In this paper we report detailed cathodoluminescence (CL) studies of deep UV emitting AlGaN multiple quantum wells (MQWs) embedded in AlN cladding layers to simulate a deep UV laser structure. These structures were produced by plasma-assisted molecular beam epitaxy (MBE) on 6H-SiC substrates. The AlGaN QWs were grown under excess gallium conditions, a growth mode consistent with liquid phase epitaxy rather than physical vapor phase epitaxy. This growth mode leads to AlGaN films with compositional inhomogeneities and thus band structure potential fluctuations. The degree of such compositional inhomogeneities depends on the amount of excess gallium and employment of indium as a surfactant during growth. The structure and microstructure of these MQWs were investigated by x-ray diffraction and TEM/STEM. Their optical properties were investigated with spatially-resolved CL spectroscopy and mapping. E-beam pumping experiments were performed by irradiating the top surface and collecting the luminescence from the cleaved edge. The observed superlinear dependence of the QW CL intensity on beam current together with linewidth narrowing strongly suggests light amplification by stimulated emission.