Fig. 4: Topological end states in truncated optical superlattices.
From: Realization of photonic charge-2 Dirac point by engineering super-modes in topological superlattices
a The upper panel: the schematic picture of the truncated optical superlattice p5[p2DAq6DBp2]5p5 with (dA,dB) = (3,0) and (δ,ξ,Δ) = (−3.8,0, −4.1). The lower panel: distributions of the electric field norm of topological end modes 1–4. b Measured reflection spectra of the sample depicted in a for transverse-magnetic (TM) and transverse-electric (TE) polarizations excited by both F and B oblique incident light with an angle of 30°. The four dips marked with black arrows correspond to topological end states 1–4. c Measured reflection spectra of the sample p5[p2DAq6DBp2]5p5 with (dA,dB) = (0,0) ((δ,ξ,Δ) = (−3.8,0,0)) for TM and TE polarizations excited by F incident light with an angle of 30°. d Eigenfrequency surfaces showing two WPs (transparent blue cones) and topological ends modes (purple and orange sheets) in the δ − Δ space with kx = 6μm−1 for both TM and TE polarizations. The experimental dips in b and c are labelled by open circles and upward-pointing triangles, respectively. For display purpose, the vertical distance between two Weyl points is deliberately magnified. e Frequencies of topological end modes for TM and TE polarizations as a function of kx for the sample used in a and b. The solid lines are results of numerical calculations, the open markers are obtained directly from experimental data, and experimental uncertainties are shown by error bars. The topological end states 1–4 shown in b are encircled by a black dashed ellipse. f, g Eigenfrequencies of topological end states for TM and TE polarizations in the f Δ = −4.1 THz and g Δ = 0 THz plane. The black regions in f and g refer to the bands of super-modes and the dashed lines in d, f, and g correspond to the calculated dispersion of topological end modes.
