1. INTRODUCTION

Nonlinear optical processes are of paramount importance in both science and technology, ranging from supercontinuum generation that unlocked frequency metrology to squeezed light generation as used in gravitational wave detection or optical parametric oscillators that generate mid-infrared radiation for spectroscopy [1,2]. Advances in integrated nonlinear devices have enabled to access weak nonlinear optical processes with continuous wave lasers, at only milli-Watt pump power levels and triggered the development of chip-scale optical frequency combs, i.e., microcombs [3,4]. These devices utilize the Kerr-nonlinearity-induced parametric oscillations and interactions for broadband optical frequency conversion. After the first demonstration of ultralow-threshold optical parametric oscillators (OPOs) in a high quality factor toroid cavity [5], there has been an ongoing effort to improve key parameters such as output power, conversion efficiency, and wavelength tunability [6–11]. Such compact and versatile devices hold immense potential for a wide range of applications [12], including optical communications [13], and photon pair generation [14]. The integration of OPOs on a chip offers several advantages including enhanced stability, reduced footprint, and compatibility with existing semiconductor manufacturing processes [15,16]. The latter is of particular importance since it allows one to develop heterogeneously integrated devices having a relatively stable semiconductor distributed feedback laser as a pump [17]. These factors make chip-integrated OPOs highly attractive for practical applications where space constraints and cost effectiveness are crucial considerations. One of the key properties of the integrated OPO is the tunability of signal and idler wavelengths [18–22]. However, an outstanding challenge remains: the realization of signal/idler frequency tuning without relying on a broadly tunable (often exceeding units of THz) and expensive external pump laser.

Over the past decade silicon nitride, first considered as a capping layer for transistors, has evolved into a leading platform for low-loss nonlinear integrated photonics including massively parallel [23], dual-comb [24], and chaotic LiDARs [25], as well as optical frequency synthesis [26] and optical clocks [27]. Coupled resonator systems are a prominent example of breakthrough enabled by accessing the next level of complexity. Such systems have demonstrated the presence of emergent phenomena [28–31] and operation on both sides of an exceptional point [32], and increased the efficiency of microcomb generation [33]. Moreover, it even becomes possible to generate soliton pulse pairs in coupled normal-dispersion resonators [34,35]. This capability arises from the hybridization of initially normal dispersion and the formation of effective anomalous dispersion.

In this paper, we theoretically and experimentally investigate optical parametric oscillation in an alternating-dispersion photonic dimer, i.e., a system of two coupled optical microring resonators [28,29,32,30,36] with opposite signs of group velocity dispersion (GVD) [see Fig. 1(a)]. Optical coupling results in the interaction of the two fundamental mode families and the hybridization of their dispersion profiles. Active control over the hybridization regime in our scheme is carried out with heaters [37]. By applying the voltage to the integrated heating element, we can dynamically adjust the curvature of the hybridized dispersion. This causes a change in the spectral position of the signal and idler. Our approach enables the tunable OPO with a nearly fixed pump laser operating wavelength (signal/idler to pump tuning range 50 times exceeding previous schemes [19,20]), overcoming the limitations of the previous techniques.

 

Fig. 1. Parametric gain in the hybrid-dispersion photonic dimer. (a) Schematics of two coupled resonators with opposite signs of ${{\rm D}_2}$. The external laser excites the system through the normal-dispersion resonator. The output signal is measured from both add and drop ports. The signal collected from the drop port demonstrates the pump filtering effect. (b) Integrated dispersion hybridization for different inter-ring detunings (voltages applied to one of the heaters). (c) Intercavity power in the normal-dispersion resonator as a function of pump and inter-ring detuning. (d), (e) Gain lobes tunability for different inter-ring detunings and fixed pump detuning [dashed line in subplot (c)] in the hybrid photonic dimer.

