Two numbers, one wave
When light enters a material two things happen: it slows down and it fades. We bundle both into a single complex number called the refractive index:
ñ(E) = n(E) + i·κ(E)The real part n sets how much the wavelength shrinks inside the material (light slows from c to c/n). The imaginary part κ sets how quickly the amplitude decays — which we measure as absorption.
Where the numbers come from
Both n(E) and κ(E) are not free parameters of the material; they are dictated by its allowed electronic transitions. The simplest way to model a single transition is a damped oscillator (a Lorentzian). Move its centre, width, and strength around to see how n and κ deform in lockstep:
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.
The handle the simulator turns
In CrSBr the dominant transition near 1.375 eV is the exciton. Its position depends on the local spin arrangement. That is exactly the chain through which a flipped spin ends up shifting a dip in R(E).
- Refractive index is one complex number per photon energy.
- Real part = how much light slows. Imaginary part = how much light fades.
- Each electronic resonance carves a paired bump-and-peak into the spectrum.