Harnessing micro-Fabry-Perot reference cavities in photonic integrated circuits

Self-injection locking (SIL) utilizes optical feedback to lock a laser frequency’s to an external cavity, causing the laser to inherit the noise characteristics of the cavity. Recent studies have used silicon nitride ring resonators to self-injection lock chip-scale semiconductor lasers, greatly improving their phase noise characteristics [16, 23, 2, 24]. These demonstrations have relied on Rayleigh back-scattering to produce resonant feedback necessary for self-injection locking. However, thermo-refractive noise and scattering losses limit the achievable quality factors and noise characteristics of such waveguide-based resonators [25, 20]. Alternatively, if such dielectric ring resonators can be replaced by vacuum-gap µFP reference cavities, thermorefractive noise could be practically eliminated, offering a path to lasers with greatly improved phase noise and frequency stability. However, self-injection locking of integrated lasers will require new strategies to interface such µFP cavities with photonic integrated circuits to produce resonant feedback.

Established methods for producing resonant feedback have relied on circulators to redirect the transmission response of the FP cavity into the laser [26]. However, this strategy would be challenging to implement using photonic integrated circuits, as isolators and circulators are not widely available; moreover, it would be difficult to access both ports of the µFP cavity using a single chip. Alternatively, resonant feedback can be produced by partial excitation of higher order modes using a tilted cavity configuration; however, this approach requires a more complex alignment procedure, and it results in excess coupling losses that unnecessarily reduce the efficiency of laser feedback [27, 28, 29, 30].

To address these challenges, we demonstrate a new circuit interface that transforms the reflection response of the µFP cavity to produce resonant feedback necessary for self-injection locking. In reflection, the cavity modes of an FP resonator appear as anti-resonances (dips) atop a high reflectivity background; such anti-resonances are unsuitable for self-injection locking. These antiresonances result from interference between light that is resonantly scattered by the cavity modes and a broadband background reflection produced by the mirrors. To utilize the µFP for self-injection locking, it is crucial to eliminate the high reflectivity background, leaving only resonant scattering (or cavity leakage field) to produce feedback; this is because broadband mirror reflections can produce parasitic resonances that destabilize the laser [13]. If the wideband mirror reflection can be eliminated, leaving only resonant backscatter from the cavity modes, efficient resonant feedback can be achieved. In this case, the sudden phase shift produced by resonant backscattering about the cavity resonance provides the optimal feedback mechanism for self-injection locking.

The circuit interface that we use to produce resonant feedback into a waveguide-based DFB laser is seen in Fig. 2(a). An on-chip directional coupler divides the incoming light, directing a portion of light into an on-chip loop-mirror that introduces an additional broadband mirror reflection. The remaining light travels to the chip facet, where it is collimated by a GRIN lens to match the mode of the co-integrated FP cavity. These two reflections interfere upon recombination at the directional coupler. With the correct phase $\phi_{2}$, the loop-mirror reflection destructively interferes with the FP cavity reflection, cancelling the broadband mirror reflections and preserving only the resonant backscattered light. This results in a resonant (Lorenzian) feedback spectrum, facilitating self-injection locking by adjusting the feedback phase $\phi_{1}$.

For the choice of GRIN lens, it is crucial to expand and collimate the beam of light emitted from the waveguide end-facet to match the µFP cavity mode. To accomplish this mode transformation using our circuit interface, we use an inverse taper at the output facet of a $\mathrm{Si_{3}N_{4}}$ waveguide, producing a mode diameter of approximately 3 $\mathrm{\mu m}$. A GRIN lens with an effective focal length of 0.46 $\mathrm{mm}$ is then used to expand this 3 $\mathrm{\mu m}$ to 240 $\mathrm{\mu m}$, matching the mode field diameter of the µFP cavity, permitting coupling losses as low as 1.5 dB. Hence, this simple and compact photonic interfacing technique, shown in Fig. 2(b), offers a practical means of co-integrating the µFP cavity with PICs, to enable high performance oscillators and lasers for next-generation photonic systems.

