A Simple Solution for an Electromagnetic Wave in a Third-Order Nonlinear Anisotropic Medium

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This work examines how a transverse magnetic mode electromagnetic wave propagates in a medium with thirdorder nonlinear and anisotropic electric permittivity. The proposed model is solved using the homotopy analysis method. Two cases are considered: the first analyzes a wave traveling through an infinite medium, and the results show a transverse rotation of the electric field, indicating that the material induces a change in longitudinal polarization. In the second case, the wave passes through a waveguide with metallic boundaries. The eigenvalues were determined and compared with those of a linear and isotropic material. The results show that nonlinearity and anisotropy eliminate the first eigenvalues, while, for large eigenvalues, both materials exhibit the same values.