The longitudinal field component induced by the dielectric screening o
f the incident radiation at the surface has recently been shown to yie
ld a considerable influence on the photoemission spectra. The hydrodyn
amic model for the electrodynamic surface response shows surprisingly
good agreement with normal emission experimental spectra for layered d
ichalcogenides. However, it is not applicable for photon frequencies b
elow the plasmon energy omega(p) and was therefore extended to a two-s
tep density model to simulate the multipol mode below omega(p). As a c
onsequence a similar behaviour in the calculated photoemission spectra
could be followed passing to low frequencies. However, the modelling
of the surface is not free of parameters, sensitively depending on the
rather arbitrary position of the outermost electron density steps. To
relate these quantities to the real density of a layered crystal, a s
elf-consistent calculation of the electrodynamic surface response, for
a system with crystalline periodicity in the surface normal direction
and full translational symmetry in the parallel direction, is in deve
lopment. In contrast to some standard applications to the jellium mode
l, Green's functions are used which prove to be very appropriate for t
his actual task.