Theory of supercontinuum and interaction of solitons with dispersive waves

Motivation Chapter 1 of this book and a number of previous publications (see, e.g., Russell, 2003; Dudley et al., 2006; Smirnov et al., 2006; Knight and Skryabin, 2007; Skryabin and Wadsworth, 2009) give excellent bibliographic and historical accounts of the supercontinuum and other nonlinear effects observed in photonic crystal fibres since, and to some extent before, the seminal results by Ranka et al. (Ranka et al., 2000) appeared in 1999-2000. Here we present a focused account of our understanding of the fibre supercontinuum based on the theory developed by the Bath group over recent years (Skryabin et al., 2003; Yulin et al., 2004; Skryabin and Yulin, 2005; Gorbach et al., 2006; Gorbach and Skryabin, 2007a, b, c) and on the experiments carried out in Los Alamos and Bath (Skryabin et al., 2003; Efimov et al., 2004, 2005, 2006; Gorbach et al., 2006; Stone and Knight, 2008), which have closely followed our theoretical work. Concepts and results systematically described below are centred around the problem of the frequency conversion due to interaction between solitons and dispersive waves (Skryabin and Yulin, 2005). In the end our approach leads to a qualitative understanding and quantitative description of the expansion of the femtosecond supercontinua (Gorbach and Skryabin, 2007b). We start this chapter by introducing the deterministic model of supercontinuum generation, discuss its limitations and move on to the soliton self-frequency shift problem, presenting it in the way trimmed for our goals.