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We analyze time-resolved spontaneous emission from excitons confined inself-assembled $\mathrm{InAs}$ quantum dots placed at various distances to asemiconductor-air interface. The modification of the local density of opticalstates due to the proximity of the interface enables unambiguous determinationof the radiative and non-radiative decay rates of the excitons. Frommeasurements at various emission energies we obtain the frequency dependence ofthe radiative decay rate, which is only revealed due to the separation of theradiative and non-radiative parts. It contains detailed information about thedependence of the exciton wavefunction on quantum dot size. The experimentalresults are compared to the quantum optics theory of a solid state emitter inan inhomogeneous environment. Using this model, we extract the frequencydependence of the overlap between the electron and hole wavefunctions. Wefurthermore discuss three models of quantum dot strain and compare the measuredwavefunction overlap to these models. The observed frequency dependence of thewavefunction overlap can be understood qualitatively in terms of the differentcompressibility of electrons and holes originating from their differenteffective masses.

Frequency dependence of the radiative decay rate of excitons in self-assembled quantum dots: experiment and theory