© 2017 SPIE. A multimode horn differs from a single mode horn in that it has a larger sized waveguide feeding it. Multimode horns can therefore be utilized as high efficiency feeds for bolometric detectors, providing increased throughput and sensitivity over single mode feeds, while also ensuring good control of the beam pattern characteristics. Although a cavity mounted bolometer can be modelled as a perfect black body radiator (using reciprocity in order to calculate beam patterns), nevertheless, this is an approximation. In this paper we present how this approach can be improved to actually include the cavity coupled bolometer, now modelled as a thin absorbing film. Generally, this is a big challenge for finite element software, in that the structures are typically electrically large. However, the radiation pattern of multimode horns can be more efficiently simulated using mode matching, typically with smooth-walled waveguide modes as the basis and computing an overall scattering matrix for the horn-waveguide-cavity system. Another issue on the optical efficiency of the detectors is the presence of any free space gaps, through which power can escape. This is best dealt with treating the system as an absorber. Appropriate reflection and transmission matrices can be determined for the cavity using the natural eigenfields of the bolometer cavity system. We discuss how the approach can be applied to proposed terahertz systems, and also present results on how the approach was applied to improve beam pattern predictions on the sky for the multi-mode HFI 857GHz channel on Planck.