poled lithium niobate (Ti:PPLN) [17], orientation-patterned gallium arsenide (GaAs) [18], aluminum nitride (AlN), photonic microring resonators [19], silicon carbide (SiC) [20], or integrated thin-film lithium niobate (TFLN) photonic circuits [21,22]. However, to date, demonstrations of synchronously pumped chip-scale OPOs have been limited to picosecond pulse durations and only demonstrated non-degenerate operation [16].

 

Fig. 1. (a) PPLN diffused waveguide design. (b) Simplified schematic of the experimental setup. The blue lines stand for the 1 µm fs pump and the red for the 2 µm OPO signal. PZT, piezo actuator; OC, output coupler; PBS, polarization beam splitter; HWP, half-wave plate; Flip, flip mirror; MSA, microwave spectrum analyzer; OSA, optical spectrum analyzer.

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In this work, we demonstrate a monolithically integrated synchronously pumped ultrafast OPO using reverse-proton-exchanged (RPE) waveguides in periodically poled lithium niobate (PPLN). When driven by 125 fs pulses centered around 1 µm from a free-running 10 GHz ultrafast laser, this device oscillates without any active feedback control. This improved mechanical stability enables a detailed characterization of ultrafast OPO operating regimes simply by tuning the repetition rate of the free-running pump laser. We observe many 2 µm resonances with thresholds between 110 and 160 mW, with the lowest threshold resonance corresponding to perfect synchronization between the pump and the OPO cold cavity. When driven further above threshold, each of these resonances achieves conversion efficiencies between 5% and 10%, and 3 dB bandwidths between 40 to 60 nm. By studying the steady-state power spectra of these resonances as a function of pump power and detuning, we observe several known pulse shaping mechanisms encountered in free-space cavities [23], namely, box-pulsing, the formation of bright-dark solitons, and non-degenerate operation. In principle, these operating regimes may be used to realize few-cycle pulses, nonclassical light, and coherent Ising machines in compact, chip-scale systems.

2. DESIGN AND FABRICATION

The monolithically integrated OPO studied here comprises three parts: a diffused waveguide, a periodically poled nonlinear section, and a pair of coated end facets to form a Fabry–Perot cavity [Fig. 1(a)]. We use the RPE process on lithium niobate to form a waveguide for both the 1047 nm pump light and the generated 2094 nm signal. The input section has a mask width of 5 µm to limit the number of 1047 nm spatial modes and simplify input coupling while still guiding 2094 nm light. The waveguide then tapers to a 9 µm-wide nonlinear section to achieve non-critical phase-matching by rendering the phase-mismatch $\Delta k = {k_{2\omega}} - 2{k_\omega}$, a weak function of the waveguide width $w$, i.e., ${\partial _w}\Delta k = 0$. While the waveguide is buried several microns below the top surface, the long evanescent tails of the waveguide mode will sample the surface conditions and incur both loss and phase-shifts. To better isolate the waveguide mode from the top surface and also symmetrize the mode in the input taper, we coat the top surface of the waveguide with tantalum pentoxide (${{\rm Ta}_2}{{\rm O}_5}$). The total length of the waveguide is 6.5 mm with an approximate free spectral range of 10.5 GHz at 2094 nm.

 

Fig. 2. (a) OPO output power as a function of pump laser repetition frequency detuning with a pump power of 170 mW. Zero detuning is defined as the lowest threshold, corresponding to synchronization (peak 0). Successive resonances are labeled according to their detuning from peak 0. (b) Conversion efficiencies for the corresponding different operation regimes.

