Two ways of describing how a material answers light. The refractive index says how much more slowly light travels inside it than in vacuum, which bends rays at a surface and sets how much light is reflected; a second part says how strongly the material absorbs. The dielectric function packs both into one quantity for each colour, describing how the material’s charges swing in the light’s electric field. These numbers are why a layer one atom thick can be seen at all on the right substrate, and why some layered crystals slow light very differently along and across their layers.
In 2D the dielectric function approaches 1 as q → 0 and the screened interaction varies rapidly at small q.
Light crossing a material drives its electrons back and forth, and the re-radiated waves add to the original one so that the combined wave travels more slowly. The refractive index n is the ratio of the speed in vacuum to the speed inside: about 1.5 for glass. Because the speed changes at a surface, rays bend there and part of the light is reflected – the more so the bigger the jump in index. A second number, the extinction coefficient κ, says how fast the light dies away as it is absorbed.
The dielectric function combines the two, ε = (n + iκ)2, and describes the same thing from the material’s side: how strongly its charges respond to an oscillating electric field at each frequency. It has peaks where the material absorbs – at band edges and, in 2D semiconductors, at exciton resonances – and its real and imaginary parts are tied together, so measuring one over a wide enough range gives the other (the Kramers–Kronig relations).
A single layer is too thin for a thickness to mean much, but it still has a dielectric function, and that is what is measured. From reflection spectra of monolayer MoS2, MoSe2, WS2 and WSe2 between 1.5 and 3 eV, an analysis constrained by the Kramers–Kronig relations gives their in-plane dielectric functions and how much light each absorbs (Li and colleagues, 2014). Graphene is simpler still: suspended in air it absorbs πα ≈ 2.3% of white light, a number set only by the fine-structure constant (Nair and colleagues, 2008).
These values are what make 2D layers visible. On silicon with a thin oxide, interference between reflections from the layer, the oxide and the silicon turns a few percent of absorption into a visible change of colour – optical contrast – and ellipsometry measures the dielectric function of whole films the same way.
Layered crystals are held together strongly within each layer and only weakly between them, and light notices: its speed depends on whether its electric field points along the layers or across them. This difference, birefringence, is unusually large. MoS2 reaches a birefringence of 1.5 in the infrared and 3 in the visible, far beyond the previous record of 0.8 in BaTiS3 and hexagonal boron nitride (Ermolaev and colleagues, 2021) – enough to guide and steer light in structures smaller than its wavelength.
The dielectric function at zero frequency and finite wavevector describes a different side of the same response: how charges screen each other. In a single layer that screening is weak, which is why excitons in 2D semiconductors are so strongly bound.
The complex refractive index ñ = n + iκ and dielectric function ε(ω) = ε1 + iε2 = ñ2 describe the linear optical response; κ and ε2 give absorption, and real and imaginary parts are tied by Kramers–Kronig relations. For monolayers ε(ω) is extracted from reflection spectra with a Kramers–Kronig-constrained analysis, as for the in-plane response of MoS2, MoSe2, WS2 and WSe2 from 1.5 to 3 eV, which also gives their absolute absorbance. Suspended graphene absorbs πα ≈ 2.3% of white light, fixed by the fine-structure constant. Layered crystals are strongly anisotropic: MoS2 reaches a birefringence of 1.5 in the infrared and 3 in the visible, against the previous best of 0.8 for BaTiS3 and hBN. The static, wavevector-dependent ε(q) is the screening that sets Coulomb interactions and exciton binding in 2D.
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