  This work presents epitaxial growth and optical spectroscopy of CdTe quantum
dots (QDs) in (Cd,Zn,Mg)Te barriers placed on the top of (Cd,Zn,Mg)Te
distributed Bragg reflector. The formed photonic mode in our half-cavity
structure permits to enhance the local excitation intensity and extraction
efficiency of the QD photoluminescence, while suppressing the reflectance
within the spectral range covering the QD transitions. This allows to perform
coherent, nonlinear, resonant spectroscopy of individual QDs. The coherence
dynamics of a charged exciton is measured via four-wave mixing, with the
estimated dephasing time $T_2=(210\,\pm\,40)$ ps. The same structure contains
QDs doped with single Mn$^{2+}$ ions, as detected in photoluminescence spectra.
Our work therefore paves the way toward investigating and controlling an
exciton coherence coupled, via $s$,$p$-$d$ exchange interaction, with an
individual spin of a magnetic dopant.
