  Semiconductor colloidal nanocrystals are excellent light emitters in terms of
efficiency and spectral control. Integrating them with a metasurface would pave
the way to ultrathin photoluminescent devices with reduced amount of active
material and performing complex functionalities such as beam shaping or
polarization control. To design such a metasurface, a quantitative model of the
emitted power is needed. Here, we report the design, fabrication and
characterization of a $\approx$ 300 nm thick light-emitting device combining a
plasmonic metasurface with an ensemble of nanoplatelets. The source has been
designed with a new methodology based on a local form of Kirchhoff's law. The
source displays record high directionality and brightness.