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To form a nonlinear resonator, we periodically pole the tapered nonlinear section and enclose the waveguide with end facet coatings. The nonlinear section uses a nominal poling period of ${\Lambda _G} = 2\pi /\Delta k = 25.3 \;{\unicode{x00B5}{\rm m}}$ to quasi-phase-match degenerate optical parametric amplification (OPA) of 2094 nm light. The length of this nonlinear section determines the total temporal walk-off accumulated during OPA due to the group velocity mismatch (GVM) of 100 fs/mm between the interacting waves (estimated from simulations [24,25]). Nonlinear sections with a group delay shorter than the pump–pulse duration $\tau$ limit the small-signal gain imparted by the pump and, therefore, increase the threshold. Conversely, nonlinear sections with an accumulated group delay much longer than the pump pulse duration will give rise to nonlinear loss via second-harmonic generation (SHG) of the steady-state signal, thereby limiting the conversion efficiency. To better optimize this trade-off, we designed the OPO chips to include many lengths of nonlinear sections. We note here that a simultaneous increase of the pump pulse duration and grating length will always reduce the OPO threshold, at the cost of generating less signal bandwidth. The waveguide front facets are optically coated to enable high transmission (${\gt}{99}\%$) of the 1 µm pump and partial reflectivity (50%) of the 2 µm signal. The coating of the back facets is designed for high reflectivity (95%) at both 1 µm and 2 µm. The small transmission (5%) on the back facets is chosen to help image the 1 µm mode in the nonlinear section, which helps couple into the TM00 waveguide mode. The two coatings have a designed total group delay dispersion (GDD) of $190\;{{\rm fs}^2}$ at 2 µm to partially compensate the total waveguide dispersion (${-}260\;{{\rm fs}^2}$). The group velocity dispersion of the waveguide is calculated numerically by taking into account both the material dispersion as well as the waveguide geometry.

The OPO chips were fabricated using a modified version of the standard wafer-scale RPE process as described in [26]. First we used electric-field poling to define the gratings over the nonlinear sections of the waveguide. To have more flexibility and tune the phase-mismatch, we prepared six different poling periods ranging from 24.8 µm to 27.3 µm. Additionally, we included four different nonlinear gratings lengths (0.5 mm, 0.75 mm, 1 mm, and 2.5 mm) to be able to vary the total accumulated group delay. Since we use a Fabry–Perot cavity, we needed to account for two passes through the nonlinear section. To accumulate gain over the full propagation length and avoid back-conversion through SHG, we need to control the relative phase of the pump and signal on the back-pass through the nonlinear section. This was achieved by adjusting the phase of the PPLN grating in steps of $\pi /8$ from 0 to $\pi$ for each period and grating length. The buried waveguides were then fabricated by AdvR Inc. using reverse proton exchange. To account for potential temperature offsets in the proton-exchange bath, we designed three different waveguide widths of 8.5 µm, 9 µm, and 9.5 µm (mask width), with corresponding input section widths of 4.5 µm, 5 µm, and 5.5 µm. In total, we swept these parameters across six chips (three periods, four nonlinear lengths, eight phases, and one waveguide width per chip) containing a total of 576 OPO cavities. The full wafer layout contained four identical copies of these chips for a total of 2304 devices. The wafer was then coated with the top layer of ${{\rm Ta}_2}{{\rm O}_5}$ and diced into chips using a laser saw, and the end facets were polished to obtain 6.5-mm-long waveguides (within $+$/− 100 microns). Before coating the end facets, we performed a SHG experiment by coupling light from a 2090 nm laser into the waveguide to determine the proper poling period and width for phase-matching. The SHG experiment identified efficient nonlinear conversion with a poling period of 25.8 µm, a waveguide width of 9 µm in the nonlinear section, and a tapered input width of 5 µm. Finally the end facets were coated using ion-beam sputtering (IBS) to form the Fabry–Perot cavities.

3. EXPERIMENTAL RESULTS AND DISCUSSION

A. Femtosecond OPO Operation Regimes

When degenerate OPOs are properly dispersion compensated and synchronously pumped by femtosecond pulses, the timing mismatch has been shown to play a dominant role in the pulse formation dynamics [13,23,27,28]. We define the timing mismatch, $\Delta {T_{{\rm RT}}} = {T_s} - {T_p}$, as the difference between the OPO cold cavity round trip time ${T_s}$ and the pump repetition period ${T_p}$. While the pump repetition period depends on the tunable pump laser cavity length, the OPO cold cavity round trip time is fixed for a given OPO cavity and corresponds to the linear behavior of the OPO cavity without any pumping. In the frequency domain, the OPO cold cavity free spectral range is ${f_{{\rm fsr}}} = 1/{T_s}$, and the pump repetition rate is ${f_{{\rm rep}}} = 1/{T_p}$. We can introduce the pump repetition frequency detuning $\Delta {f_{{\rm rep}}}$ as ${f_{{\rm rep}}} = {f_{{\rm fsr}}} + \Delta {f_{{\rm rep}}}$, which can be related to the timing mismatch,

For zero detuning ($\Delta {T_{{\rm RT}}},\Delta {f_{{\rm rep}}} = 0$), the pump repetition frequency matches the OPO cold cavity free spectral range. This corresponds to conventional degenerate OPO operation, also called synchronous operation, which exhibits the lowest threshold [13].

