Nonlinear Optics in Guided Geometries - Abstract
Amiranashvili, Shalva
Description of light with a very broad spectral bandwidth, e.g. an ultrashort optical pulse or supercontinua, requires knowledge of medium dispersion for all frequencies of interest. Here, an available dispersion curve is usually approximated by a polynomial, the corresponding expansion coefficients are further used to construct an envelope equation with the differential dispersion operator. We demonstrate that the dispersion curves are more naturally represented by rational functions. The latter correctly reproduce asymptotic behavior of the refractive index. Moreover, the fulfillment of the causality principle and the Kramers-Kronig relation can be established. In the simplest case such rational function reduces to the Padé approximant for the refractive index. Pulse propagation is now described by a nonlocal envelope equation with the pseudodifferential dispersion operator. The model can be solved numerically by a straightforward application of the split-step Fourier method. Unphysical effects and numerical stiffness are avoided and artificial spectral filters are not necessary.
Coauthors: U. Bandelow and A. Mielke