 Kramers–Kronig relations

ID: kramers-kronig-relations

ϵ_{r} (ω) \to 1

at large frequency, the

e^{- iω t}

convention gives

ϵ_{r}^{'} (ω) - 1 = \frac{2}{π} P \int_{0}^{\infty} \frac{ω ^{'} ϵ _{r}^{''} ( ω ^{'} )}{ω ^{'2} - ω ^{2}} d ω^{'} .

The integral is a Cauchy principal value. Absorption and optical dispersion therefore cannot be specified independently.

The Kramers–Kronig relations are a set of equations in the field of complex analysis and are widely used in physics, particularly in optics and electrical engineering. They provide a mathematical relationship between the real and imaginary parts of a complex function that is analytic in the upper half-plane.

 New to topics? Read the docs here!