Calculation of phase changes of electron waves near excited nanoparticles

When a metallic nanoparticle is illuminated by electromagnetic radiation of the appropriate frequency, strong electric and magnetic fields are generated close to the surface of the particle by the valence electrons of the metal. The energy in these surface excitations can be transferred to external electrons passing near the particle (energy-gain spectral spectroscopy) and they change the phase of the zero-loss component of the electron wave. This paper provides an estimate of how the phase of the wave at the image plane of a 100-kV transmission electron microscope varies with position in the image plane. For a 16-nm radius gold sphere illuminated by the light of wavelength 500 nm and irradiance 10 MW/cm², the phase in the image plane changes by 0.002 rad/nm along a radial line outside the sphere. Changes of similar magnitude have been measured in previous studies.