The next generation of space missions targeting far-infrared wavelengths will require large-format arrays of extremely sensitive detectors. The development of Transition Edge Sensor (TES) array technology is being developed for future Far-Infrared (FIR) space applications such as the SAFARI instrument for SPICA where low-noise and high sensitivity is required to achieve ambitious science goals. In this paper we describe a modal analysis of multi-moded horn antennas feeding integrating cavities housing TES detectors with superconducting film absorbers. In high sensitivity TES detector technology the ability to control the electromagnetic and thermo-mechanical environment of the detector is critical. Simulating and understanding optical behaviour of such detectors at far IR wavelengths is difficult and requires development of existing analysis tools. The proposed modal approach offers a computationally efficient technique to describe the partial coherent response of the full pixel in terms of optical efficiency and power leakage between pixels. Initial wok carried out as part of an ESA technical research project on optical analysis is described and a prototype SAFARI pixel design is analyzed where the optical coupling between the incoming field and the pixel containing horn, cavity with an air gap, and thin absorber layer are all included in the model to allow a comprehensive optical characterization. The modal approach described is based on the mode matching technique where the horn and cavity are described in the traditional way while a technique to include the absorber was developed. Radiation leakage between pixels is also included making this a powerful analysis tool.