The wave propagation and power deposition in blue-core helicon plasma are computed referring to recent experiments. It is found that the radial profile of wave electric field peaks off-axis during the blue-core formation, and the location of this peak is very close to that of particle transport barrier observed in experiment; the radial profile of wave magnetic field shows multiple radial modes inside the bluecore column, which is consistent with the experimental observation of coherent high m modes through Bessel function. The axial profiles of wave field indicate that, once the blue-core mode has been achieved, waves can only propagate inside the formed column with distinct phase compared to that outside. The wave energy distribution shows a clear and sharp boundary at the edge of blue-core column, besides which periodic structures are observed and the axial periodicity inside is nearly twice that outside. The dispersion relation inside the blue-core column exhibits multiple modes, a feature of resonant cavity that selects different modes during frequency variation, while the dispersion relation outside gives constant wave number with changed frequency. The power deposition appears to be off-axis in the radial direction and periodic in the axial direction, and mostly inside the blue-core column. Analyses based on steplike function theory and introduced blue-core constant provide consistent results. The equivalence of blue-core column to optical fiber for electromagnetic communication is also explored and inspires a novel application of helicon plasma, which may be one of the most interesting findings of present work.