Fig. 4.

Dissipative Kerr solitons in hybridised modes. a Scheme of the avoided mode crossing formation. Solid and dashed lines show the simulated integrated dispersion for the fundamental and high-order modes of 1-THz Si₃N₄ microresonator with dimensions of 1.45 × 0.74 μm. Red and blue circles schematically indicate the dispersion profile of the hybridised modes forming AMX. b Measurements⁵⁴ of the mode structure of a 1-THz Si₃N₄ microresonator with the dimensions of 1.45 × 0.74 μm simulated in (a). Mode families are distinguished based on their FSRs. General dispersion trends cannot be faithfully identified due to the bandwidth limitations of our measurement setup, however a strong local anomalous group–velocity dispersion for three consecutive resonances (i), (ii), (iii) of the TE₀₀ mode family above 1064 nm can be observed. Dashed lines fit the integrated dispersion of different modes within the measurements range. c Optical spectrum of a noisy comb state, obtained in resonance (ii) from (b). d Intensity noise measurements of the noisy modulation-instability comb (MI comb, black) and the dissipative Kerr soliton (soliton, red) states, obtained by pumping the resonance (i) from (b). e Optical spectra of the DKS states obtained by pumping resonances (i), (ii), (iii) from b. Grey circles indicate the positions of primary comb lines. f Response measurements of DKS states represented in (e). The positions of characteristic $\mathcal{C}$-resonance and $\mathcal{S}$-resonance are indicated with C and S letters, correspondingly