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Level 2 · How matter responds to light

Refractive index n(E)

n + iκ

A complex number that tells light how much to slow down (real part) and how much to fade (imaginary part) inside a material.

Build on:Photon & energy of light,Atoms & electrons

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:

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.

Real (blue) and imaginary (red) parts of the refractive index near a single resonance. The real part bumps up before E₀ and dips after — this is anomalous dispersion.

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).

Key takeaways
  • 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.
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