  We present polarized |S|=0.99$\pm$0.01, and unpolarized |S|=0.03$\pm$0.01
emission from a single emitter embedded in a single, cylindrically symmetric
device design. We show that the polarization stems from a position offset of
the single emitter with respect to the cavity center, which breaks the
cylindrical symmetry, and a position-dependent coupling to the frequency
degenerate eigenmodes of the resonator structure. The experimental results are
interpreted by using numerical simulations and by experimental mapping of the
polarization-resolved far-field emission patterns. Our findings can be
generalized to any nanophotonic structure where two orthogonal eigenmodes are
not fully spatially overlapping.

Optics;Mesoscale and Nanoscale Physics;Quantum Physics