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 confinement 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 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.