  Affine Toda field theories with a purely transmitting integrable defect are
considered and the model based on a_2 is analysed in detail. After providing a
complete characterization of the problem in a classical framework, a suitable
quantum transmission matrix, able to describe the interaction between an
integrable defect and solitons, is found. Two independent paths are taken to
reach the result. One is an investigation of the triangle equations using the
S-matrix for the imaginary coupling bulk affine Toda field theories proposed by
Hollowood, and the other uses a functional integral approach together with a
bootstrap procedure. Evidence to support the results is collected in various
ways: for instance, through the calculation of the transmission factors for the
lightest breathers. While previous discoveries within the sine-Gordon model
motivated this study, there are several new phenomena displayed in the a_2
model including intriguing disparities between the classical and the quantum
pictures. For example, in the quantum framework, for a specific range of the
coupling constant that excludes a neighbourhood of the classical limit, there
is an unstable bound state.
