Multiple scale method for a wave packet propagating in a nonlinear planar optical waveguide with gain and loss

The article deals with the propagation of a wave packet in a planar waveguide with optical nonlinearity of the third order. On one side of the waveguide there is an active medium and on the other side a conventional dielectric with losses is applied. Gain and loss are described by the imaginary part of the linear dielectric susceptibility of the corresponding signs for all three layers. As a result of a regular decomposition procedure using the multiple-scale method, a reduced (2 + 1) model for the propagation of a quasimonochromatic wave of a single mode is mathematically correctly derived. The envelope of the wave packet is described by the modification of the Ginzburg–Landau equation. Nontrivial expressions for the model parameters are established through the initial physical characteristics of the problem. (paper)