(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Amiranashvili, Shalva; Mielke, Alexander; Bandelow, Uwe
Padé approximant is superior to Taylor expansion when functions
contain poles. This is especially important for response functions in complex
frequency domain, where singularities are present and intimately related to
resonances and absorption. Therefore we introduce a diagonal Padé
approximant for the complex refractive index and apply it to the description
of short optical pulses. This yields a new nonlocal envelope equation for
pulse propagation. The model offers a global representation of arbitrary
medium dispersion and absorption, e.g., the fulfillment of the Kramers-Kronig
relation can be established. In practice, the model yields an adequate
description of spectrally broad pulses for which the polynomial dispersion
operator diverges and can induce huge errors.
