  Surface plasmons are usually described as surface waves with either a complex
wavevector or a complex frequency. When discussing their merits in terms of
field confinment or enhancement of the local density of states, controversies
regularly arise as the results depend on the choice of a complex wavevector or
a complex frequency. In particular, the shape of the dispersion curves depends
on this choice. When discussing diffraction of surface plasmon a scalar
approximation is often used. In this work, we derive two equivalent vectorial
representations of a surface plasmon field using an expansion over surface
waves with either a complex wavevector or a complex frequency. These
representations can be used to account for propagation and diffraction of
surface waves. They can also be used to discuss the issue of field confinment
and local density of states as they have a non-ambiguous relation with the two
dispersion relations.
