  Acquiring precise information about the mode content of a laser is critical
for multiplexed optical communications, optical imaging with active wave-front
control, and quantum-limited interferometric measurements. Hologram-based mode
decomposition devices, such as spatial light modulators, allow a fast, direct
measurement of the mode content, but they have limited precision due to
cross-coupling between modes. Here we report the first proof-of-principle
demonstration of mode decomposition with a metasurface, resulting in
significantly enhanced precision. A mode-weight fluctuation of $6\times
10^{-7}$ was be measured with 1 second of averaging at a Fourier frequency of
80 Hz, an improvement of more than three orders of magnitude compared to the
state-of-the-art spatial light modulator decomposition. The improvement is
attributable to the reduction in cross-coupling enabled by the exceptional
small pixel size of the metasurface. We show a systematic study of the limiting
sources of noise, and we show that there is a promising path towards complete
mode decomposition with similar precision.
