Boundary effects in Cherenkov radiation

Abstract

The effect of dielectric boundaries on the Cherenkov radiation ͑CR͒ produced when a fast point charge moves inside or near a material is analyzed for different shapes of the sample. Calculations are offered for a charge moving near both planar and nonplanar surfaces. CR is found to be produced even when the external charge moves outside a semi-infinite medium. For charges moving near planar boundaries, the reflected radiation interferes with the direct CR, leading to oscillations in the emission probability as a function of the impact parameter relative to the interfaces. Thin-film guided modes are excited by penetrating electrons and our calculations agree reasonably well with available experiments. The bulk limit in the emission probability is recovered for charges passing by the center of cylinders or spheres of increasingly large radius. Recent experiments of energy loss of electrons passing near dielectric spheres are explained thanks to the inclusion of retardation effects in the sphere response. These effects lead to an efficient channel of radiative energy losses. Finally, the diffraction of CR in void inclusions is proposed as a tool for providing information on otherwise inaccessible buried structures.

Čerenkov losses: A limit for bandgap determination and Kramers–Kronig analysis

“…8) is compared with the experiment. Second, the influence of the surfaces can be identified as a damping of the energetically lowest Č erenkov bulk contributions and are described in detail in Garcia de Abajo et al (2004) andFestenberg (1969). This damping comes from the fact that the endpoints of the Fourier integral along the trajectory of the swift electron represent the sample thickness and are not infinite any more.…”

“…The phenomenon of delocalization has been discussed by several groups (Allen et al, 2005;Hugo et al, 1988;Muller and Silcox, 1995;Allen and Rossouw, 1993). Č erenkov losses of the probing electron beam were studied some 30-35 years ago (Festenberg and Kröger, 1968;Kröger, 1968;Chen et al, 1975) but are scarcely present in the more recent experimental literature (see for example: (Moreau et al, 1997;Aizpurua et al, 1999;Midgley, 1999;Garcia de Abajo et al, 2003;Garcia de Abajo et al, 2004)). Especially, knowledge about the influence of Č erenkov losses on the VEELS signal is not widely spread.…”

Detection of water and its derivatives on individual nanoparticles using vibrational electron energy-loss spectroscopy

“…The above equation ignores relativistic effects that may be observed in low-loss EELS especially when the electron beam exceeds the speed of light in the medium i.e. the Cherenkov condition is satisfied [31][32][33][34][35][36]. The…”

Excitation of Mesoscopic Plasmonic Tapers by Relativistic Electrons: Phase Matching versus Eigenmode Resonances

“…However, it is exactly this projection that sets an interesting selection rule for EELS since in inelastic electron scattering the momentum transfer from the electron to the specimen and vice versa is huge. 21 Moreover, when the dimension of the specimen along the electron trajectory is mesoscopic rather than nanoscopic, a dynamic interchange of momentum and energy between the electron and specimen can take place, as will be shown here.…”