Novel dynamical behavior of rogue waves in erbium doped fiber with inhomogeneous broadening

Abstract

Under investigation is the generalized nonlinear Schrödinger–Maxwell–Bloch equation (GNLS-MB) with inhomogeneous broadening, which determines the wave propagation in optical fibers doped with erbium atoms. We construct first- and second-order rogue wave solutions for the GNLS-MB equation using the similarity reduction technique. We investigate the characteristics of rogue wave solutions by tailoring dispersion and nonlinearity parameters into various forms. Specifically, we examine two cases: (i) a non-zero gain parameter and (ii) a zero gain parameter. We report interesting features of rogue wave structures, illustrated with 2D and 3D graphical representations. Our observations indicate that rogue waves emerge on diverse backgrounds for the non-zero value of the gain parameter, while alternative fascinating patterns are observed when the gain parameter is zero. These findings will be helpful in understanding the dynamics of rogue waves with inhomogeneous effects.