High power, high gain lasers are vulnerable to parasitic oscillations, which are unwanted laser modes that rely on stray wall reflections for their optical feedback. Since parasitics reduce power in the intended laser mode and can cause thermal damage to structural hardware, it is important to know the gain threshold required to support parasitics in various laser medium geometries. When the walls are diffusely reflecting, as in many high power laser devices, a diffuse parasitic mode that fills essentially the entire gain medium can form. A differential equation is derived for the radiant intensity of a diffuse parasitic in the absence of diffraction. An expansion in angular functions leads to a Helmholtz-like equation and suitable boundary conditions at the walls. These equations are solved to give the radiant intensity within a rectangular laser region with specified reflectivities at the bounding walls. Limiting cases are discussed and numerical results are given for the diffuse parasitic gain threshold in rectangular gain regions bounded by two, four, or six partially reflecting walls. A computer code is provided for calculating the gain threshold for other combinations of wall reflectivities.
Arthur N. Chester, "Gain Thresholds for Diffuse Parasitic Laser Modes," Appl. Opt. 12, 2139-2146 (1973)