When we tune the timing mismatch by changing the pump repetition frequency ($\Delta {T_{{\rm RT}}},\Delta {f_{{\rm rep}}} \ne 0$), we also change the pump carrier frequency. Degenerate OPA is a phase-sensitive process that provides gain when the intracavity signal pulse acquires $n\pi$ phase relative to the pump on each round trip, where $n$ is an integer. In the context of an OPO, this phase-sensitive amplification restricts oscillation to frequencies that satisfy ${f_{{\rm ceo,s}}} = {f_{{\rm ceo,p}}}/2$ or ${f_{{\rm ceo,s}}} = {f_{{\rm ceo,p}}}/2 + {f_{{\rm rep}}}/2$, where ${f_{{\rm ceo,s}}}$ is the absolute frequency of the signal mode, modulo ${f_{{\rm rep}}}$. Sweeping $\Delta {T_{{\rm RT}}}$, therefore, results in discrete resonances separated by a timing mismatch equal to the pump period for one cycle $\Delta {T_{{\rm RT}}} = {\lambda _p}/c \approx 3.5\;{\rm fs} $. We emphasize here that the behavior of these resonances depends strongly on the sign and magnitude of $\Delta {T_{{\rm RT}}}$ [28]. For a negative detuning, $\Delta {T_{{\rm RT}}},\Delta {f_{{\rm rep}}} \lt 0$, the signal and idler separate into two distinct spectral peaks; therefore, all resonances with $\Delta {T_{{\rm RT}}} \lt 0$ are referred to as non-degenerate resonances. Finally a positive detuning $\Delta {T_{{\rm RT}}},\Delta {f_{{\rm rep}}} \gt 0$ will lead to the simulton operation, which corresponds to the creation of simultaneous bright-dark solitons of the signal at $\omega$ and the pump at $2\omega$ [13,29,30]. Simulton operation is characterized by higher conversion efficiencies and broader ${{\rm sech}^2}$ spectral bandwidth as compared to the synchronous operation regime [13,27]. In most experimental realizations of synchronously pumped OPOs, the pump repetition rate is fixed, and the OPO cavity is tunable. Therefore, synchronization and control of the timing mismatch is obtained by changing the OPO cavity length, keeping the pump laser fixed. In the context of a monolithically integrated OPO, this timing mismatch will be controlled using a femtosecond pump laser with a highly tunable repetition rate.

 

Fig. 3. (a) Measured OPO optical spectra as a function of the pump laser repetition frequency detuning $\Delta {f_{{\rm rep}}} = {T_{{\rm RT}}} \cdot f_{{\rm fsr}}^2$ for a pump power of 170 mW. The zero detuning point sets the synchronized frequency, where a positive detuning causes the OPO to operate in the degenerate regime and a negative detuning causes the peak to bifurcate into a bimodal spectrum. It is measured at the pump repetition frequency ${f_{{\rm rep}}} = 10.426605\;{\rm GHz} $. (b) Coarsely sampled waterfall plot of the same data that facilitates quantitative comparison of the generate power spectra as a function of detuning. Adjacent traces are detuned by 4 kHz, corresponding to discrete steps of the timing mismatch $\Delta {T_{{\rm RT}}}$ of 36.8 attoseconds.