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2. RESULTS

The spectral position of the fundamental-TE modes in the resonator with respect to the pumped mode ${\omega _0}$ can be written as

An example of hybridized dispersion at different detunings is shown in Fig. 1(b). Here optical modes of the resonators are split most strongly in the vicinity of the crossings of the initial integrated dispersions. Qualitatively, it results in an additional phase-matching condition for the four-wave mixing processes that we exploit for the OPO generation. Applying the voltage to the heaters, we shift the relative positions of the two parabolas, thereby changing the positions of the modulation instability gain lobes [see Fig. 1(d)]. We analyze this effect quantitatively by examination of the Jacobian matrix eigenvalues of the two coupled Lugiato–Lefever equations (LLEs) (see Supplement 1). We operate the device in the regime when the pumped mode $\mu= 0$ is strongly localized in the normal-dispersion resonator where $\Delta (0) \gg \kappa$. The simulated intracavity power for different inter-ring detunings $\delta$ and pump frequencies ${\omega _p}$ is shown in Fig. 1(c). Fixing ${\omega _p}$ [white dashed line in Fig. 1(c)], we calculate the position of the parametric gain lobes as presented in Figs. 1(d) and 1(e). We observe that with varying inter-ring detuning $\delta$, one achieves tunability of the parametric gain and hence the spectral position of the signal/idler.

 

Fig. 2. Voltage-controlled OPO. (a), (b) LLE-based numerical and experimental OPO tuning by thermal tuning of the normal-dispersion resonator. Inset in (a) is a photo of the experimental device. Thick lines in (b) are optical spectra with inter-ring detunings $\delta$ equal to ${-}{16}\;{\rm GHz}$, ${-}{11}\;{\rm GHz}$, and ${-}{2}\;{\rm GHz}$. The gap corresponds to the region forbidden by mode crossings. (c)–(e) OPO spectra combined with integrated dispersion measurements for the same inter-ring detuning.

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We demonstrate voltage-tunable OPO using a ${\rm Si_3}{\rm N_4}$ dimer (LGT 1 wafer, A2 chip) with FSR = 458 GHz and $D_2^{\rm a}/2\pi = 12.6\;{\rm MHz} $ and $D_2^{\rm n}/2\pi = - 1.2\;{\rm MHz} $ for anomalous and normal resonators (see the resonator design procedure in Supplement 1). First, we create a numerical model for signal/idler generation using two coupled LLEs describing the optical interaction in the two opposite-dispersion rings, using experimentally measured values of the FSR and dispersion. In our numerical experiment, we pump the normal-dispersion resonator with fixed pump detuning and power while changing the detuning of the anomalous resonator. We set the inter-ring coupling rate ${J}$ to 2 GHz. The generated signal and idler spectral position, shown in Fig. 2(a), qualitatively matches results from Fig. 1(d) and demonstrates OPO signal tunability of 20 THz with fixed pump laser frequency. The effect is also reproduced qualitatively for other values of J in the 1–5 GHz range.

Experimental measurements are performed on hybrid photonic dimers fabricated by LIGENTEC SA [see inset in Fig. 2(a)]. Microheaters are designed so as not to cover the resonators’ coupling regions and minimize thermal cross-talk. All experimental data presented in Fig. 2(b) are obtained using a single experimental device (see the experimental setup in Supplement 1). We observe a broad range of operating wavelengths and precise control over the OPO’s signal/idler position. Gaps in Fig. 2(b) depict the inter-ring detuning range where sidebands are generated in the enhanced mode crossings [30]. In contrast to numerical simulations, the current experimental demonstration of the tunable OPO required an adjustment of the pump frequency by 20 GHz due to the thermal cross-talk between the heaters. This can be mitigated by utilizing piezoelectric actuators [39] that adjust the resonance conditions through the stress-optic effect and are not susceptible to cross-talk. Therefore, to tune the signal and idler, we heat the normal-dispersion resonator. This results in the need to tune the pump frequency in the 20 GHz range. Nevertheless, the achieved signal/idler operating range is $\approx 20\;{\rm THz} $. Thus, the laser tunability requirements are orders of magnitude lower than that required by previous schemes.

