Theoretical maximum of the power efficiency of a pulsed injection laser with a Fabry-Perot cavity

Abstract

The maximum power efficiency of an injection laser operating in a Fabry-Perot mode is analyzed with a phenomenological theory which assumes that internal heating can be neglected. The efficiency is expressed in terms of two dimensionless geometric variables related to the length and the reflection coefficients of the cavity, and of a pair of dimensionless device parameters determined by the threshold constants, the product device resistance times area, and the output per unit width of junction. The power efficiency is maximized subject to independent variation of the two geometrical variables, and the optimum geometrical conditions are expressed as the only positive real root of a cubic equation. At low and at high efficiencies, the root has a simple approximate form. A graph of the root for all values of the device parameters is presented. The limiting efficiency is a monotonic function of a single parameter, the electrical quality factor, which is the ratio of the equivalent photon voltage of the radiation to the ohmic drop in the device at threshold. At low temperature where the electrical quality factor is large, the limiting efficiency is nearly independent of temperature, is proportional to the internal quantum efficiency, and can be close to unity. At higher temperatures where the factor becomes small, the limiting efficiency is proportional to the square of the internal quantum efficiency and drops toward zero. Measured values of the electrical quality factor of GaAs lasers show that the maximum power efficiency at 300°K is less than five per cent while at 80°K it exceeds fifty per cent. For device development, the best monitor of relative efficiency of a low-temperature laser is the differential external quantum efficiency, while for higher temperatures it is the threshold current density. The cavity length and reflection coefficients for optimum efficiency depend on the threshold parameters and the design power, but not in a critical way. A graph of the power efficiency against the electrical quality factor with cavity design as a parameter shows that a change from the optimum length by the factor one-half or two leaves the efficiency above 90 per cent of its optimum. The reflectivity has even less effect. The design tolerance for operation of a series-connected array of lasers is also discussed.