Narrow-linewidth lasers are key elements for a wide range of applications that require extreme coherence length or high spectral purity, such as high-speed coherent optical communications systems [1], high-resolution spectroscopy [2], high-resolution optical sensing [3], ultraprecise timing [4], and spectrally pure photonic microwave generation [5]. Although current commercial solid-state lasers [6] or fiber lasers [7] have exhibited high performance, these devices are generally composed of discrete components with large footprints that are a challenge to integrate with other on-chip optical microsystems. Therefore, for those applications where size, weight, and power (SWaP) are critical operational parameters, the chip-scale semiconductor laser is a more favorable choice. However, limited to the low-quality-factor laser cavity due to the small size, traditional monolithic III-V semiconductor lasers have demonstrated the best linewidth in the tens of kilohertz and mostly in the megahertz level [8], which can not fully meet the requirements of narrow linewidth for the aforementioned applications.

In recent years, there has been significant interest in reducing the laser linewidth by using the on-chip low-loss passive resonator to increase the photon lifetime of the laser cavity [9]. These chip-scale narrow-linewidth lasers have been developed by heterogeneously integrating III-V gain materials along with the low-loss passive waveguide on the same chip [10,11] or butt-coupling the III-V gain chip to the external cavity on a silicon [12,13] or silicon nitride (Si3N4) [14–19] waveguide platform. From a performance standpoint, in contrast with silicon, a Si3N4 platform has several advantages. The low waveguide propagating loss [20] leads to an extremely extended photon lifetime, resulting in a better linewidth reduction performance. Besides, Si3N4 is not limited by the two-photon absorption effect [21], thus supporting higher on-chip light power. Compared with silicon, Si3N4 features wider transparency [22], enabling applications in different optical bands.

To support the above analysis, we built a transfer-matrix-based [27] theoretical model for calculating spectral transmission responses of the SHDA-MRR. Assuming there is no radiation loss in the microring coupling region, and the intrinsic backscattering [26] induced by the sidewall roughness and the waveguide coupling is negligible relative to subwavelength-hole-defect-induced backscattering, the optical-field transmission functions of reflection and through responses are obtained and shown in the following equations: Hreflection=−iκsκ2τsa2(1−κ2)−2a1−κ2τs−κs2+1,(1)Hthrough=−τsa21−κ2−a(2−κ2)τs−κs2+1−κ2τsa2(1−κ2)−2a1−κ2τs−κs2+1.(2)

In the above equations, κs and τs are the subwavelength-hole-defect-induced backward scattering coefficient and scattering loss coefficient, κ is the optical-field coupling coefficient in the microring-waveguide coupling region, and a=e−αLcei2πnLcλ is the round-trip complex transmission coefficient. Here, α is the optical-field propagating loss coefficient, Lc is the perimeter of the microring resonator, n is the effective refractive index, and λ is the incident light wavelength. It should be noted that the location of the inserted subwavelength hole defect has no impact on transmission responses of the SHDA-MRR, which can be confirmed in Eqs. (1) and (2).

Notably, for SHDA-MRR, different reflection responses can be obtained by designing the backward scattering coefficient (κs), as shown in Fig. 3(b). When κs=0.00064, this relatively small backscattering induced by the subwavelength hole defect results in the insufficient buildup of the CW mode and the weak inter-cavity modal coupling between CW and CCW modes. In this case, the SHDA-MRR is not suitable as an external reflector for the self-injection-based hybrid laser because of the low reflection strength. With κs increasing from 0.00064 to 0.064, the reflection strength of the SHDA-MRR is gradually enhanced but reaches an eventual saturation as the modal coupling between CW and CCW modes becomes strong. For instance, when κs=0.064, the resonant peak of the reflection response obviously splits, due to the entirely broken degeneracy of two counterpropagating modes [30]. However, based on relevant studies [31], this larger resonance splitting impacts the self-injection locking process and worsens the frequency stabilization performance. Therefore, in SHDA-MRR, we should choose a reasonable backward scattering coefficient (κs) to achieve the desired reflection response for the good-performance self-injection locking process and linewidth reduction.

