Despite numerous applications of two-dimensional (2D) plasmons for electromagnetic energy manipulation at the nanoscale, their quantitative refraction and reflection laws (analogs of Fresnel formulas in optics) have not yet been established. This fact can be traced to the strong nonlocality of equations governing the 2D plasmon propagation. Here, we tackle this difficulty by direct solution of the plasmon scattering problem with the Wiener-Hopf technique. We obtain the reflection and transmission coefficients for 2D plasmons at the discontinuity of 2D conductivity at arbitrary incidence angle, for both gated and nongated 2D systems. At a certain incidence angle, the absolute reflectivity has a pronounced dip, reaching zero for gated plasmons. The dip is associated with wave passage causing no dynamic charge accumulation at the boundary. For all incidence angles, the reflection has a nontrivial phase different from zero and $\pi$.

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• Plasmonics
• Waveguides
• Two-dimensional electron system