The modification of the Kronig-Kramers relations under saturation conditions

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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.