Effect of two photon absorption on nonlinear pulse propagation in gain medium

The effects of two photon absorption (TPA) and gain dispersion on soliton propagation in amplified medium are investigated. For finite gain bandwidth, the effect of gain dispersion becomes significant along with TPA and is treated as perturbation in fundamental soliton propagation. Including these perturbing effects an analytical expression of integrated intensity is formulated applying a completely new methodology by adopting Rayleigh’s dissipation function in the framework of variational approach. With classical analogy, the Euler–Lagrange equation in non-conservative system is used to solve the problem analytically. In order to justify the analytical prediction a numerical verification is made by split-step beam propagation method following Ginzburg–Landau equation.