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. 2023 Sep 12;10(10):3715-3722.
doi: 10.1021/acsphotonics.3c00879. eCollection 2023 Oct 18.

Topological Darkness in Optical Heterostructures: Prediction and Confirmation

Affiliations

Topological Darkness in Optical Heterostructures: Prediction and Confirmation

Emma Cusworth et al. ACS Photonics. .

Abstract

Topological darkness is a new phenomenon that guarantees zero reflection/transmission of light from an optical sample and hence provides topologically nontrivial phase singularities. Here we consider topological darkness in an optical heterostructure that consists of an (unknown) layer placed on a composite substrate and suggest an algorithm that can be used to predict and confirm the presence of topological darkness. The algorithm is based on a combination of optical measurements and the Fresnel equations. We apply this algorithm to ultrathin Pd films fabricated on a Si/SiO2/Cr substrate and extract four different points of topological darkness. Our results will be useful for topological photonics and label-free optical biosensing based on phase interrogation.

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Conflict of interest statement

The authors declare no competing financial interest.

Figures

Figure 1
Figure 1
Concept of TD. (a) Schematics of a sample. All of the sample layers have fixed thicknesses. Red arrows show incident and reflected light. (b) The red point of intersection of spectral dispersion curve n(λ), k(λ) of the top layer with the zero reflection surface (the orange surface with mash) is topologically protected.
Figure 2
Figure 2
Topological darkness in composite heterostructures. (a) Ellipsometric reflection spectra for different angles of incidence for a 5 nm layer of chromium placed on a composite substrate made of 290 nm of SiO2 on Si. (b) Ellipsometric reflection spectra Ψ(λ) observed at an angle of incidence 58° for the same sample. The inset shows the ellipsometric phase Δ behavior. (c) Composite heterostructures discussed in this work. (d) The algorithm of predicting and confirming TD. (e) Optical constants of the top layer extracted from ellipsometry measurements. (f) The red point of intersection of spectral dispersion curve n(λ), k(λ) of the top layer with the zero-reflection surface (the orange surface with mash), is topologically protected.
Figure 3
Figure 3
Topological darkness in composite heterostructures: prediction and confirmation. (a) A schematic drawing of the studied sample. Each layer is labeled with its thickness. (b) Measured ellipsometric reflection spectra as a function of incident angle. The dotted lines show the transfer-matrix fitting of the spectra. (c) The optical constant of the Pd film used for fitting. (d) Zero reflection surfaces for the studied structure calculated for p-polarized light. (e) The intersection of the dispersion curve of the Pd film (n(λ), k(λ), and λ) with ZRSs. The red intersection points predict 4 points of TD. (f) The experimental ellipsometric reflection, Ψ, showing 4 points of TD (where Ψ = 0 and, hence, rp = 0) observed at the predicted angles of incidence.
Figure 4
Figure 4
Properties of topological darkness. (a) 3D graph of ellipsometric reflection spectra. (b) cos(Δ) as a function of wavelength and angle of incidence. (c) A zoomed-in part of cos(Δ) as a function of wavelength and angle of incidence. (d) ZRSs in the (n, k, θ) space.

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