Smooth and flat phase-locked Kerr frequency comb generation by higher order mode suppression

High-Q microresonator is perceived as a promising platform for optical frequency comb generation, via dissipative soliton formation. In order to achieve a higher quality factor and obtain the necessary anomalous dispersion, multi-mode waveguides were previously implemented in Si3N4 microresonators. However, coupling between different transverse mode families in multi-mode waveguides results in periodic disruption of dispersion and quality factor, and consequently causes perturbation to dissipative soliton formation and amplitude modulation to the corresponding spectrum. Careful choice of pump wavelength to avoid the mode crossing region is thus critical in conventional Si3N4 microresonators. Here, we report a novel design of Si3N4 microresonator in which single-mode operation, high quality factor, and anomalous dispersion are attained simultaneously. The novel microresonator is consisted of uniform single-mode waveguides in the semi-circle region, to eliminate bending induced mode coupling, and adiabatically tapered waveguides in the straight region, to avoid excitation of higher order modes. The intrinsic quality factor of the microresonator reaches 1.36 × 106 while the group velocity dispersion remains to be anomalous at −50 fs2/mm. With this novel microresonator, we demonstrate that broadband phase-locked Kerr frequency combs with flat and smooth spectra can be generated by pumping at any resonances in the optical C-band.

mode crossing region and increase of cavity's free spectral range (FSR) are thus necessary for dissipative soliton formation in conventional Si 3 N 4 microresonators.
Here we report a novel design of Si 3 N 4 microresonator in which single-mode operation, high quality factor, and anomalous dispersion are attained simultaneously. No higher order mode is observed throughout the optical C/L-band in the transmission spectrum. A high resolution coherent swept wavelength interferometer is implemented to determine the intrinsic quality factor and the group velocity dispersion (GVD, β 2 ) of the microresonator. They are measured at 1.36 × 10 6 and − 50 fs 2 /mm, respectively. We demonstrate that phase-locked Kerr frequency combs can be generated by pumping at any resonances in the optical C-band. The spectra spanning more than 20 THz (full width at − 20 dB) are smooth without periodic amplitude modulations.
For applications such as high speed communication and astrospectrograph calibration, it is beneficial to have a broadband optical frequency comb with a smooth and flat spectral shape 32,33 . Such an unstructured spectrum is difficult to attain in a multi-mode microresonator (Fig. 1), especially in Si 3 N 4 microresonators where mode coupling is facilitated by the strong sidewall scattering 26 . Reducing the waveguide cross-section to 1 × 0.8 μ m 2 is a solution to eliminate higher order modes, but it results in a larger optical mode overlap with the waveguide boundary and consequently lowers the achievable quality factor. Compared to the multi-mode microresonator (Q I = 1,560,000), the microresonator made of a 1 × 0.8 μ m 2 waveguide only has an intrinsic quality factor of 830,000 (Table 1). Such decrease in the intrinsic quality factor leads to a reduction of cavity-enhanced Kerr effect by 3.5 times           1, 560, 000 830, 000 2 10 . Furthermore, such single-mode waveguide features positive GVD and large third-order dispersion (TOD, β 3 ) for all optical communication wavelengths (Fig. 2a,b), inhibiting the Kerr frequency comb and dissipative cavity soliton generation. Our strategy to suppress higher order modes while maintaining high quality factor and anomalous dispersion is two-fold (Fig. 2c). First, a uniform single-mode waveguide (1 × 0.8 μ m 2 ) is included in the semi-circle region where the waveguide is curved, as bending introduces significant mode coupling if a multi-mode waveguide is used. The diameter of the semi-circle is 200 μ m. Second, the microresonator is enclosed by adding straight waveguides with adiabatically tapered widths to join the two semi-circles. Each straight waveguide is 800 μ m long with the width tapered linearly from 1 μ m at the two ends to 2 μ m at the middle, ensuring selective excitation of the fundamental mode in the otherwise multi-mode waveguide segment. The tapered waveguide accounts for >70% of the cavity length, thus the quality factor is minimally compromised (Table 1) and the average GVD remains to be anomalous in this novel Si 3 N 4 microresonator (Fig. 2a). The average TOD is calculated as − 155 fs 3 / mm ( Fig. 2b) and its perturbative effect on the dissipative cavity soliton is evaluated by introducing the normal- where β 1 is the group velocity and Q L is the loaded quality factor 34 . In the designed microresonator, d 3 = − 0.016 ≪ 1 and thus it is still in the GVD-dominant regime that is beneficial for soliton formation and symmetric Kerr frequency comb generation. By numerically solving the Lugiato-Lefever equation (LLE) which describes the dynamics of dissipative cavity solitons 35 , it is shown that a stable 50-fs long pulse can be generated from the designed miroresonator (Fig. 2d).
