Electromagnetic field in an active slab: conditions for spontaneous oscillation

In this work we analyze the conditions for the propagation of plane waves due to spontaneous oscillation within an active slab of width d and complex relative permittivity ˜b. The slab is immersed in transparent, semi-infinite media of relative permittivities a and c respectively, without external field sources -except, of course, the power source used for pumping the active medium in the slab. It is well known that, if there is enough gain in the active medium, it may sustain spontaneous oscillations of the electromagnetic field, which result in an impaired operation. This model gives a limiting value of the small signal gain to avoid this condition. It is applicable to disk lasers, amplifiers and other optoelectronic devices in which pumping is confined to a region with transverse dimensions much larger than its length.