Thermodynamic efficiency of a finite gain laser

The thermodynamic limitations on the efficiency of a laser are considered with special reference to operation at a finite gain. An entropy cycle is used to determine both the thermodynamic threshold condition and to limit the entropy generated during lasing at a finite gain. A lower limit for the required number density of systems in the lasing level is derived. Comparison is also made with the rate equations analysis of the system thereby showing that the efficiency is always below the thermodynamic value, due to loss mechanisms. The results are given in a form equally applicable to physical and chemical pumping processes.