Fig. 2: Supersymmetric topological photonic structures.
From: Topological state engineering via supersymmetric transformations
Eigenvalue spectrum of (a) the superpartner SP1 lattice, obtained by removing a bulk state (m = 1), (b) the Su-Schrieffer-Heeger (SSH) lattice, and (c) the superpartner SPN/2 lattice obtained by eliminating an edge state (m = N/2). The energy gap is 2|c1 − c2| and cT = c1 + c2. Sketch of the (d) SP1, (e) SSH, and (f) SPN/2 lattices. Detuning (coupling) is indicated by the size (spacing) of (between) the circles. The intensity of the color inside each waveguide is proportional to the amplitude of the state. Experimentally observed light evolution along the propagation direction and output intensities for the (g) nontopological edge state, (h) topological edge state, and (i) topological interface state. The total length of the sample is L = 10 cm and the wavelength used to excite the waveguides is λ = 633 nm. The SSH, SP1, and SPN/2 lattices are composed of N = 50, N = 49, and N = 109 waveguides, respectively. The original SSH lattice used to synthetize the SP1 (SPN/2) lattice is composed of N = 50 (N = 110) waveguides, c1 = 0.5 cm—1 and c2 = 1.0 cm—1 (c2 = 1.8 cm—1). The different number of waveguides and coupling coefficients used to create the superpartner structures are due to experimental restrictions. In particular, the SP1 lattice has weaker couplings to adjust the detunings below 2 cm—1 in order to guarantee that the couplings stay constant when changing the detuning.
