Spectral, temporal and polarization characteristics of spontaneous and stimulated luminescence of Al0.5Ga0.5N/AlN structures grown by molecular beam epitaxy were studied at the optical pulsed pumping with λ = 266 nm. Samples with a high degree of silicon doping were investigated. The vast majority of radiation falls on transitions within the band gap between the levels of defects. As a result, the radiation band embracing the whole visible range of more than 300 THz is observed in both spontaneous radiation and induced luminescence. In spontaneous radiation the band has a smooth spectral intensity distribution over the wavelengths, whereas induced radiation has its sharp peaks corresponding to the mode structure of the planar waveguide. The measured gain of the active medium is g ≈ 70 cm-1 for a weak signal.