We consider exciton recombination lasing in heterostructure traps for
Bose-Einstein condensation of dipolar excitons. We show that such structures suit well for class D lasers where cavity decay strongly exceeds polarization decay. We evaluate lasing threshold taking into account specific inhomogeneous broadening of the exciton spectral line owing to Bose-Einstein condensation phenomenon under quasi-equilibrium conditions.
It is found that narrowing of the exciton momentum distribution just before the condensation onset considerably lowers lasing threshold. At the same time, it is pointed out that a subsequent formation of condensate itself does not help lasing much. We conclude that it is possible to achieve lasing on polariton modes in nowadays experiments aimed on Bose-Einstein condensation of excitons.