Solitons and ultra-short optical waves: The short-pulse equation versus the nonlinear schrödinger equation
Summary: This chapter presents a comparison between the standard center-frequency expansion commonly used today for modeling optical transmission systems and mode-locked lasers, and a new, short-pulse theory that attempts to directly account for the broadband nature of ultra-short pulses. The radically different asymptotic regimes used in both theories are highlighted and contrasted, suggesting that serious consideration should be taken in developing further short-pulse theory. The chapter first introduces governing Maxwell's equations. It then considers the reduction of the governing equations under linear propagation effects and the asymptotic scalings of the nonlinear Schrodinger equation (NLS) and short-pulse equation (SPE). The chapter augments the linear propagation by considering an instantaneous nonlinear response. It also considers a more realistic nonlinear time-response, and the application of the SPE theory to mode-locked lasers and contrasts it to standard NLS approaches. Controlled Vocabulary Terms: electromagnetic pulse; Maxwell equations; Schrodinger equation
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Kutz, Jose Nathan and Farnum, Edward, "Solitons and ultra-short optical waves: The short-pulse equation versus the nonlinear schrödinger equation" (2013). Kean Publications. 2046.