This thesis presents the theory and applications of electromagnetic field calculation using orthogonal Gaussian beam modes within the context of far-infrared imaging systems. Laguerre and Hermite-Gaussian modes have been frequently reported in the analysis of paraxial millimetre-wave propagation in astronomical optical systems. Here the method of Gaussian beam mode analysis (GBMA) is extended to fields of optical research that have until recently been associated with wavelengths in the visible band. Using recently derived expressions for the non-paraxial diffraction of Hermite-Gaussian modes, the author demonstrates the modal calculation of far-field intensity distributions with less angular restriction on the accuracy of the method compared to the conventional paraxial description of orthogonal Gaussian modes. This method shows excellent agreement with predictions from more rigourous fullwave numerical methods such as the finite-difference time-domain algorithm, which is also described as a software tool in the modelling of horn and lens antennas. The properties of diffraction limited Bessel beams is described using the Laguerre-Gaussian expansion of conical lenses, and experimental measurements of a conical lens is presented to explore the validity of the use of these optical elements as horn coupled devices in millimetre wave imaging systems. A study of diffractive Fresnel lenses has been undertaken with a comparison of experimentally measured fields with those predicted by the modal techniques. The effects of such lenses on ultrashort paraxial pulses are also investigated using a novel numerical description of few-cycle fields as a superposition of pulsed Laguerre- Gaussian modes. The application of digital holography in the far-infra red band has the prospect of diffraction limited imaging systems without creating distortions and aberrations which is a common problem in conventional techniques using lenses and mirrors. The author presents results from a simple proof-of-concept system which exhibits the potential of this technique for application in, for example, mm-wave security imaging.