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B. Experimental Setup

The experimental setup is illustrated in Fig. 1(b). Our pump laser is a femtosecond Yb:CALGO laser developed in the Institute for Quantum Electronics at ETH Zürich [31] emitting pulses of 125 fs with 600 mW of power at 1047 nm. One end mirror of the laser cavity is mounted to a piezoelectric actuator and mounted on a manual linear translation stage to enable fine and coarse cavity tuning of the repetition frequency in the range of ${10.5}\;{\pm}\;{0.5}\;{\rm GHz}$. We note, however, that all data presented here were taken without any active cavity length stabilization. The 1047 nm pump light is coupled into the waveguide using an anti-reflection-coated molded aspheric lens (C240TMD-C), enabling fundamental-mode coupling with efficiencies between 60 and 75%. The waveguide is mounted on a copper mount temperature stabilized at 20°C. A dichroic mirror permits coupling of the pump and collection of the OPO signal from the same side of the waveguide. The 2 µm light is then collected to characterize both the signal power and the generated power spectral density. The pump repetition frequency is consistently monitored to precisely measure the timing mismatch between the pump repetition period and the OPO cold cavity round trip time and determine the regime of operation.

C. Conversion Efficiency

We first characterize the conversion efficiency of the OPO as a function of input pump power and timing mismatch. The conversion efficiencies are calculated by dividing the 2 µm power output from the 50% coupler by the in-coupled pump power. Figure 2(a) illustrates the discrete resonances separated by 3.5 fs that we could reach in this experiment when scanning the pump repetition frequency for a fixed pump power of 170 mW. Figure 2(b) shows the measured conversion efficiencies as a function of the pump power, with the peaks labeled according to the sign of the detuning. The lowest threshold resonance, denoted by peak 0, corresponds to perfect synchronization between the pump laser and the OPO cavity ($\Delta {T_{{\rm RT}}},\Delta {f_{{\rm rep}}} = 0$) [13]. This threshold is obtained with a pump power of 115 mW. From this resonance, a negative detuning ($\Delta {T_{{\rm RT}}},\Delta {f_{{\rm rep}}} \lt 0$) leads to non-degenerate operation. We measured three consecutive resonances designed as peaks ${-}{1}$, ${-}{2}$, and ${-}{3}$. As expected from typical free-space OPO operation, these peaks exhibit higher thresholds and lower conversion efficiencies than the synchronous peak. From peak 0, a positive detuning ($\Delta {T_{{\rm RT}}},\Delta {f_{{\rm rep}}} \gt 0$) leads to two simulton resonances designed as peaks +1 and +2, which have higher, sharper thresholds accompanied by larger slope efficiencies, which surpass the other regimes with increasing pump power. This behavior is typical from the formation of temporal simultons [13]. These resonances also exhibit the largest end-to-end conversion efficiencies (10%).

We operated our OPOs in the longest nonlinear section (2.5 mm), which enabled low power threshold but limited the conversion efficiencies because the signal is back-converted to the pump through SHG due to an excessive accumulated temporal walk-off (500 fs) compared to the pump pulse duration (125 fs). Furthermore, our simulations predict a threshold of 60 mW from these waveguides. The observed threshold of 115 mW instead suggests that an excess propagation loss of 1.3 dB exists inside the cavity. During this experiment, we were limited by the emergence of photorefractive effects that manifested as a constant drift of the synchronized frequency, restricting operation below ${\sim}200\;{\rm mW} $ of pump power. While in principle devices with shorter (0.5–1-mm-long) nonlinear sections should oscillate with comparable thresholds and higher conversion efficiencies, we did not observe oscillation in these devices. Further study of OPOs with shorter nonlinear sections will be the subject of future work.

D. Optical Spectrum

To further characterize these different dynamical regimes, we study the spectral behavior of the resonances as a function of timing mismatch (Fig. 3) and pump power (Fig. 4). Figure 3(a) is a conventional resonance diagram providing a qualitative comparison of the evolution of the different dynamical regimes. We also include a waterfall plot [Fig. 3(b)] where the synchronous and simulton traces are displaced by steps of 4 kHz of timing mismatch. It allows for a more quantitative comparison of these different operating regimes and shows the dynamics of the peak splitting. We see the synchronization point, $\Delta {f_{{\rm rep}}} = 0$, in peak 0. From this point, the spectra for the three negatively detuned resonances will split into distinct signal and idler spectral peaks, the distinctive signature of non-degenerate operation. This behavior is also clearly illustrated for peak ${-}{1}$ in Fig. 4.