The microresonator was fabricated with CMOS-compatible processes: first, a 5 μ m thick under-cladding oxide was deposited to suppress substrate loss. An 800 nm thick Si 3 N 4 layer was then deposited via low-pressure chemical vapor deposition, patterned by optimized deep-ultraviolet lithography, and etched via optimized reactive ion dry etching. Annealing at a temperature of 1150 °C was then applied to the chip for 3 hours to reduce the waveguide propagation loss. Finally the silicon nitride spiral resonators were over-cladded with a 3 μ m thick oxide layer. Characterization of the fabricated microresonator is summarized in Fig. 3. A high resolution coherent swept wavelength interferometer (SWI) was implemented to characterize the cold cavity properties, Q and GVD, of the microresonator 17 . The wavelength of a tunable external cavity diode laser (ECDL) was linearly tuned from 1530 nm to 1590 nm at a scan speed of 60 nm/s. The laser was set to be purely TE polarized by inserting a polarizer with an extinction ratio of > 100 before the coupling optics. Similarly, an analyzer was used at the output to guarantee exclusive collection of either TE polarized (Fig. 3a) or TM polarized (Fig. 3c) transmission spectra. To ensure uniform optical frequency sampling of 7 MHz, 10% of the ECDL output was tapped to an unbalanced  Mach-Zehnder interferometer, and the photodetector output was used as the sampling clock of the data acquisition. To minimize the thermally induced resonance shift, the on-chip temperature was actively controlled to ensure the temperature drift in 1 second was within 1 mK. The accuracy of our ECDL is 200 MHz, and thus an absolute optical frequency calibration is necessary for precise characterization of the cold cavity properties. 1% of the ECDL output was thus tapped to a fiber coupled hydrogen cyanide (HCN) gas cell and the transmission spectrum of the gas cell was recorded simultaneously with that of the microresonator. Figure 3a shows the cold cavity transmission of the microresonator, calibrated with 51 absorption features of the HCN gas cell. No higher order transverse modes are observed throughout the optical C/L bands in the spectrum. The inset shows the resonance at 1556 nm, which is undercoupled with a loaded Q of 1,000,000 and intrinsic Q of 1,360,000. 10 transmission spectra were taken and independently fitted to determine the mean value of the GVD and the error bar of the dispersion measurements. Figure 3b shows the wavelength dependence of the free spectral range (FSR), measuring a FSR of 64.24 GHz and a mode non-equidistance of 196 ± 10 kHz at 1556 nm. The GVD extracted from the measurements is anomalous at − 50 ± 2.6 fs 2 /mm. A closer look at the transmission spectrum reveals that the two resonances around 1558 nm are hybridized modes from polarization coupling (green lines in Fig. 3a). Such polarization coupling mainly originates from fabrication imperfections such as surface roughness and sidewall angle 30 . The strength of the polarization coupling is rather weak and the slight dispersion disruption around 1558 nm is negligible in the Kerr frequency comb formation, as evidenced by the smooth spectral shapes shown in Fig. 4. Moreover, the 7.5 THz period of the polarization coupling is comparably larger than the 1.5 THz cycle of the higher order mode coupling. Thus the polarization coupling occurs less frequently and introduces fewer perturbations to dissipative soliton formation. Since coupling strength is inversely proportional to the difference in resonance frequencies of the interacting TE and TM modes, we further identify the on-chip temperature as a convenient control parameter to adjust the impact of polarization coupling. For instance, the cavity loading can be changed from 65% (right inset of Fig. 3a) to 40% (Fig. 3c) via increasing the on-chip temperature by 7 °C with a thermoelectric cooling device.
For Kerr frequency comb generation, the microresonator was pumped with an on-chip power up to 1.7 watts. A flat and smooth phase-locked Kerr frequency comb can be generated by pumping at any resonances in the optical C-band, thanks to the absence of quality factor and dispersion disturbance induced by mode couplings. Figure 4a shows three example spectra pumping at 1551.83 nm, 1556.48 nm, and 1561.58 nm. Importantly, the spectral shapes resemble one another and periodic amplitude modulations are not observed, distinctly different from Fig. 1 where the comb spectrum is structured by the mode coupling characteristics. Tuning speed of the , of 196 ± 10 kHz. The extracted group velocity dispersion is anomalous at − 50 ± 2.6 fs 2 /mm. The slight dispersion disruption around 1558 nm is negligible in the Kerr frequency comb formation, evidenced by the smooth spectral shapes shown in pump frequency has been shown to be a critical parameter to drive the Kerr frequency comb into low-phase noise soliton state, circumventing the thermal effect of the microresonator 16 . To find the proper tuning speed, pump power transmission was monitored while pump frequency was scanned, via control of the piezoelectric transducer, across a cavity resonance with tuning speeds varying from 1 nm/s to 100 nm/s. When the tuning speed was higher than 40 nm/s, a characteristic step signature of low-phase noise soliton state was observed. Figure 4b shows the pump power transmission with the pump frequency tuning speed set at 60 nm/s. Coherence of the Kerr frequency comb was characterized by measuring the RF amplitude noise with a scan range much larger than the cavity linewidth 15,36,37 . Pump mode was removed with a fiber WDM filter to avoid saturation of the photodetector. Figure 4c shows RF amplitude noise of the Kerr frequency comb at different states, showing the transition from a high-phase noise state (state 1) to the low-phase noise soliton state (state 2). In state 3, the pump was off-resonance and Kerr frequency comb was not generated. At the proper pump-resonance detuning, the RF amplitude noise dropped by more than two orders of magnitude (state 1 to state 2) and reached the background noise of the photodetector (state 3). The RF amplitude noise measurements confirm the generation of phase-locked Kerr frequency combs.
In summary, we report a novel design of Si 3 N 4 microresonator which can be used to attain single-mode operation, high quality factor, and anomalous dispersion all simultaneously. The microresonator is consisted of uniform single-mode waveguides in the semi-circle region, to eliminate bending induced mode coupling, and adiabatically tapered waveguides in the straight region, to ensure selective excitation of the fundamental mode. The intrinsic Q of the novel single-mode microresonator is 1.36 × 10 6 , 1.6 times larger than that of a conventional single-mode microresonator. More importantly, the GVD remains to be anomalous at − 50 fs 2 /mm. With the novel single-mode microresonator, we demonstrate the generation of phase-locked Kerr frequency combs pumped at any resonances in the optical C-band. The spectra spanning more than 20 THz (full width at − 20 dB) are smooth and flat without periodic amplitude modulations.