Generation, dynamics, and stability analysis of diffraction managed soliton in patterned metamaterial

This paper presents the propagation of electromagnetic waves through a periodic array of positive- and negative-diffraction metamaterials with cubic-quintic nonlinearity. The governing nonlinear Schrödinger equation is solved analytically as well as numerically by using the Lagrangian variational method and the Split Step Fourier method, respectively. Breather-like diffraction-managed solitons have been generated and stabilized for a large range of system parameters. These diffraction-managed solitons have been observed to possess greater energy compared to conventional solitons in constant diffraction material. The initial beam energy for such soliton formation is determined for a large variety of diffraction-managed metamaterials. The stability of diffraction-managed solitons has been studied using phase diagrams and perturbation methods, identifying different classes of stability zones. The soliton dynamics have been examined in the presence of higher-order diffractions, specifically third- and fourth-order diffractions. Third-order diffraction induces beam width asymmetry, while fourth-order effects are marginal. Also, soliton interactions have been investigated for higher-order diffraction.