  We investigate the generation of entanglement between two quantum emitters
through the inverse-design engineering of their photonic environment. By means
of a topology-optimization approach acting at the level of the electromagnetic
Dyadic Green's function, we generate dielectric cloaks operating at different
inter-emitter distances and incoherent pumping strengths. We show that the
structures obtained maximize the dissipative coupling between the emitters
under extremely different Purcell factor conditions, and yield steady-state
concurrence values much larger than those attainable in free space. Finally, we
benchmark our design strategy by proving that the entanglement enabled by our
devices approaches the limit of maximum-entangled-mixed-states.
