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.
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