The Atacama Large Millimetre Array will be a single research instrument composed of up to 50 high precision antennas, located at the Chajnantor plain in the district of San Pedro de Atacama, 5000m above sea level. Each ALMA telescope will contain 10 frequency channels/bands, ranging from 30 to 950GHz. Radiation from the secondary reflector is collected to the receivers of each wavelength channel through their accompanying front end optics. We present a full electromagnetic treatment of the front end optics for band 5 (163 - 211 GHz) and band 9 (602 - 720 GHz). A full quasi optical and physical optics analysis of the band 5 front end optics, using the antenna analysis tool, GRASP9  is presented. Potential optimisation for the system is presented, namely a reflector edge taper and a comparison of two surface geometries. A similar analysis of the band 9 system is presented. Full electromagnetic simulations are compared with cold beam pattern measurements made at the Space Research Organisation of the Netherlands [2, 3]. Analysis of the effect of the polarizing grid is presented, with suggested modifications to improve cross polar levels.