Fig. 1. Structure of the SiN microresonator.SiN微腔结构示意图

Fig. 2. Second harmonic waves generates inside the SiN microresonator (δ₁ = 0, E_in = 1 W^1/2): (a) Evolution of the second harmonic waves; (b) curves of the fundamental frequency waves power and (c) the second frequency waves power vary with the round trip number; (d) stationary distribution of the fundamental frequency waves light field and (e) the second frequency waves light field; (f) spectra of the fundamental frequency waves and (g) the second frequency waves. SiN光学微腔中二次谐波的产生 (δ₁ = 0, E_in = 1 W^1/2)　(a) 倍频光场在腔内的演化过程; (b) 基频光功率随光在腔内循环次数的变化曲线; (c) 倍频光功率随光在腔内循环次数的变化曲线; (d)基频场的稳定分布; (e)倍频光场的稳定分布; (f)基频光的光谱; (g) 基频光的光谱

Fig. 3. Light field evolution in the microresonator with the frequency detuning (δ₁ = 0.1 and E_in = 1 W^1/2): (a) Curves of the fundamental frequency waves power and (b) the second frequency waves power vary with the round trip number; evolution of (c) the fundamental frequency waves (d) the second frequency waves after the light fields are stable; stationary distribution of (e) the fundamental frequency waves light field and (f) the second frequency waves light field. 发生频率失谐后, 微腔内光场变化情况 (δ₁ = 0.1, E_in = 1 W^1/2)　(a) 基频光功率和(b)倍频光功率随光在腔内循环次数的变化曲线; 光场稳定后, (c)基频光场和(d)倍频光场随时间的演化; (e) 基频光场和(f)倍频广场的稳定分布

Fig. 4. Influence of the frequency detuning δ₁ on the power change curves: (a) Curves of the power variation for the fundamental frequency waves, 0.02 ≤ δ₁ ≤ 0.08; (b) curves of the power variation for the fundamental frequency waves, 0.2 ≤ δ₁ ≤ 0.8; (c) curves of the power variation for the second harmonic waves, 0.02 ≤ δ₁ ≤ 0.08; (d) curves of the power variation for the second harmonic waves, 0.2 ≤ δ₁ ≤ 0.8. 失谐参量δ₁取不同值时, 微腔内基频光和倍频光功率变化曲线　(a) 0.02 ≤ δ₁ ≤ 0.08时, 基频光功率变化曲线; (b) 0.2 ≤ δ₁ ≤ 0.8时, 基频光功率变化曲线; (c) 0.02 ≤ δ₁ ≤ 0.08时, 倍频光功率变化曲线; (d) 0.2 ≤ δ₁ ≤ 0.8时, 倍频光功率变化曲线

Fig. 5. Stable evolution of the dual light fields when δ₁ = 1: (a) Evolution of the fundamental frequency waves; (b) evolution of the second harmonic waves; (c) intensity profiles of the fundamental frequency waves at six different moments within a period, the waveforms are plotted every hundred times; (d) intensity profiles of the second harmonic waves at six different moments within a period, the waveforms are plotted every hundred times. 失谐参量δ₁ = 1时, 腔内光场稳定后基频光和倍频光的光场演化　(a) 基频光场的演化; (b) 倍频光场的演化; (c) 基频光光场变化周期内, 光在腔内每循环100次, 绘制其波形; (d) 倍频光光场变化周期内, 光在腔内每循环100次, 绘制其波形

Fig. 6. Chaos inside the microresonator, when the value of detuning parameter is too large: (a) Chaos of the fundamental frequency waves; (b) chaos of the second harmonic waves; (c) intensity profile of the fundamental frequency waves in a moment; (d) intensity profile of the second harmonic waves in a moment; (e) spectrum of the fundamental frequency waves; (f) spectrum of the second harmonic waves.失谐参量δ₁取值过大时, 腔内光场的混沌状态　(a) 基频光光场的混沌状态; (b) 倍频光光场的混沌状态; (c) 某一时刻基频光场的分布; (d) 某一时刻倍频光场的分布; (e) 与图(c)中光场对应的基频光光谱; (f) 与图(d)中光场对应的倍频光光谱

