  High-energy (1-100 keV) electrons can coherently couple to plasmonic and
dielectric nanostructures creating cathodoluminescence (CL) of which the
spectral features reveal details of the material's resonant modes at
deep-subwavelength spatial resolution. While CL provides fundamental insight in
optical modes, detecting its phase has remained elusive. Here, we introduce
Fourier-transform CL holography as a method to determine the far-field phase
distribution of scattered plasmonic fields. We record far-field interferences
between a transition radiation reference field and surface plasmons scattered
from plasmonic nanoholes, nanocubes and helical nano-apertures and reconstruct
the angle-resolved phase distributions. From the derived fields we derive the
relative strength and phase of induced scattering dipoles. The data show that
each electron wavepacket collapses at the sample surface and coherently excites
transition radiation and surface plasmon quanta. Fourier-transform CL
holography opens up a new world of coherent light scattering and surface wave
studies with nanoscale spatial resolution.
