Experimental realization of topologically controlled THz localization. (a) Illustration of nonlinear generation and confinement of THz-waves in an SSH-type microstructure. The LN structure undergoes a transition from L-LD, through equidistant, to S-SD regions along the +z-axis, illustrated by colors shaded from orange into blue. The polarization of the THz electric field and that of the optical pump beam are all along the direction of the LN crystalline axis (z-axis). (b) Microscope image of the LN array structure fabricated by fs-laser writing. The thickness of the LN chip is 50 μm in the y-direction. The total length of the microstructure along the z-direction is L=6mm. d1 and d2 are the spacings between neighboring LN stripes corresponding to the coupling coefficients c1 and c2, respectively. At the dashed yellow line, z = L/2 and d1 = d2 = 55 μm, which leads to an equidistant structure. Credit: Light: Science & Applications (2022). DOI: 10.1038/s41377-022-00823-7

Eigenvalues and representative eigenmode distributions in the SSH-type LN topological structure. (a) Calculated eigenvalue distribution of the microstructure along the z-axis. The yellow line represents the equidistant structure at z = L/2 (d1 = d2 = 55 μm), which marks the phase transition point. The left side of the yellow line (z < L/2) is the L-LD region, where topological defect modes are denoted by red dots. The right side (z > L/2) indicates the S-SD region, where topologically nontrivial and trivial defect modes are marked by green and blue dots, respectively. Gray dots represent the bulk modes. b1 Topological defect mode around 0.3 THz in the L-LD structure at z = 0. b2 The mode around 0.3 THz in the equidistant structure at z = L/2. b3, b4 Topological trivial mode around 0.42 THz (b3) and nontrivial mode around 0.3 THz (b4) in the S-SD structure at z = L. Credit: Light: Science & Applications (2022). DOI: 10.1038/s41377-022-00823-7

Experimental (top two rows) and numerical (bottom two rows) demonstrations of topologically controlled THz confinement in the LN chip from L-LD, through equidistant, to S-SD regions of the wedge-shaped SSH photonic lattice. (a–e) correspond to locations (A–E) marked in Fig. 1b. a1–e1 Measured spectra at the corresponding positions. a2–e2 Energy distribution of the modes showing different confinement of the generated THz waves in the LN chip. a3–e3 Simulated x−t diagrams showing the THz waves evolution in different regions, where a4–e4 are the corresponding spectra. The lattice sites are illustrated by white tick marks in a3–e3, and a in (a1, a4) is the lattice constant for the corresponding L-LD structure. Credit: Light: Science & Applications (2022). DOI: 10.1038/s41377-022-00823-7

Distinction between topologically nontrivial and trivial defect modes under chiral perturbations. (a1) Calculation of the eigenvalue distribution ε under 500 sets of off-diagonal perturbations in the L-LD structure. The red dots (forming a line) represent the eigenvalues associated to the topological mode and the gray dots show the distribution of the bulk modes. (a2) Simulation of the x−t diagram for the central defect excitation under perturbations. (a3) The corresponding spectrum of (a2). b1–b3 have the same layout as (a1–a3) but for the S-SD structure, where green and blue dots denote nontrivial and trivial defect modes, respectively. c Plot of p versus perturbation strength ξ, where p=nbulk/nall, with nbulk defined as the number of perturbation sets that result in coupling of the trivial defect mode with the bulk modes and nall as the total number of perturbation sets (in this case nall=500). Red and green lines illustrate the nontrivial modes in the L-LD and S-SD structures, respectively, while the blue line is for the trivial defect mode in the S-SD structure. Credit: Light: Science & Applications (2022). DOI: 10.1038/s41377-022-00823-7