Modified Hilbert Transform Pair and Kramers-Kronig Relations for ComplexPermittivities

摘要

Modified versions of the Hilbert transform pair and the Kramers-Kronig relationsare derived for the complex permittivity of a plasma/dielectric medium which is singular at the frequency of the applied electric field equal to 0. Such a complex permittivity exists when the plasma/dielectric model allows a loss term but no restoring term. Permittivity, in which both loss and restoring terms are included, is shown to satisfy the standard Hilbert transform pair and, thus, the Kramers-Kronig relations.