The modification of the Kronig-Kramers relations under saturation conditions

Abstract

When the real and imaginary parts of the susceptibility, χ′ and χ″ respectively, of narrow saturated absorption lines are of Lorentzian form, it is shown that a constant A can always be found such that χ′ and A χ″ are a Kronig-Kramers transform pair. Lines made up of weighted linear super-positions of Lorentzian lines having the same shape and the same saturation behaviour also possess this property, as do certain continuous distributions of narrow Lorentzian lines. The Kronig-Kramers calculation of a saturated absorption lineshape from a saturated dispersion signal is therefore very likely to yield the true lineshape.