The circuit interface of Fig. 2(c) is used to control the optical feedback parameters of this system, as necessary to obtain a stable self-injection locking. The interface circuit includes integrated heaters that allow for adjustment of the coupler splitting ratio, the feedback phase $\phi_{1}$, and the interferometer phase $\phi_{2}$. Piezo actuators on both the DFB laser and the µFP cavity are also used for fine-tuning $\phi_{1}$ and $\phi_{2}$ by modulating their separation from the photonic circuit. When $\phi_{1}$ and $\phi_{2}$ are adjusted to produce a self-injection locked state, the frequency of the laser emission becomes resonant with the µFP cavity, producing a dramatic increase in the light intensity within the µFP cavity. Light transmitted from the µFP cavity is collected through free space and monitored with a photodetector to observe the onset of the self-injection locking process. The output from the SIL laser is then coupled into the fiber-based apparatus of Fig. 2(c,i) for phase noise measurements.

Two complementary techniques are used to quantify the phase noise of the self-injection-locked laser. To measure the phase noise at low offset frequencies, we analyze the beat note between the integrated SIL laser and another frequency-stabilized reference laser using a phase noise analyzer, as shown in Fig. 2(c,i). The stable laser is comprised of a fiber laser that is PDH-locked to a 10 cm long table-top FP reference cavity housed in a vacuum chamber that is known to have low phase noise at low offset frequency (0 dBc/Hz at 1 Hz offset frequency). However, since the PDH feedback loop introduces excess noise, seen as a servo bump at offset frequencies above 10 kHz, a complementary measurement method is required to analyze the phase noise of SIL laser at higher offset frequencies. Here we use the fiber interferometer with 800 m delay seen in Fig. 2(c,ii) to perform self-heterodyne measurements. This complementary approach is ideal for phase noise measurements at high offset frequencies since the fiber interferometer is essentially free of technical noise for frequencies above 5 kHz. Combining these two techniques, we obtain a complete picture of phase noise spectrum of the SIL laser from 1Hz to 1MHz, as seen in Fig. 2(d).

The measurements of Fig. 2(d) reveal a dramatic reduction in the phase noise of the DFB laser when it is injection locked to the µFP cavity. Self-injection locking is seen to reduce the phase noise of the DFB laser by eight, seven, and six orders of magnitude at offset frequencies of 1 kHz, 10 kHz, and 100 kHz, corresponding to phase noise levels of $-$65 dBc/Hz, $-$97 dBc/Hz, and $-$122 dBc/Hz, respectively. Further analysis of the phase noise spectrum reveals a fundamental linewidth of 35 mHz and a 1/$\pi$ integral linewidth of 150 Hz. The reduction in laser linewidth produced by self-injection locking is further demonstrated in the direct RF beat note spectrum between the SIL laser and a stable reference laser, as shown in Fig. 2(e). It is important to note that the linewidth in Fig. 2(e,ii) is constrained by the resolution bandwidth (RBW) of the electronic spectrum analyzer. Note that these measurements were performed with a relatively large resolution bandwidth ($>$3 kHz) to ensure a stable beat note spectrum within the acquisition time. The Allan deviation, which is indicative of fractional frequency stability for different averaging times, is seen in Fig. 2(f), revealing $5\times 10^{-13}$ at 10 ms averaging time. After removing linear drift of 109 Hz/s, the system exhibits a fractional frequency stability better than $5\times 10^{-12}$ from 1 ms to 50 s averaging times.

Note that these measurements correspond to record-level phase noise among state-of-the-art chip-integrated systems[20] and were obtained without tight environmental controls. The measurements described above were obtained without active temperature stabilization of the cavity, illustrating the temperature insensitivity and robustness of such in-vacuum bonded µFP reference cavities. Deviations from the thermal noise limit at low offset frequencies are attributed to mechanical noise from the translation stages used to position the cavity and DFB laser. Hence, the low offset phase noise and frequency drift are likely to greatly improve when this system is fully co-integrated.

