Fig. 3: Engineering SSH edge modes.

a Schematic of the SSH model. Each unit cell contains two cavities A and B, both with frequency ω_r. J₁ and J₂ are respectively the intracell and intercell coupling. b Simulated phase transition diagram of the SSH model from trivial (J₁ > J₂) to topological (J₁ < J₂) phase, with \({J}^{{\prime} }=0\). The black lines represent the bulk modes for a CCA with N = 32. For J₁ ≠ J₂, the system presents a bandgap of size \({\Delta }_{\,{\mbox{Bulk}}\,}^{32}\). In the non-trivial phase, two hybridized SSH edge modes (red and orange) are enabled at the center of the bandgap and are separated by \({\Delta }_{\,{\mbox{Topo}}\,}^{32}\). The gray area represents the phase transition diagram N → ∞. c (e) Simulated photonic population of the CCA with N = 64 in correspondence of the symmetric (red) and antisymmetric (orange) hybridized SSH edge modes in the weakly localized configuration, J₂/J₁ = 1.22 (strongly localized configuration, J₂/J₁ = 1.57) according to the eigenvectors of the CCAs Hamiltonian (see Methods). d (f) Left: Transmission spectrum ∣S₂₁∣, for CCAs with J₂/J₁ = 1.22 (J₂/J₁ = 1.57) and N = 16, 32 and 64. Right: Reflection spectra Arg S_11,22, as a function of the frequency detuning \(f-\overline{{f}_{Topo}}\), for a frequency region of 100 MHz around the SSH edge modes. \(\overline{{f}_{{{{\rm{Topo}}}}}}\) is the mean frequency of the two SSH edge modes. The modes in red and orange represent the symmetric and antisymmetric hybridized SSH edge modes, respectively.