Symmetry protection against mode crossings for dissipative Kerr soliton generation in microresonator chains

The analogy between molecules and coupled cavities has been pointed out in a variety of works [1] . As molecular energy surfaces, transverse modes of an integrated microresonator experience avoided mode crossings (AMXs) which perturb an ideal dispersion profile [2] . Chromatic dispersion balancing the Kerr nonliterary in such resonators can result in the generation of dissipative Kerr solitons (DKSs) [3] . Even though AMX can be employed, it remains an undesirable effect which induces a perturbation on the DKS state [2] . The possibility of DKS generation in a photonic dimer (two coupled microresonators) has been recently reported [4] . DKSs can be generated in one of the hybridized dimer supermodes: symmetric (S) and antisymmetric (AS). The linear transmission spectroscopy of the photonic dimer revealed that the AS supermode family is protected against the AMXs while the S supermode family interacts with higher-order modes stronger than expected (see Fig. 1a ), thereby disrupting the DKS generation. We term the effect of vanishing interaction between transverse modes as symmetry protection.