Silicon photonics and related integrated photonic platforms have shown to be fundamental in resolving technical challenges in a variety of fields, optical communications, sensing, biology, and food quality monitoring, to name a few of them [1–5]. As a consequence, the great interest of the industry in providing increasingly reliable and high-throughput systems for such applications, along with the need to scale the technology [6,7], led to the implementation of new silicon-photonics-based structures. For instance, one enabling device for future applications in communications is represented by tunable sources of THz signals (0.05–1 THz) [8–11]. A possible path to the realization of such a component is the use of highly stable, frequency-locked, semiconductor lasers, arranged in a heterodyne beating note scheme [12–15]. However, the emission frequency of semiconductor sources is very sensitive to local temperature variations and thermal fluctuations that could arise from environmental conditions, diffusion currents, or fabrication errors [16,17]. Additionally, the execution of complex functions requires the integration of an increasing number of components and devices on the same chip, possibly leading to the generation of thermal cross-talk between closely spaced devices. This could be the case of multiple lasers integrated in the same array [18,19] or reconfigurable photonic networks that widely employ thermal actuators as the tuning mechanism [20–22]. A frequency drift of the light source could result in a strong performance impairment, for example, in super-channel transmission schemes this might lead to an overlap of sub-carriers, thus affecting the complexity of the digital signal processing (DSP) steps and/or the data rate of the transmitting signals [23,24]. Thermal cross-talk-related effects in densely packed circuits can be mitigated via different approaches; one of the proposed solutions relies on the use of insulation trenches [25–27]; however, these structures are only beneficial when utilized to thermally isolate relatively large photonic devices, such as Mach-Zehnder interferometers, and are therefore not suitable for use with, for example, microring resonators (MRRs) [28,29]. In contrast, feedback-based solutions rely on specific algorithms that are able to correct any thermal drift that might arise in the circuit; they do not need any additional fabrication steps and are independent of the circuit topology [29,30].

In this paper we describe the design and characterization of a silicon nitride (SiN) photonic integrated circuit (PIC) with the ability to independently manage multiple C-band semiconductor lasers and retain their frequency stability within an accuracy of approximately 10 MHz, even with a laser subjected to an artificial thermal stimulus (test ramp of −125MHz/hour), while a beating note of 50 GHz is considered between this laser and an unperturbed one. This result is achieved by locking the frequency of each laser to the resonance(s) of a high-Q ring resonator fabricated onto the SiN PIC, acting as a wavelength reference and frequency meter. Specifically, as shown in Section 2, the PIC is able to retrieve a signal error related to the frequency drift of each light source and provide a dedicated electrical feedback signal to each laser tuning circuitry. The correction time is below 200 ms and is only limited by the thermo-optic response of the driving circuit of the lasers.

The paper is organized as follows. We first discuss the laser frequency stabilization algorithm that we implemented in a closed-loop configuration followed by a section describing the design and the characterization of the SiN PIC. Here we explain the criteria we followed in the design and show the experimental implementation of the algorithm discussed in the previous section. The last part is devoted to the use of the SiN PIC to stabilize and frequency-lock two narrow-linewidth semiconductor lasers, utilized to generate a 50 GHz beating note. The stability of the generated frequency tone is investigated through the use of an artificial thermal stimulus, applied to the semiconductor lasers, mimicking the thermal noise that might be naturally present in a complex integrated circuit.

Different frequency stabilization methods can be already found in the literature [31,32]. Our system offers two main advantages with respect to the other approaches: (i) it can be employed with any integrated laser technology (with the availability of a feedback line access) and (ii) supports simultaneously the stabilization of 16 units, thus making the system suitable for large scale photonic circuit integration. To the best of our knowledge, our results demonstrate, for the first time, the capability to perform precise frequency locking of multiple sources exploiting a single PIC with a 5mm×10mm footprint and an enhanced thermal stability, providing an unprecedented tool for the development of Tb/s transmission links based on the generation of THz beat notes.

The basic working principle of the proposed stabilization scheme is based on a negative feedback loop, as schematically shown in Fig. 1(a). Specifically, the emission frequency of each laser source is aligned to the inflection point of a resonance of a high-Q-factor periodic transmission filter [FL—frequency locker; see Fig. 1(b)]. In this way, any frequency drift Δf that might occur on the laser line under consideration is translated into a power variation ΔP at the output [PD1 in Fig. 1(a)]; the power fluctuation is photo-detected via on-chip photo-detectors and sent to an external micro-controller coded in Python that instructs the emitting device with an appropriate feedback signal that is proportional to the recorded power variation. In order to eliminate any ambiguity that might originate from power fluctuations of the source itself, the laser signals are also coupled to another output (PD2) that does not involve the FL. By calculating the ratio between the electrical signals at the two outputs, the frequency fluctuations can be isolated, discarding any laser power fluctuation that might also take place during the operation.

