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- ItemGeneralized Lighthill criterion for the modulation instability(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Amiranashvili, Shalva; Tobisch, ElenaAn @universal modulation instability is subject to Lighthill criterion: nonlinearity and dispersion should make opposite contributions to the wave frequency. Recent studies of wave instabilities in optical fibers with the minimum chromatic dispersion revealed situations in which the criterion is violated and fast unstable modulations appear due to the four wave mixing process. We derive a generalized criterion, it applies to an arbitrary dispersion and to both slow and fast unstable modulations. Since the fast modulations depend on nonlinear dispersion, we also demonstrate how to describe them in the framework of a single generalized nonlinear Schrödinger equation.
- ItemModeling of ultrashort optical pulses in nonlinear fibers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Amiranashvili, ShalvaThis work deals with theoretical aspects of pulse propagation. The core focus is on extreme, few-cycle pulses in optical fibers, pulses that are strongly affected by both dispersion and nonlinearity. Using Hamil- tonian methods, we discuss how the meaning of pulse envelope changes, as pulses become shorter and shorter, and why an envelope equation can still be used. We also discuss how the standard set of dispersion coefficients yields useful rational approximations for the chromatic dispersion in optical fibers. Three more specific problems are addressed thereafter. First, we present an alternative framework for ultra- short pulses in which non-envelope propagation models are used. The approach yields the limiting, shortest solitons and reveals their universal features. Second, we describe how one can manipulate an ultrashort pulse, i.e., to change its amplitude and duration in a predictable manner. Quantitative theory of the manipu- lation is presented based on perturbation theory for solitons and analogy between classical fiber optics and quantum mechanics. Last but not least, we consider a recently found alternative to the standard split-step approach for numerical solutions of the pulse propagation equations.