A two-dimensional, full-wave, frequency domain, cold plasma model is used to study electromagnetic power propagation and absorption in a helicon plasma thruster, including its far plume region and surrounding space. Results show that a fraction of power is absorbed in the plume region, and that power deposition in the source is essentially unperturbed by the simulation domain size, the presence of metallic obstacles, nor the plasma density in the environment. An electron-cyclotron resonance (ECR) surface always exists downstream that effectively prevents radiation to the space beyond. In the presence of an overdense environmental plasma, like the one expected in a vacuum chamber, fields are fully evanescent beyond this transition, and vacuum chamber boundary conditions affect little the wavefields before this surface. In the absence of an environmental plasma, a double transition exists at the interface between the plasma and vacuum that hinders accurate numerical simulation in the plume region.