We also analyze the dynamics of the self-injection locking by slowly modulating the DFB laser current to observe shifts in the RF beat note spectrum with a stable reference laser, as depicted in Fig. 3(a). This system enters and exits the SIL state at points b to b’ and f to f’, respectively, demonstrating a locking range of 265 MHz. Comparison with a theoretical model of the self-injection locking process suggests that the onset of self-injection locking occurs earlier than expected; this is likely due to laser relaxation oscillations produced by the semiconductor gain medium [24]. The asymmetric feature for two directions of SIL is due to the fact that the feedback phase $\phi_{1}$ is non-zero [24]. It is also notable that away from the µFP resonance, the relationship between output frequency and DFB laser frequency diverges from the identity line, indicating that mirror reflections are not entirely cancelled, leaving a small amount of residual broadband feedback. Nevertheless, provided that this feedback remains sufficiently weak to avoid destabilizing the laser, it appears to have little impact on the performance of the SIL laser.

Beyond self-injection locking, new circuit interfaces for efficient interrogation of µFP cavity modes can enable complementary applications involving on-chip frequency metrology and microwave photonic signal processing. For example, PDH-locking provides a very versitile means of harnessing reference cavities with many practical advantages. Since PDH-locking can be implemented with low incident optical powers ($\sim\!10$ µW) relative to self-injection locking ($>\!1$ mW), photothermal noise is greatly reduced, permitting us to more readily reach the thermal noise limit (Fig. 2d). Additionally, PDH-locking enables frequency tunability and lower phase noise at low offset frequencies, making it indispensable for the most demanding applications requiring precise frequency control [10, 5]. Alternatively, such ultra-high Q-factor µFP cavities can be used for microwave-photonic filtering and signal processing [31]. Applications such as PDH-locking and microwave photonic signal processing require a photonic interface for efficient interrogation of µFP cavities while protecting on-chip lasers from strong feedback and reflections. Optical circulators are often used for redirecting reflected light for such applications [32, 33], but circulators and isolators are not yet widely available in integrated photonics due to the incompatibility of magnetic media with CMOS fabrication processes.

To address this challenge, we use a novel reflection cancellation circuit that adapts conventional schemes for a poor man’s isolator into a circuit architecture [11]. This second strategy for interfacing and integrating the µFP cavity uses a silicon photonic circuit fabricated from a silicon-on-insulator platform. This circuit is comprised of a two-port interferometer that connects to an inverse-designed two-port polarization-splitting grating coupler (PSGC), as described in [11]. By fine-tuning the on-chip phase shifter, this vertical-emission PSGC efficiently couples circularly polarized light into the µFP cavity, permitting interrogation of the reflection response of the cavity. Making use of the fact that the chirality of circularly polarized light is reversed upon the reflection from µFP cavity, this circuit achieves a function very similar to that of a circulator [11].

Efficient coupling into the µFP is achieved by using a GRIN lens to expand the beam produced by PSGC. The PSGC is designed to produce vertical emission of a 10.4 µm mode field diameter. This beam is expanded to produce a collimated 240 µm mode field diameter at the input µFP cavity using a GRIN lens with an effective focal length of 0.94 mm. The GRIN lens and µFP cavity are then co-integrated with PIC using a custom spacer that provides mechanical stability for the bonded assembly, as is shown in Fig 4(b). Using this integration method, light can be coupled from the silicon circuit into the µFP cavity with an efficiency of -2.8 dB. A fiber array was bonded the chip-integrated µFP module to interrogate the response of this multi-port photonic interface.

Figure 4(c) shows the optical reflection from Port A and the transmission to Port B as a function of laser detuning from the cavity resonance. As seen in Fig. 4(c), this circuit maps the µFP cavity reflection response to output port while simultaneously suppressing back-reflections from input port. The relative magnitude of the transmission and reflection reveal 10 dB back-reflection suppression, to aid in protecting an on-chip laser from unwanted feedback. Such a fully integrated module is readily suitable for an on-chip PDH locking system (Fig. 4(d)) as proposed in [5]. Together with many other applications such as photonic RF filtering and microwave signal generators, the co-integration of vacuum-gap µFP cavities paves the way for a next-generation of compact, high-performance RF photonic systems.