We study theoretically the surface plasmon electromagnetic field in the plane of the interface along which it propagates. Arbitrary Surface plasmon fields are expressed by a linear superposition of elementary surface plasmon modes, thus obtaining an expression for the inplane components similar to the angular spectrum model, which establishes the formal foundations of a two-dimensional surface plasmon optics. From this representation, we obtain the general description for surface plasmon modes be having as in-plane diffraction free beams. These new modes with their corresponding phase parameters are used to study surface plasmon self-imaging phenomenon and the synthesis of surface plasmon singularity regions (caustics) of surface plasmon fields, proposing experimental means to observe both.