For an accurate and flexible backward scattering coefficient, we propose that the inter-cavity backscattering and the modal coupling can be manipulated by etching a subwavelength hole defect with varied sizes in the microring waveguide. To verify this statement, we simulate κs and τs with various hole-defect sizes in the fundamental-TE-mode Si3N4 waveguide (2.8 μm wide and 0.1 μm thick) with SiO2 cladding [see Fig. 3(f)], by employing the three-dimensional finite-difference time-domain (3D-FDTD) method. In this simulation, we fix the hole-defect length at 0.2 μm and change the hole-defect width. As shown in Fig. 3(d), with the hole-defect width (L) increasing from 0.2 to 1.0 μm, the backward scattering coefficient κs gradually increases from 0.0026 to 0.0123. However, the scattering loss simultaneously becomes larger with the enhancement of the subwavelength-hole-defect-induced backscattering. As shown in Fig. 3(e), the subwavelength-hole-defect-induced backscattering is basically maintained within the wavelength ranging from 1530 to 1570 nm. In summary, based on the above simulation results, this subwavelength hole defect etched in the microring waveguide provides a feasible scheme for generating the manipulated inter-cavity backscattering. Compared to the commonly used high-Q WGMRs [18,24,25], where the intrinsic inter-cavity Rayleigh scattering induces the modal coupling between CW and CCW modes, the SHDA-MRR features a flexible and adjustable subwavelength-hole-defect-induced backward scattering coefficient.

As displayed in the optical microscope image in Fig. 4, the width of the single-mode Si3N4 waveguide for the wavelength of 1550 nm is set to be 2.8 μm, and the radius of the SHDA-MRR is set to be 600 μm. Based on the simulation results in Figs. 3(a) and 3(d), a strip-type hole defect with the size 0.5μm×0.2μm is etched in this SHDA-MRR waveguide for κs=0.0064, and the microring coupling gap is designed to be 0.9 μm for κ=0.2. This introduced subwavelength hole defect is specifically designed to be located far away from the coupling section to avoid influencing the light coupling between the microring and the bus waveguide. Moreover, a phase shifter of 800 μm is placed adjacent to the SHDA-MRR to achieve the phase-matching condition [31], for facilitating the best self-injection locking process.

Here, we have three main reasons for choosing this Si3N4 waveguide platform to demonstrate the SHDA-MRR: the low propagation loss of this high-aspect-ratio Si3N4 waveguide [32–34] leads to a higher loaded Q (QL) of the SHDA-MRR, which generally means a narrower intrinsic linewidth of a self-injection-based hybrid laser; the broad transparency (∼400–2350nm) [22] of Si3N4 makes the SHDA-MRR structure applicable for the laser linewidth reduction over an extremely wide wavelength range; and the relatively low thermal drift coefficient of the Si3N4 waveguide [35] helps to improve the long-term stability of the hybrid laser under self-injection locking [25].

We employ the OSA to measure the lasing spectrum of the hybrid laser, with the DFB laser (injection current of 200 mA) self-injection locked to a reflection resonance of the SHDA-MRR. As shown in Fig. 6(b), the demonstrated hybrid laser exhibits an enhanced SMSR of 50 dB, compared with the 45 dB SMSR of the free-running DFB laser. Due to the SHDA-MRR induced on-chip loss (under the self-injection locking) of 1 dB and the chip-fiber coupling loss of 1.8 dB, the actual fiber-coupled output power is measured to be 11.7 dBm, and the on-chip power is estimated to be 13.5 dBm.

To characterize the performance of this fabricated Si3N4 SHDA-MRR on the self-injection-based laser linewidth reduction, we measure the phase noise power spectral density (PSD) [38] of the hybrid laser and the free-running DFB laser, using the delayed self-heterodyne (DSH) method [8], as shown schematically in Fig. 6(a). In the DSH configuration, the laser output is sent to a fiber interferometer with a delay fiber of 40 m in one path, which is much shorter than the laser coherence length. In another path, an acousto-optic modulator is used to generate a frequency shift of 80 MHz. The radio-frequency (RF) beat signal from the photodiode is evaluated with an electrical signal analyzer (Agilent E5052). With this scheme, the fluctuations of the instantaneous laser frequency are converted to fluctuations of interferometer output amplitude [8]. Compared with another widely used DSH technique with a large fiber delay longer than the laser coherence time, our employed method is less susceptible to technical noises from the surrounding environment. We obtain the laser single-sided phase noise PSD [LΔϕ(f)] from the directly measured phase noise PSD [SΔϕ(f)=2LΔϕ(f)] of RF beat signals, as shown in Fig. 6(c). Compared to the free-running DFB laser, the corresponding hybrid laser’s single-sided phase noise is significantly suppressed to −88.7dBc from −54dBc, at the frequency offset of 1 kHz. The laser frequency noise PSD [Sν(f)] is related to the directly measured SΔϕ(f) by the following equation [38]: Sν(f)=f24[sin(πfτ)]2SΔϕ(f),(3)and the delay τ in the DSH setup is extracted as 159 ns from the measured phase noise spectra. Based on the laser frequency noise PSD, the laser intrinsic linewidth (quantum-limited Lorentzian linewidth) can be accurately acquired as ΔνLorentzian=πSν0; here Sν0 is the white frequency floor at higher frequencies [8], where the measurement is free from the 1/f noise [39] and other typical technical noises [8,25]. The frequency noise spectra shown in Fig. 6(d) indicate white noise floors of 15,800Hz2/Hz for the free-running DFB laser, and 10.9Hz2/Hz for the hybrid laser, corresponding to 49.6 kHz and 34.2 Hz intrinsic linewidths, respectively. Therefore, the fabricated Si3N4-based SHDA-MRR has been demonstrated to suppress the DFB laser intrinsic linewidth by about 1450 with the self-injection locking, corresponding to a linewidth reduction factor η calculated to be 1450≈38.1.

