  Optically active defects in diamond are widely used as bright single-photon
sources for quantum sensing, computing, and communication. For many
applications, it is useful to place the emitter close to the diamond surface,
where the radiative properties of the emitter are strongly modified by its
dielectric environment. It is well-known that the radiative power from an
electric dipole decreases as the emitter approaches an interface with a
lower-index dielectric, leading to an increase in the radiative lifetime. For
emitters in crystalline solids, modeling of this effect needs to take into
account the crystal orientation and direction of the surface cut, which can
greatly impact the emission characteristics. In this paper, we provide a
framework for analyzing the emission rates of shallow (<100 nm) defects, in
which optical transitions are derived from electric dipoles in a plane
perpendicular to their spin axis. We present our calculations for the
depth-dependent radiative lifetime for color centers in (100)-, (110)-, and
(111)-cut diamond, which can be extended to other vacancy defects in diamond.

Optics;Applied Physics;Quantum Physics