We propose an original method based on generalized plane waves and approximated coefficients for the numerical approximation of the Helmholtz equation with a smooth nonconstant coefficient. This is justified by a high-order convergence estimate rate. Our motivation stems from Maxwell's equations with Hermitian dielectric tensor epsilon which are used to model reflectometry in fusion plasma. Simplified models split them into two different propagation modes. Some numerical results are presented in dimensions 1 and 2