Kramers-Kronig relations Guide, Meaning , Facts, Information and Description

In mathematics and physics, the Kramers-Kronig relations describe the relation between the real and imaginary part of a certain class of complex-valued functions. The requirements for a function to which they apply can be interpreted as that the function must represent the Fourier transform of a linear and causal physical process. If we write

,

where and are real-valued "well-behaving" functions, then the Kramers-Kronig relations are

.

The Kramers-Kronig relations are related to the Hilbert transform, and are most often applied on the permittivity of materials. However, it must be noticed that in this case,

,

where is the electric susceptibility of the material. The susceptibility can be interpreted as the Fourier transform of the time-dependent polarization in the material after an infinitely short pulsed electric field, in other words the impulse response of the polarization.

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