  Single nanoscopic emitters embedded in crystalline matrix have become a
valuable resource for emerging nanophotonic and quantum technologies. The
generally anisotropic nature of the matrix strongly affects the emission
properties of the quantum emitters, in particular, when the matrix is assembled
in nanophotonic structures. We report on rigorous analysis and engineering of
spontaneous emission from single emitters coupled to nanoantenna and planar
anisotropic antenna structures. By developing a convenient theoretical method
with efficient numerical implementation, we show that accurate modeling of the
anisotropy is essential in predicting the emission pattern for many important
systems, such as single molecules in solid-state matrix, isolated defects in 2D
materials and so on. In particular, we illustrate the amplified effects of
material anisotropy and geometrical anisotropy for emitters coupled to planar
antenna and nanoantenna structures. We show that with proper design of the
anisotropies strong enhancement of the emission rate and nearly collimated beam
from single emitters can be simultaneously achieved.
