Fig. 1: Principle of Lorentz imaging of optical fields.

a A plane-wave electron beam probes the near field of a nanostructure, here a nanosphere with a dipolar field induced by external illumination. Stimulated inelastic scattering populates sidebands in the electron spectrum and imprints a spatial phase profile. b, c Simulated magnitude of the first electron sideband (b) after energy-filtering and associated phase profile (c) with lineouts shown below (green = 0 and blue = π/2; see also phase lineouts of gain and loss sidebands below). d, e Simulated Lorentz images under overfocus conditions for loss (−ℏω) and gain (ℏω) filtered sidebands, exhibiting sensitivity to the phase profile.