In order to directly show the correspondence between signal/idler frequency tuning and the dispersion hybridization regime, we performed dispersion characterization using the frequency-comb-calibrated diode laser spectrometer [40]. The measurements are carried out with all the same inter-ring detuning values as shown in Fig. 2(b). The results for selected inter-ring detunings are shown as dots in Figs. 2(c)–2(e), and juxtaposed with the corresponding optical spectra [thick lines in Fig. 2(b)]. To highlight the hybridization effect on the dispersion profile, we added the experimentally fitted dispersion in the uncoupled regime ($\delta \gt 100\,\,{\rm GHz}$) depicted with dashed lines (the fitting procedure is described in Supplement 1). Thus, we clearly see that signal/idler lines are formed in the vicinity of the strongest mode interaction region and follow it when we change the inter-ring detuning. The change of the dispersion curvature near the intersection of normal- and anomalous-dispersion parabolas [e.g., Fig. 1(b) for $\delta = - 5\;{\rm GHz}$, at 180 THz and 205 THz] enables the phase-matching condition—which is the key to our approach to the OPO tunability.

One of the key applications that can be influenced by the voltage-tunable OPO is quantum communication [14]. In this regard, the presence of a strong pump often represents an issue for sensitive quantum detectors. Our scheme provides the possibility of (potentially strong) pump filtering. Two factors contributing to this process are pump mode hybridization and drop port employment. While the strong mode hybridization modifies the curvature of the dispersion at the distinct mode numbers and $\delta \gg J$ [see Fig. 3(b) in the vicinity of 180 THz and 205 THz], the field at the weakly hybridized pump mode is primarily located in the normal-dispersion resonator [see central sketch Fig. 3(a)]. Conversely, in the vicinity of the points of strongest interaction, the optical power leaks to the auxiliary resonator. This allows the detection of the signal/idler lines with the suppressed pump on the second ring drop port. We calculate the dependence of pump suppression on the inter-ring detuning as shown in Supplement 1. However, in the fabricated device, the location of the drop port led to a cross-talk effect at the output. The experimental result in Fig. 3(c) depicts the constant pump suppression of approximately 22 dB and partial enhancement of the sideband power.

 

Fig. 3. OPO pump suppression in the drop port output. (a) Layout for pump suppression effect. At the pump frequency, the optical power is localized in the normal-dispersion ring. In the vicinity of the strongest mode interaction, power is distributed equally. (b) Schematic representation of hybridized dispersion with pump, signal, and idler frequencies separation. (c) The experimental optical spectrum for both rings at $\delta = - 5\;{\rm GHz}$. Blue and red colors indicate the add/drop port measurements of the optical spectrum, respectively.

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Finally, we note that there are immediate improvements that can be envisaged in the system to further boost its performance. First, integrated actuators will completely eliminate the thermal cross-talk between the resonators as well as the requirement for pump laser tunability. Second, further optimization of the dispersion profile could extend the operation bandwidth up the octave-spanning operation regimes [for example, see Formula (12) in Supplement 1] and result in further pump suppression at the drop port. Third, further optimization of the bus-to-ring coupling will provide enhanced efficiency of the OPO. Thus, we believe that our proof-of-concept device can evolve into a reliable tool for modern photonic applications.

3. CONCLUSION

In conclusion, the development of a broadband voltage-tunable OPO integrated on a chip represents a significant milestone in the field of integrated photonics. Our scheme, employing two coupled resonators with opposite dispersion, enables exceptional tunability without the need for a broadly tunable and expensive laser source. This scheme paves the way for the realization of compact, cost-effective, and highly tunable OPOs that can be seamlessly integrated into various photonic systems. Furthermore, the ability to achieve broadband voltage tunability without the need for a broadly tunable laser represents a significant leap forward in the field of integrated photonics. This advancement not only eliminates the reliance on costly external laser sources, but also enhances the device’s overall efficiency and performance.