We present a monolithic semiconductor microcavity design for enhanced light-matter interaction and photon extraction efficiency of an embedded quantum emitter such as a quantum dot or color center. The microcavity is a hemispherical Fabry-Perot design consisting of a planar back mirror and a top curved mirror. Higher order modes are suppressed in the structure by reducing the height of the curved mirror, leading to efficient photon extraction into a fundamental mode with a Gaussian far-field radiation pattern. The cavity finesse can be varied easily by changing the reflectivity of the mirrors and we consider two specific cases: a low-finesse structure for enhanced broad band photon extraction from self-assembled quantum dots and a moderate-finesse cavity for enhanced extraction of single photons from the zero-phonon line of color centers in diamond. We also consider the impact of structural imperfections on the cavity performance. Finally, we present the fabrication and optical characterisation of monolithic GaAs hemispherical microcavities.
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