 

Fig. 4. Power spectral density of the OPO signal as a function of pump power for operation in the non-degenerate regime (peak ${-}{1}$), synchronous regime (peak 0), and simulton regimes (peak 1 and 2). Insets, 3 dB bandwidth of the optical spectra as a function of pump power.

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The synchronized peak 0 and positively detuned peak 1 exhibit sidelobes, more pronounced at high pump power. This phenomenon, theoretically expected [23], comes from an interplay between gain clipping and saturation, which gives the pulses a boxlike shape in time, thereby filtering the optical spectrum with a sinc-shape that gets narrower with increasing pump power. From Fig. 4, we see that peak 0 has a low-power single peak ${{\rm sech}^2}$ spectrum with a 3 dB bandwidth of 43 nm (inset of Fig. 4). With increasing pump power, the bandwidth reduces, and we can see the filtering from box-pulsing with stronger lobes emerging.

A particularity of simulton regimes, in addition to the higher conversion efficiencies displayed in Fig. 2, is a favorable bandwidth scaling with increasing peak number [13,23,27]: peak 1 exhibits a broad optical spectrum with a 3 dB bandwidth of 55 nm. However, when increasing the pump power, this peak exhibits a transition from simulton operation to box-pulsing, which filters the generated bandwidth to ${\lt}40\;{\rm nm} $. Peak 2 presents the broadest optical bandwidth (63 nm, 3 dB), which could not be driven strongly enough to reach box-pulsing. We note here that, since box-pulsing only dominates far above threshold, peak 2 exhibits the least spectral filtering. This bandwidth supports a ${{\rm sech}^2}$-shaped transform limited pulse duration of 73 fs. Unfortunately, the peak power was insufficient to perform any pulse duration measurement.

When compared to the performance of OPOs based on free-space cavities [13,32,33], the conversion efficiencies and bandwidths reported here are 3–4 times below the state of the art. The efficiency of our devices is likely limited both by the excess propagation loss of 1.3 dB and by two-photon loss due to SHG in the long nonlinear section. The bandwidth of these devices was limited by the total GDD accumulated over the long nonlinear section. Future generations of devices with lower propagation loss will operate with shorter nonlinear sections, which may eliminate both of these limitations. In principle, such devices can achieve comparable efficiencies and bandwidths to the state of the art. Lastly, we note that the use of TFLN may eliminate all of these problems: TFLN devices have achieved propagation losses as small as 3 dB/m, have been dispersion engineered to achieve arbitrarily large OPA bandwidths, and can be fabricated from MgO-doped thin films to greatly reduce photorefractive effects.

E. Power Stability Over Time

Operation of degenerate femtosecond OPOs typically requires active cavity length stabilization such as dither-lock or wavelength stabilization [34]. Some results have been demonstrated with self-stabilizing degenerate operation [10,35], demonstrating passive self-phase-locking between the pump and the signal without any electronic feedback. All the measurements presented here were performed free-running, without any repetition frequency or cavity locking. Figure 5 shows the measured OPO output power of the first simulton resonance (peak 1) over time. The OPO could operate stably for minutes, with the signal output power slowly dropping over time. At lower powers, this drift is likely due to slow changes in the pump frequency or the timing mismatch. We observe much faster drifts at high power due to a combination of thermal and photorefractive tuning of the cavity resonances.

 

Fig. 5. OPO signal output power stability over time for operation in the simulton regime (peak 1) for a pump power of 150 mW.

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4. CONCLUSION

We have demonstrated, to the best of our knowledge, the first femtosecond monolithically integrated OPO. Our current design enables the study of the different dynamical regimes predicted theoretically: non-degeneracy, synchronous-pumping, and simulton operation. The 10 GHz cavity enables stable operation for several minutes without any active feedback control. The current power scaling of monolithically integrated femtosecond OPOs is limited by photorefractive effects, which can be eliminated either by reducing the propagation losses (thereby lowering the required power) or by using MgO-doped TFLN. We believe our results provide a promising milestone toward densely integrated femtosecond OPOs, which may be used as a chip-scale source of MIR combs, and integrated platforms for both classical and quantum computation.