Simple rate equation model for hypothetical doubly stimulated emission of both photons and phonons in quantum-well lasers

The dissipation processes by which electrons and holes lose energy after being trapped in quantum wells might, in a sufficiently heavily pumped quantum well laser, lead to the buildup of such a high phonon population that phonon-assisted laser action by doubly stimulated emission of photons and phonons acquires a higher gain than unassisted laser action. The resulting mode switching exhibits a pronounced hysteresis with pump rate, which should be a characteristic identifying feature of phonon-assisted laser action.