Fig. 3: Nonlinear evolution of eigenvalues and coupling to the edge states in topologically nontrivial SSH lattices. | Light: Science & Applications

Fig. 3: Nonlinear evolution of eigenvalues and coupling to the edge states in topologically nontrivial SSH lattices.

From: Nontrivial coupling of light into a defect: the interplay of nonlinearity and topology

Fig. 3

a Two linear edge states (red and black) found in the SSH lattice (dark blue) used in our theoretical analysis. Band structure and nonlinearity-induced eigenvalue shifting under normal (straight) excitation conditions at low (b) and high (c) nonlinearity; the insets show the linear topological edge mode (green dashed line) and the nonlinear edge mode (red solid line). The evolving nonlinear eigenvalues \(\beta _{NL,n}(z)\) are shown for z > 0. For comparison, the linear spectrum βL,n is shown for z < 0. The red line is the eigenvalue of the (left) nonlinear edge mode, and the black line corresponds to the (right) linear edge mode, which is not excited. The thick blue lines are the bands. d Nonlinear eigenvalue evolution under tilted excitation conditions (corresponding to the left panels of Fig. 1). The red (black) line denotes the nonlinear (linear) edge eigenvalue as in b, c, while the individual blue dotted lines correspond to nonlinear localized states not inherited from the linear topological edge states. The three stages of the dynamics described in the text are denoted with the magenta, gray, and green shaded regions, respectively. e The overlap of the whole beam with the linear edge state Fall(z). f The overlap of the linear and nonlinear edge modes Fedge(z) at the three stages of evolution. See the text for details

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