Fig. 1: Construction of a quadrupole higher-order topological insulator using a synthetic frequency dimension in a photonic molecule array.
From: Higher-order topological insulators in synthetic dimensions
a Tight-binding lattice of a quadrupole topological insulator. Blue and red lines represent positive and negative real values of the coupling strength. Thin and thick lines represent intra-cell and inter-cell coupling strengths of magnitude γ and λ, respectively. Each vertical column is an SSH strip with the same coupling strength sign throughout, whereas adjacent vertical lines have a phase offset in the coupling strength of π. b Implementation of the SSH strip in the synthetic frequency dimension using modulated coupled rings (photonic molecule), with JA(t) as in Eq. (1). c Mode structure of the system in b with sets of frequency modes separated by the FSR Ω in the absence of modulation and coupling. d Mode spectrum of the coupled ring system or photonic molecule. Each set is separated by a frequency difference equal to the coupling constant between the rings, 2K. The modulation introduces coupling between the supermodes. e Several of the synthetic SSH strips in b can be evanescently coupled with alternating coupling strengths γ and λ to realize the quadrupole HOTI lattice in a. We note that the modulation pattern of the unit cell of four rings has a quadrupole nature
