A note on Bragg-case Pendellösung and dispersion surface

It is usual to state, since Ewald [Ann. Phys. (1917), 54, 519-597], that Bragg-case Pendellösung involves two wavefields belonging to the same branch of the dispersion surface. However, in the Bragg geometry or when crystals are highly absorbing, the dispersion surface can no longer be approximated by the dispersion surface valid for a non-absorbing infinite medium. When considering the real part of the dispersion surface, it is found that the interfering wavefields producing Pendellösung in the Bragg geometry belong in fact to different branches. This paradox is explained by noting that the actual dispersion surface in the semi-infinite medium where the wavefields are generated by the incident wave differs from the dispersion surface in an infinite medium.