Integral method to study transition radiation from surfaces with arbitrary profile

Transition radiation is produced when an electron moving at constant speed crosses the boundary separating two media with different optical properties. We propose an alternative description of this phenomenon, based on an integral representation of the electromagnetic field and show that the approach gives known results for a flat surface. Compared to previously published methods, based either on the reciprocity theorem in electromagnetism or on a four-dimensional Fourier representation of the field generated by the moving electron, this method has the advantage that it can be applied to general boundary geometries.