refind.kramers_kronig

refind.kramers_kronig(nu, k, dir='forward')

Calculate the Kramers-Kronig transformation of extinction coefficient spectrum k as function of wavenumber nu (or frequency) and vice-versa.

The extinction coefficient is the imaginary part of the refractive index, which is related to the absorption coefficient alpha through k = alpha x lambda0 / (4 pi), where lambda0 is the vacuum wavelength. Calculates dn = n(nu’) - n(infinity) = 2/pi x Pint( nu x k / (nu^2 - nu’^2) dnu), where Pint is Cauchy’s principal value integral.

The method is based on Maclaurin’s formula and details are found in Ohta et a., Appl. Spectrosc. 42, 952 (1988).

Note

The same function can be used for angular frequency instead of wavenumber and for susceptibility instead of refractive index.

Important

k and nu have to be sampled on the same uniform grid!!!

Parameters:

• nu (array) – Wavenumber axis.
• k (array) – Extinction coefficient spectrum (same shape as nu).
• dir (str) – Direction is ‘forward’ (default) or ‘backward’, where ‘forward’ calculates the real part and ‘backward’ calculates the imaginary part.

Returns:

Real part of refractive index change, dn, as obtained by Kramers-Kronig transformation (same shape as nu).