Electromagnetic ion cyclotron (EMIC) waves are known to be excited by the cyclotron instability associated with hot and anisotropic ion distributions in the equatorial region of the magnetosphere and are thought to play a key role in radiation belt losses. Although detection of these waves at the ground can provide a global view of the EMIC wave environment, it is not clear what signatures, if any, would be expected. One of the significant scientific issues concerning EMIC waves is to understand how these waves are detected at the ground. In order to solve this puzzle, it is necessary to understand the propagation characteristics of the field‐aligned EMIC waves, which include polarization reversal, cutoff, resonance, and mode coupling between different wave modes, in a dipolar magnetic field. However, the inability of ray tracing to adequately describe wave propagation near the crossover cutoff‐resonance frequencies in multi‐ion plasmas is one of reasons why these scientific questions remain unsolved. Using a recently developed 2‐D full‐wave code that solves the full‐wave equations in global magnetospheric geometry, we demonstrate how EMIC waves propagate from the equatorial region to higher magnetic latitude in an electron‐proton‐He+ plasma. We find that polarization reversal occurs at the crossover frequency from left‐hand polarization (LHP) to right‐hand (RHP) polarization and such RHP EMIC waves can either propagate to the inner magnetosphere or reflect to the outer magnetosphere at the Buchsbaum resonance location. We also find that mode coupling from guided LHP EMIC waves to unguided RHP or LHP waves (i.e., fast mode) occurs.