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- ItemCalculation of ultrashort pulse propagation based on rational approximations for medium dispersion(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Amiranashvili, Shalva; Bandelow, Uwe; Mielke, AlexanderUltrashort optical pulses contain only a few optical cycles and exhibit broad spectra. Their carrier frequency is therefore not well defined and their description in terms of the standard slowly varying envelope approximation becomes questionable. Existing modeling approaches can be divided in two classes, namely generalized envelope equations, that stem from the nonlinear Schrödinger equation, and non-envelope equations which treat the field directly. Based on fundamental physical rules we will present an approach that effectively interpolates between these classes and provides a suitable setting for accurate and highly efficient numerical treatment of pulse propagation along nonlinear and dispersive optical media.
- ItemPadé approximant for refractive index and nonlocal envelope equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Amiranashvili, Shalva; Mielke, Alexander; Bandelow, UwePadé 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.