From humble beginnings in 2008, a group met to propose the idea of observing the Cosmic Microwave Background (CMB) in order to determine its polarisation properties, i.e. E- and B-modes. B-modes, a smoking gun for inflation theory, are a long sought after observation for cosmologists. From this the QUBIC collaboration was born. Here we explore the scientific justification for such a mission and the aims of the QUBIC telescope in furthering this knowledge with emphasis on the author’s contribution to this end. B-modes are far fainter than any other signal that cosmology has attempted detection of before making them a challenge and requiring a new type of telescope with exceptional sensitivity and control of systematics. The author was heavily involved in the design and analysis of the optical combiner here at the Department of Experimental Physics in Maynooth University. This thesis describes the analysis techniques used for the characterisation of the operation of the QUBIC instrument. These techniques: TE/TM mode matching, Gaussian beam mode analysis and physical optics were used in determination of the behaviour of the instrument in 2 bands, 150 GHz and 220 GHz with 25% bandwidth in each case. The analysis was done mainly using 2 software packages, SCATTER and MODAL, both of which are in-house developments and as such offer customisation of their capabilities. QUBIC required detailed analysis which led to design modifications and allowed for confident design of new elements for inclusion in the optical-combiner. I present an optical design for QUBIC, a bolometric interferometer for cosmology which, at the time printing, is under construction awaiting shipping to Dome-C Antarctica to commence observation.