Causality constrains the real and imaginary parts of a frequency-dependent linear response. For a dielectric with at large frequency, the convention givesThe integral is a Cauchy principal value. Absorption and optical dispersion therefore cannot be specified independently.
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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.