Mathematical modelling of thermal hot-spots in semiconductor laser operation

A new mathematical model describing the coupling of electrical, optical and thermal effects in semiconductor lasers is introduced. The underlying (perfect) isothermal system has a transcritical bifurcation as the current varies. The steady-state light intensity is found to exhibit exponential growth as the wave traverses the laser and the steady-state electron concentration satisfies an integral equation, the solution of which specifies the threshold current. The (imperfect) isothermal and thermal problems also have this behaviour at leading order. In the thermal problem, an asymptotic analysis results in the decoupling of the various time-scales and length-scales leading to considerable simplification. Composite asymptotic expansions are constructed on each time-scale and compared with numerical results. These analytical solutions provide valuable insight and predict the role played by the various physical processes. In particular, the temperature rise of the active region is found to exhibit localized hot-spots at both mirrors, in contrast to the temperature rise of the surround where no such hot-spots are observed.