  Diffraction of light at lateral inhomogenities is a central process in the
near-field studies of nanoscale phenomena, especially the propagation of
surface waves. Theoretical description of this process is extremely challenging
due to breakdown of plane-wave methods. Here, we present and analyze an exact
solution for electromagnetic wave diffraction at the linear junction between
two-dimensional electron systems (2DES) with dissimilar surface conductivities.
The field at the junction is a combination of three components with different
spatial structure: free-field component, non-resonant edge component, and
surface plasmon-polariton (SPP). We find closed-form expressions for efficiency
of photon-to-plasmon conversion by the edge being the ratio of electric fields
in SPP and incident wave. Particularly, the conversion efficiency can
considerably exceed unity for the contact between metal and 2DES with large
impedance. Our findings can be considered as a first step toward quantitative
near-field microscopy of inhomogeneous systems and polaritonic interferometry.
