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Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: nonlinear Schrödinger equation ×

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Now showing 1 - 4 of 4
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    Numerical methods for accurate description of ultrashort pulses in optical fibers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Amiranashvili, Shalva; Radziunas, Mindaugas; Bandelow, Uwe; C̆iegis, Raimondas
    We consider a one-dimensional first-order nonlinear wave equation (the so-called forward Maxwell equation, FME) that applies to a few-cycle optical pulse propagating along a preferred direction in a nonlinear medium, e.g., ultrashort pulses in nonlinear fibers. The model is a good approximation to the standard second-order wave equation under assumption of weak nonlinearity. We compare FME to the commonly accepted generalized nonlinear Schrödinger equation, which quantifies the envelope of a quickly oscillating wave field based on the slowly varying envelope approximation. In our numerical example, we demonstrate that FME, in contrast to the envelope model, reveals new spectral lines when applied to few-cycle pulses. We analyze and compare pseudo-spectral numerical schemes employing symmetric splitting for both models. Finally, we adopt these schemes to a parallel computation and discuss scalability of the parallelization.
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    Modeling of ultrashort optical pulses in nonlinear fibers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Amiranashvili, Shalva
    This 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.
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    Adjustable pulse compression scheme for generation of few-cycle pulses in the mid-infrared
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Demircan, Ayhan; Amiranashvili, Shalva; Brée, Carsten; Morgner, Uwe; Steinmeyer, Günter
    An novel adjustable adiabatic soliton compression scheme is presented, enabling a coherent pulse source with pedestal-free few-cycle pulses in the infrared or mid-infrared regime. This scheme relies on interaction of a dispersive wave and a soliton copropagating at nearly identical group velocities in a fiber with enhanced infrared transmission. The compression is achieved directly in one stage, without necessity of an external compensation scheme. Numerical simulations are employed to demonstrate this scheme for silica and fluoride fibers, indicating ultimate limitations as well as the possibility of compression down to the single-cycle regime. Such output pulses appear ideally suited as seed sources for parametric amplification schemes in the mid-infrared.
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    Additive splitting methods for parallel solution of evolution problems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Amiranashvili, Shalva; Radziunas, Mindaugas; Bandelow, Uwe; Busch, Kurt; Čiegis, Raimondas
    We demonstrate how a multiplicative splitting method of order P can be used to construct an additive splitting method of order P + 3. The weight coefficients of the additive method depend only on P, which must be an odd number. Specifically we discuss a fourth-order additive method, which is yielded by the Lie-Trotter splitting. We provide error estimates, stability analysis, and numerical examples with the special discussion of the parallelization properties and applications to nonlinear optics.