Symmetry protection of topological states in multimode photonic resonator chains.

The driven dissipative nonlinear multimode photonic dimer is considered as the simplest case of solitons in photonic lattices. It supports a variety of emergent nonlinear phenomena including gear soliton generation, symmetry breaking and soliton hopping. Surprisingly, it has been discovered that the accessibility of solitons in dimers drastically varies for the symmetric and anti-symmetric supermode families. Linear measurements reveal that the coupling between transverse modes, that give rise to avoided mode crossings, can be almost completely suppressed. We explain the origin of this phenomenon which we refer to as symmetry protection. We show its crucial influence on the dissipative Kerr soliton formation process in lattices of coupled high Q resonators of any type. Examining topologically protected states in the Su-Schrieffer-Heeger model of coupled resonators, we demonstrate that topological protection is not sufficient against the transversal mode crossing induced disorder. Finally, we show that the topological edge state can be symmetry protected by carefully choosing the balance between intra- and inter-resonator coupling to higher-order transverse modes, which suppresses mode crossings.