Surface plasmon Fourier optics

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