Additionally, a stable frequency grid can then be obtained by locking multiple sources to the resonances of the same on-chip FL [as shown in Fig. 1(c)]. The proposed schematic is equipped with 16 inputs that allow to manage up to an equivalent number of sources. In order to provide dedicated feedback to each frequency, the radiation of each input laser is modulated by operating 16 MRRs as optical intensity modulators (M1 to M16) that assign a code division multiple access (CDMA) [33] sequence to each input. As a consequence, the feedback signal related to each laser can be recovered by a decoding step that is carried out by the external micro-controller.

We selected a low-loss SiN platform for the implementation of the photonic circuit described in the previous section. This technology allowed to realize (i) 103-Q level ring resonators [34,35] with low loss and high stability with respect to thermal fluctuations, (ii) free spectral range (FSR) values on the order of 0.05 to 0.25 THz with no variations over the C-band (i.e., a low-dispersion platform [36]), and (iii) the ability to realize kHz-rate optical modulators with minimal optical loss and low electrical power consumption.

The expected FSR and 3 dB bandwidth for the i-th modulator were ∼250GHz and ∼10GHz, respectively, widely satisfying the aforementioned relationship. A total of four bus waveguides were required to retrieve the information related to 16 possible input laser sources. Two 2×1 multi-mode interferometers (MMIs) were used to couple two pairs of waveguides [refer to Fig. 1(a)]. An additional 2×2 MMI was necessary to merge the two remaining waveguides and split them into two outputs. One branch is directly read at the output [corresponding to PD2 in Fig. 1(a)], while the other is first coupled to the FL and its output is sent to PD1. Both the input and the output ports were provided with inverted-taper-based fiber coupling devices. Before proceeding to the final packaging, the chip was first characterized using a standard input/output fiber experimental set-up aiming at extracting the transfer functions of the fabricated modulators and devices. Coupling loss and waveguide propagation loss were estimated to be 1.7 dB/facet and 0.2 dB/cm, respectively. In Fig. 2(c) we report the experimental transfer function extracted for one representative modulator device (M1) depicted in blue, while in green we report the transfer function of the FL device, recorded at the PD1 output. The results showed very good agreement with the design target (see Table 1).

Thermal actuators were integrated both on the modulators and on the FL, so that the transfer function of every device could be accurately tuned along the C-band. A measured thermal tuning efficiency of almost 4.4 pm/mW was retrieved for the generic modulator [Fig. 3(a)]. Dynamic characterization was also performed at a frequency of 1 kbit/s using an on–off keying (OOK) test signal [set-up and measurements depicted in Fig. 3(b)]. Results showed that an extinction ratio (ER) of 10 dB and an open eye diagram could be obtained by applying an electrical power of 30 mW.

The PIC was subsequently fully packaged [see Fig. 4(a)] and integrated with two edge-illuminated InGaAs photo-detectors (bandwidth of 1.5 GHz) aligned at the PD1 and PD2 outputs, while polarization maintaining (PM) single mode fibers were aligned and packaged at the input ports, as shown in Fig. 4(b). Transimpedance amplifiers and electrical connections to the heaters were provided by an on-chip analog front-end aimed to detect the photocurrents of the reversely biased pin junctions and thermally tune the MRRs (modulators and FL), respectively. The chip was finally mounted on a temperature-controlled case.

The PIC was tested in three different experiments. The first test was carried out in order to verify that the outputs of PD1 and PD2 were correctly monitoring the frequency fluctuations of a test laser. In the second set of experiments, we tested the PIC and the developed correction algorithm with a single narrowband semiconductor laser. The final test allowed to test the system when two lasers were simultaneously fed into the chip. In this case we monitored the beat signal produced by their interference, to test the ability of the system to stabilize a beat note at 0.05 THz.

In Fig. 5(a) we show the experimental set-up we utilized to test the capability of the system to monitor the frequency fluctuations of a laser under test. We sent a commercial Keysight 8168F laser to our chip and we used the system to record the ratio between the PD2 and PD1 ports, as depicted in Fig. 5(b). The absolute frequency of the laser under test was independently monitored via a commercial Yokogawa AQ6151 wavelength meter [see Fig. 5(c)]. The results revealed that the ratio correctly traced the frequency variations of the laser over a 30 min time span. As expected, no variations were recorded at the ratio when the output power of the laser was manually varied.

