Modeling of ultrashort optical pulses in nonlinear fibers
- Amiranashvili, Shalva
2020 Mathematics Subject Classification
- 78-02 78A40 78A60 78M22 35Q60
- Nonlinear fibers, ultrashort pulses, pulse propagation, hamiltonian mechanics for waves, nonlinear Schrödinger equation, generalized nonlinear Schrödinger equation, rational approximation, Padé approximant, short-pulse equation, soliton, wave scattering, soliton perturbation theory, pulse manipulation, split-step methods
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.