The contribution of multiple reflections to transition radiation

Abstract An electron passing through a slab induces transition radiation, and the multiple reflections inside the slab boundaries can influence the observed intensity. We employ the polarization current method to derive a reflectionless solution and compare it with that of Pafomov, which accounts for the multiple reflections exactly. Our findings demonstrate that depending on the slab thickness, permittivity, the angle and frequency of the radiation, the electron velocity, Pafomov and reflectionless solutions can differ or be in a rather good agreement. We search for the parameters that allow for a simplified description. Pafomov and reflectionless solutions are compared both in the optical and x-ray energy ranges. We show there are the set of discrete solutions for the slab thickness ensuring destructive interference between the forward and backward transition radiation, causing the two solutions to agree well with each other. In between these points, the reflectionless scenario generally significantly deviates from that of Pafomov, in the optical range. For x-ray transition radiation, the Pafomov solution deviates from reflectionless only at high angles of emission. Searching for an agreement of the exact and simplified solutions is crucial for a possibility to qualitatively describe polarization radiation from targets of complex shape.