EQMResearch group
Level 2 · How matter responds to light

Dielectric function ε(E)

The full optical fingerprint of a material. Excitons show up here as bumps that turn into dips and peaks in the reflectance.

Build on:Refractive index n(E),Exciton

The optical fingerprint of a material

The dielectric function ε(E) = ε₁ + i ε₂ is just another way of writing the refractive index, since ñ² = ε. It is the quantity electrodynamics cares about.

For our purposes it is the sum of all the optical contributions of a material: a flat background ε∞from high-energy transitions, plus one Lorentzian for every discrete transition we care about. CrSBr's simplified model has a single Lorentzian — the exciton — sitting on top of ε∞ ≈ 7.9.

ε(E) = ε∞ + f / (E₀² − E² − iγE)

See it move

Tweak the resonance and watch n and κ deform — the very same plot you saw on the refractive-index page, because they are two faces of the same coin:

E₀ = 1.375 eVEnergy (eV) →nκ1.251.381.50

ε(E) = ε∞ + f / (E₀² − E² − iγE). The real part of n bumps up before the resonance and dips after it (anomalous dispersion); the absorption κ peaks right at E₀ — same shape as a Lorentzian.

Key takeaways
  • ε(E) = sum of background + one Lorentz term per electronic transition.
  • In CrSBr a single exciton dominates the part of the spectrum we look at.
  • The simulator builds a per-layer ε(E) on the fly from the phase window.
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