  We examine, both experimentally and theoretically, an interaction of tightly
focused polarized light with a slit on a metal surface supporting
plasmon-polariton modes. Remarkably, this simple system can be highly sensitive
to the polarization of the incident light and offers a perfect
quantum-weak-measurement tool with a built-in post-selection in the
plasmon-polariton mode. We observe the plasmonic spin Hall effect in both
coordinate and momentum spaces which is interpreted as weak measurements of the
helicity of light with real and imaginary weak values determined by the input
polarization. Our experiment combines advantages of (i) quantum weak
measurements, (ii) near-field plasmonic systems, and (iii) high-numerical
aperture microscopy in employing spin-orbit interaction of light and probing
light chirality.
