Numerical investigation of turnkey soliton generation in an organically coated microresonator

Kerr soliton frequency-comb generation in microresonators has attracted extensive interest since soliton microcombs offer the potential for integration and can be widely used in many fields, such as spectroscopy, communications, precision metrology, sensing, etc. Here, the mechanism of turnkey soliton generation in a microresonator with an organic material coating is illustrated and investigated in both analytical and numerical ways. In particular, based on the thermal curve under a stable state and soliton power from analytical analysis, the turnkey soliton generation regime is calculated and proved by coupled equations with the split-step Fourier method. In addition, the physical parameters of the hybrid modes in the coated resonators are studied, and a suitable design is given in this paper. This research will be helpful for increasing the accessibility of Kerr solitons and make them easier to integrate.

Figure 1

Influence of the thermo-optic effect on soliton generation. The three panels demonstrate the intracavity energy when the input laser is scanned towards a longer wavelength of silica wedge resonators with a wedge angle of $8^{\circ }$ and different coating thicknesses. The design of the silica wedge resonators is given in Sec. 2c. The input power is 0.7 W, and the scanning speed is about 1.5 THz/s in all panels. The results are calculated under critical coupling, and the thermal process is amplified 100 times. (a) The PDMS layer thickness is 1200 nm, and the TOC is almost zero. This plot shows the process of soliton generation without the thermo-optic effect. Different states of the process are shaded in different colors (gray scales). The purple dashed line and red dotted line demonstrate the directions of the process move with and without coating compensation, respectively. (b) This silica wedge resonator does not have a PDMS coating, and its TOC is positive. The red dashed line shows the resonance frequency drift caused by the thermo-optic effect. When it comes into the soliton regime, the plunge of the intracavity energy (temperature) causes a positive thermal drift which pulls the input laser out of the soliton regime, and this makes the soliton step become very short. (c) The PDMS layer thickness is 1210 nm, and it suffers a negative thermo-optic effect. The soliton step is slightly extended by the negative thermo-optic effect.

Figure 2

Simulated frequency response of the thermo-optic effect. This result is acquired by a SiN microresonator with a waveguide width of $0.6\mu \text{m}$ and a PMMA coating thickness of 280 nm. The design of the SiN ring resonators is given in Sec. 2c.

Figure 3

Turnkey soliton generation. The turnkey solitons are generated in a SiN ring resonator which is designed in Sec. 2c. The width of the SiN is $0.6\mu \text{m}$, and the PMMA coating thickness is 275 nm. (a) Process of an automatically generated soliton. The inset illustrates the mechanism of the transition to the soliton state, and the blue (light gray) line demonstrates the bistability caused by the Kerr nonlinearity. The black line is acquired from the numerical calculation of the LLE, and it shows the real path of the self-start soliton generation in the simulation. The red (dark gray) line is the thermo-optic curve which is derived from Eq. (6) when it reaches the steady state. Intersections of the red (dark gray) line and soliton steps (dashed lines) mean these soliton numbers can reach the thermal equilibrium. (b) Representative switching-on soliton results from 10 consecutive runs. The bottom panel shows the corresponding thermal drift according to the top panel. Detuning $\zeta$ is 2.5. The ones which are failed to generate solitons do not have intersections with the thermo-optic curve. Their soliton power is too high, and the thermal drift pulls them out of the soliton regime. The breather soliton means the intersections are in the breather soliton regime. Namely, the soliton number $N$ is too small. (c) Calculated turnkey soliton generation regime. The black dashed lines are set by the different soliton numbers. The parametric threshold has upper and lower detuning limits for a determined input power as there are two detunings for one determined intracavity power. (d) Success rates of different pump detunings when $f^2=15$. Every detuning is calculated 50 times. (e) The counts of stabilizing to different soliton numbers in (d).

Figure 4

Results of designed PDMS-coated silica wedge resonators. (a) Geometry and mode energy distribution of the designed silica resonators. The energy distribution in the air is neglected since it is too small. In the simulations, the PDMS coatings are assumed to cover the silica evenly on all surfaces. The diameter and the thickness are included only for silica. (b) Threshold power of the designed silica resonators with different wedge angles. The inset shows the absorption $Q$, and the scattering $Q$ is set as 100 million in the calculations. (c) TOC of the designed silica resonators with different wedge angles. (d) $D_2/2\pi$ of the designed silica resonators with different wedge angles.

Figure 5

Results of designed PMMA-coated SiN ring resonators. (a) Geometry and mode energy distribution of the designed SiN resonators. (b) Threshold power of the designed SiN resonators with different widths. The inset shows the absorption $Q$, and the scattering $Q$ is set as 1 million in the calculations. (c) TOC of the designed SiN resonators with different widths. (d) $D_2/2\pi$ of the designed SiN resonators with different widths.