In the second set of experiments, we replaced the optical source with an external cavity tunable laser prototyped by Huawei. This C-band operating semiconductor laser featured a linewidth of about 10 kHz and an output power of a few tens of mW (see Fig. 6). First, the frequency stability of the laser under test was evaluated in free-running operation as shown in Fig. 6(a). Then the feedback of the system was activated [see Fig. 6(b)] with the aim of stabilizing the thermal drift of the light source. The results of the tests are shown in a histogram where the frequency was acquired every 10 s. The tolerable threshold for the single laser was set to an arbitrary absolute value of 50 MHz in order to point out the operation limits of the algorithm. When the feedback was deactivated, the frequency was continuously drifting over a 2 h time window, crossing the 50 MHz limit after 50 min acquisition. In this case the event counts were evenly distributed over the different frequency values. Due to the minimal resolution of the wavelength meter, a slight spreading was applied to each sample in order to make the distribution easily visible. When the feedback system was enabled, the frequency variations were kept within an accuracy of a few MHz over the same time period, showing few counts outside of the permitted frequency window (Gaussian-like distribution).

The frequency locking of two laser lines (CH1 and CH2) was then demonstrated by tuning the emission of the two lasers in correspondence with the inflection points of two subsequent resonances of the FL that are 50 GHz apart. The thermo-optic modulators assigned a CDMA sequence (with a 1 kHz bit rate) to each laser under use; thus the frequency variations related to each laser could be independently detected at the photodiodes.

A schematic of the set-up that was employed is shown in Fig. 7. A fraction of the power of each laser was tapped and coupled through a set of 3 dB optical fiber couplers. The extracted power was amplified via an EDFA and sent to a high-speed photodiode that allowed the detection of the 50 GHz tone. The algorithm effectiveness and stability were monitored by mixing the 50 GHz tone with a signal frequency tone (fWG) generated by a commercial radio frequency synthesizer (Anritsu MG3695B) operating at 46 GHz. The down-converted low-frequency (∼4GHz) signal at the output of the mixer was read by an RF spectrum analyzer (RFSA, Agilent E4446A, resolution bandwidth of 3 MHz).

The system was tested with three different thermal stimuli, going from the slowest to the fastest one, that were applied to one of the two lasers under consideration. The first stimulus was a slow ramp (2 h duration) that was calibrated to induce a −250MHz frequency drift to one of the lasers under consideration. As shown in Fig. 8(a), red line, when the algorithm was turned off and no feedback signal was fed to the laser, the beating note showed a frequency drift with respect to the nominal value of −250MHz, following exactly the thermal stimulus artificially applied to the laser. When the feedback was turned on the system was able to keep the beat frequency constant at 50 GHz (to within ±10MHz) as shown in Fig. 8(a), blue line. Similarly, a second test was utilized to test the system response against the application of a co-sinusoidal stimulus (induced peak to peak change in the beating note frequency of 500 MHz), as shown in Fig. 8(b). Also in this case the system responded to the externally induced noise by stabilizing the system around the designated 50 GHz beating note frequency. As a final test, we applied a 50 s square wave stimulus to the system in order to excite a −500MHz change in the beating note, as shown in Fig. 8(c), red line. As expected, the algorithm was able to correct the steep change. Spurious peaks related to the slow thermo-optic transient of the laser tuning (∼600ms) and the minimal time response of the algorithm (200 ms) were still observed during the correction (blue curve) limiting the fast response of the system.

The design and experimental demonstration of an electrical closed-loop configuration based on a packaged integrated silicon nitride circuit that allows the stabilization of multiple laser sources placed on a 50 GHz-spaced grid have been presented. The enabling building block consists of a high-Q ring resonator, whose resonance is used as a reference to lock the laser frequency by thermal tuning of its position. The FL has been designed to provide a free spectral range that ensures a channel spacing of 50 GHz between adjacent channels. The system was tested with two 50 GHz-spaced semiconductor lasers that were fed to the SiN PIC and different thermal stimuli were applied to one of them, so that it was possible to mimic the thermal drift of the laser frequency in a crowded chip. The experimental results were obtained by the heterodyne detection of the generated 50 GHz beat note, showing the adaptive response of the circuit both to steep and slowly varying changes. A −125MHz/hour ramp was promptly counteracted by the negative feedback, showing the possibility of mitigating the effect of thermal cross-talk produced by the neighboring components in a densely integrated chip (∼fewMHz/s expected variation).

Thanks to the PIC design, the system allows to lock 16 laser sources, and might be used to generate a super-channel on a dense WDM scheme (up to 800 GHz with the current implementation). This architecture can find also application in heterodyne generation of sub THz or THz signals, where the emission frequency is set by the separation between two laser sources. The algorithm was demonstrated for a 50 GHz tone generation, but in principle, a multiple of this frequency can be generated and stabilized by the algorithm. In conclusion, the developed integrated platform together with the locking algorithm has been demonstrated as a simple and powerful method to mitigate thermal cross-talk in a crowded chip, offering potential benefits to the implementation of stable THz-frequency sources and the generation of superchannels capable of Tb/s communications. Future efforts will be devoted to increasing the number of stabilized lasers that the silicon nitride platform can manage and realizing a THz beat note by widely spreading two lasers from one another.