Let us now focus our attention on the wavevector matching between the original guided mode and the different plane waves composing the rainbow. Despite Eq. (2) suggests that the plane waves at extremely high frequencies can be excited, we have to consider that very few energy can be coupled in that direction due to the high wavevector mismatching. To quantify the amount of energy coupled to each radiated plane wave, we must impose the continuity of the induction field across the interface.
