Most present ion cyclotron resonant frequency (ICRF) heating codes and antenna codes assume the antenna sitting in a vacuum region and consider the fast wave only, which implicitly performs an abrupt density transition from vacuum to above lower hybrid (LH) resonance. The impact of the appearance of the LH resonance is entirely overlooked in their simulations. We studied the impact of densities that decay continuously inside the antenna box on near field patterns and power coupling. A new full wave code based on the COMSOL Finite Element Solver has been developed to investigate this topic. It is shown that: up to the memory limits of the adopted workstation, the local RF field pattern in low-density regions below the LH resonance changes with the grid size. Interestingly and importantly, however, the total coupled toroidal spectrum is almost independent on the mesh size and is weakly affected by the presence of the density profile inside the antenna box in dipole toroidal strap phasing. This suggests one can drop out this density for coupling studies to speed up the computation. Simulation also shows that varying the density gradient in the fast wave evanescence region has no significant effect on wave coupling.