Orientation-dependent spontaneous emission rates of a two-level quantum emitter in any nanophotonic environment

We study theoretically the rate of spontaneous emission of a two-level quantum emitter embedded in realistic systems: near a mirror, near a plasmonic sphere, or in a 3D photonic bandgap crystal. At constant frequency and position, we find striking (up to $10^{2}\times$) variations in emission rate by varying the orientation of the transition dipole moment. We present a general representation of rate versus orientation that only invokes symmetry of the Green function. The concomitant 3-dimensional geometric surfaces provide much insight in how preferred orientations for enhancement (or inhibition) depend on the emitter's frequency and location, and on optimal strategies to actively switch emission rates by controlling oriented dipoles.