The theoretical model of a single-mode semiconductor laser coupled to an external wavelength-selective feedback cavity has been well studied [40–42], and the maximum efficiency of self-injection locking can be approximated by the following expression [40]: η=1+(1+αH2)PrP0τSHDA−MRRτcold.(4)The laser intrinsic linewidth can be reduced by η2. Here, αH is the linewidth enhancement factor [43], τSHDA−MRR and τcold are the effective delay time provided by the Si3N4 SHDA-MRR chip and the DFB laser cavity, and Pr/P0 represents the power ratio reflected back to the DFB laser (including the coupling loss). Based on the above experimental demonstration, the variables in Eq. (4) are reasonably estimated to be αH=2.5, Pr/P0=−12dB, τSHDA−MRR=1.7ns, and τcold=16ps, and the theoretical linewidth reduction factor η is calculated to be 72.8. The experimentally demonstrated η is a bit lower than the theoretical value obtained by Eq. (4), and one possible reason is that we have not tuned the self-injection locking process to the optimal locking phase or the optimal locking point, which has been discussed in detail in Ref. [31].

Such a high-power hybrid laser with an ultranarrow intrinsic linewidth is required as a critical component in high-speed coherent optical communications systems [1], where the laser frequency noise at high frequencies is of more importance, for low-phase-error coherent communication links. However, for many metrology applications, such as high-resolution spectroscopy [2], high-resolution optical sensing [3], and light detection and ranging (lidar) [44], the frequency noise at low frequencies eventually limits the metrology resolution. Therefore, in these applications, the full width at half-maximum (FWHM) linewidth (also known as the integral linewidth) can be of major importance. The integral linewidth [8] represents the “slow linewidth” obtained after a long-time averaging, and this measurement comprises technical noises in the low-frequency range, such as noises from the thermal drift and fluctuations of the injection current.

The laser integral linewidth (Δνint) can be determined from the laser frequency noise PSD by the following expression [8]: ∫Δνint∞Sν(f)f2df=1π(rad2).(5)As shown in the calculated integral phase noise spectra in Fig. 6(e), integral linewidths of the free-running DFB laser and the hybrid laser are estimated to be 90 and 3 kHz, respectively. Thus, the fabricated Si3N4-based SHDA-MRR is demonstrated to suppress the DFB laser integral linewidth by about 30 with the self-injection locking. However, limited by the 1/f noise and other technical noises in the low-frequency range [8,39], the performance of the SHDA-MRR for realizing the integral linewidth reduction is not as good as the aforementioned experimental results about intrinsic linewidth reduction. This can be further improved by optically locking the hybrid laser to another high-Q etalon using Pound–Drever–Hall (PDH) techniques to suppress the laser frequency noise in the low-frequency range [45].

As shown in Fig. 5, the SHDA-MRR features periodic resonances with an FSR of 0.4 nm, and each reflection resonance can be continuously tuned across one FSR using the thermo-optic effect. Therefore, we can lock a reflection resonance of the SHDA-MRR to the DFB laser at arbitrary wavelengths. Moreover, due to the broad transparency of the Si3N4, the SHDA-MRR can be designed to be applied in different optical bands. Thus, the Si3N4-based SHDA-MRR has provided a robust solution to realize the hybrid linewidth reduction.

In conclusion, we have demonstrated a hybrid integrated laser with 34.2 Hz intrinsic and 3 kHz integral linewidths, based on the proposed Si3N4 SHDA-MRR structure for the self-injection locking. The hybrid laser exhibits a large SMSR of 50 dB and high fiber-coupled output power of 11.7 dBm. In SHDA-MRR, the reflection response can be accurately manipulated by designing the size of the embedded subwavelength hole defect. With further joint optimization of cavity parameters, this Si3N4 SHDA-MRR is expected to reduce the laser intrinsic linewidth to a sub-hertz level. Therefore, this work explores a low-cost and robust linewidth reduction scheme based on the commercially available DFB laser, for the applications of high-speed coherent optical communications systems, high-resolution optical sensing, and lidar. Substituting the DFB laser with a Fabry–Perot semiconductor laser [19], the hybrid laser has the potential to reach a widely tunable single-longitudinal-mode output as well.