Fig. 1. Theoretical predictions of double topological darkness (zero-reflections). (a) Schematics of light reflection for observing PSs from the ultra-thin absorbing dielectric on a metal substrate. The effective medium layer (EML) has fixed thickness. (b) The yellow point of intersection of spectral dispersion curve n(λ), k(λ) of the top layer Ge with the ZRS with a blue point for p-polarized light and ZRS with a red point for s-polarized light are topologically protected.

Fig. 2. Double topological PS effect in ultra-thin absorbing dielectric structures. Schematic of the Ge (26 nm)/Ag system exhibiting: (a) p-polarized topological darkness point effect, and (b) s-polarized topological darkness point effect. TMM calculated angular reflectivity spectra for: (c) p-polarized and (d) s-polarized reflectance spectrum of the thin-film absorber. (e, f) Show the reflectance measurements, respectively. The yellow circle regions refer to wavelength and angle pairs where the polarization darkness points occur for p-polarized light and s-polarized light. Reflectance spectra are shown for p-polarization at (g) 80.2° and for s-polarization at 29.4°, with measured data represented by hollow triangles and calculated data by solid lines.

Fig. 3. Experimental observation of PSs. (a−c) Simulated and (b−d) experimental ellipsometric parameters amplitude (Ψ) and phase (Δ) for Ge (26 nm)/Ag system. The yellow circle regions refer to wavelength and angle pairs where the topological PSs for p-polarized light (Ψ = 0° at 80.2° 587.8 nm) and s-polarized light (Ψ = 90° at 29.4° 937.1 nm) occur. (e, f) Ellipsometry parameters Ψ and Δ at the above two angles (80.2° and 29.4°) for p- and s-polarized light, represented by solid circles for measured data and solid lines for TMM calculations.

Fig. 4. Topological nature of darkness points associated with spectral PSs. (a) Schematic of the multi-port multimode system. (b) Analyses using a multiple scattering model along with the thin-film system to determine the typical reflection phase. (c, d) Investigation of the ellipsometry parameters Ψ and Δ at the aforementioned angles (80.2° and 29.4°) for p- and s-polarized light, measured with solid circles and calculated using TCMT represented by solid line.

Fig. 5. Double topological PSs in ultrathin absorbing dielectric structures with PVA film. Schematic of the PVA (40 nm)/Ge (26 nm)/Ag system exhibiting (a) the p-polarized topological darkness point effect and (b) the s-polarized topological darkness point effect. (c, d) Investigation of the ellipsometry parameters Ψ and Δ at the aforementioned angles (73.0° and 48.0°) for p- and s-polarized light, measured with solid circles and calculated using TMM represented by solid lines.

Fig. 6. Humidity sensor based on topology of PVA film on Ge/Ag. (a, b) The dependence of ellipsometric parameters Δ and Ψ on the humidity of air recorded at the incidence angle of 73.0° with p-polarization topological darkness points, corresponding to the PS. The insets show the magnified view of Δ and Ψ. (c) The jump of Δ with increased humidity at λ = 734.3 nm to 741.6 nm. The error bars represent the standard deviation of multiple measurements. (d) Spectral shift of the resonance position of Ψ spectrum with increased humidity of air.

Fig. 7. Humidity sensor based on topology of PVA film on Ge/Ag. (a, b) The dependence of ellipsometric parameters Δ and Ψ on the humidity of air recorded at the incidence angle of 48.0° with s-polarization topological darkness points, corresponding to the PS. The insets show the magnified view of Δ and Ψ. (c) The jump of Δ with increased humidity at λ = 937.8 nm to 940.7 nm. The error bars represent the standard deviation of multiple measurements. (d) Spectral shift of the resonance position of Ψ spectrum with increased humidity of air.