Kramers-Kronig Relation

Dispersion: Wavelength Dependence

• Optical Properties vary with wavelength.
• Transparent regions (normal dispersion).
• Absorbing regions (anomalous dispersion).

The Dielectric Function ɛ(ω)

• The Dielectric Function ɛ(E) or ɛ(ω), is the Dielectric Polarization as a function of Energy (or Frequency).

• Regions of transparency can be modeled by Cauchy model, which is not constrained by KK consistency.
• Regions of absorption must account for both real and imaginary optical constants.
• Kramers-Kronig consistency is used to calculate the shape of the real component after the imaginary behavior is described by the oscillator.
• In the following equations, ɛ1(ω) represents the real part of the dielectric function, whereas ɛ2(ω) shows the imaginary part of the dielectric function.