Relativistic Electron Energy Loss and Electron-Induced Photon Emission in Inhomogeneous Dielectrics

Electron loss and electron-induced photon-emission probabilities are calculated near arbitrarily shaped dielectrics described by frequency-dependent response functions. The exact solution of Maxwell's equations is reduced to self-consistent equations involving integrals over the interfaces. The particular case of axially symmetric interfaces of arbitrary shape is discussed in detail. Photon-emission probabilities are shown to be of the same order of magnitude as loss probabilities in some cases, suggesting the possibility of measuring electron-induced radiation as a new microscopy technique.