Modeling transmission and reflection Mueller matrices of dielectric half-wave plates

We present a simple analytical model describing multiple reflections in dielectric and optically active waveplates, for both normal and slant incidence, including absorption. We compute from first principles the transmission and reflection Mueller matrices of the waveplate. The model is used to simulate the performance of a Stokes polarimeter for mm-waves, in the framework of current attempts to precisely measure the linear polarization of the Cosmic Microwave Background (CMB). We study the spectral response of these optical devices, taking into account band and angle averaging effects and confirm the presence of a much richer spectral dependence than in an ideal phase retarder. We also present the matrix elements for the reflection matrix, which is useful to estimate systematic effects in some polarimeter configurations. The formulas we have derived can be used to quickly simulate the performance of future CMB polarimeters.