Fig. 7. Influence of the pump power on the power change curves: (a) Power variation for the fundamental frequency waves; (b) power variation for the second harmonic waves.抽运功率对腔内光功率的影响　(a)腔内基频光功率的变化情况; (b)腔内倍频光功率的变化情况

Fig. 8. Evolution of the light field in the microresonator at E_in = 100 W^1/2: (a) Curve of power variation for the fundamental frequency waves; (b) curve of power variation for the second harmonic waves; (c) periodic evolution of the fundamental frequency waves; (d) periodic evolution of the second harmonic waves. E_in = 100 W^1/2时, 微腔内光场的演化　(a) 基频光功率的变化曲线; (b) 倍频光功率的变化曲线; (c) 光场稳定后, 腔内基频光光场的周期性演化; (d) 光场稳定后, 腔内倍频光光场的周期性演化

Fig. 9. Curves of the power variation for the fundamental frequency waves and the second harmonic waves: Power variation for (a) the fundamental frequency waves and (b) the second harmonic waves at E_in = 800 W^1/2; power variation for (c) the fundamental frequency waves and (d) the second harmonic waves at E_in = 1000 W^1/2; power variation for (e) the fundamental frequency waves and (f) the second harmonic waves at E_in = 1200 W^1/2. 基频光和倍频光的功率变化曲线　 E_in = 800 W^1/2时(a)基频光和(b)倍频光的功率变化; E_in = 1000 W^1/2时(c)基频光和(d) 倍频光的功率变化; E_in = 1200 W^1/2时(e)基频光和(f)倍频光的功率变化

Fig. 10. Turning patterns in the microresonator, when FSR = 300 GHz (E_in = 100 W^1/2, δ₁ = 0.1): (a) Curves of the power variation for the fundamental frequency waves; (b) curves of the power variation for the second harmonic waves; (c) evolution of the fundamental frequency waves; (d) evolution of the second harmonic waves; (e)spectra of the fundamental harmonic waves; (f) spectra of the second harmonic waves. 微腔FSR = 300 GHz时, 微腔内出现“图灵环”(E_in = 100 W^1/2, δ₁ = 0.1)　(a)基频光功率变化曲线; (b)倍频光功率变化曲线; (c) 腔内光场稳定后, 基频光光场随时间的演化; (d) 腔内光场稳定后, 倍频光光场随时间的演化; (e) 腔内光场稳定后, 基频光的光谱; (f) 腔内光场稳定后, 倍频光的光谱

Fig. 11. Stable intensity profile and spectra of the fundamental frequency waves for FSR = 298 GHz: (a) Intensity profile of the fundamental frequency waves; (c) spectrum of the fundamental frequency waves; (b) intensity profile of second harmonic waves; (d) spectrum of second harmonic waves.微腔FSR = 298 GHz时, 稳定后的光场分布及光谱　(a)基频光的光场分布; (b) 倍频光的光场分布; (c) 基频光光谱; (d) 倍频光光谱

Fig. 12. Stable intensity profile and spectra of the fundamental frequency waves for FSR = 295 GH: (a) Evolution of the fundamental frequency waves; (b) evolution of the second frequency waves; (c) intensity profile of the fundamental frequency waves; (d) spectrum of the fundamental frequency waves; (e) intensity profile of the second harmonic waves; (f) spectrum of the second harmonic waves.微腔FSR = 295 GHz时, 稳定后的基频光和倍频光光场分布及光谱　(a) 基频光光场随时间的演化; (b) 倍频光光场随时间的演化; (c) 基频光场的瞬时分布; (d) 倍频光场的瞬时分布; (e) 基频光场的光谱; (f) 倍频光场的光谱