  We have employed Bloch-wave engineering to realize submicron diameter
ultra-high quality factor GaAs/AlAs micropillars (MPs). The design features a
tapered cavity in which the fundamental Bloch mode is subject to an adiabatic
transition to match the Bragg mirror Bloch mode. The resulting reduced
scattering loss leads to record-high visibility of the strong coupling in MPs
with modest oscillator strength quantum dots. A quality factor of 13,600 and a
Rabi splitting of 85 \mueV with an estimated visibility v of 0.38 are observed
for a small mode volume MP with a diameter dc of 850 nm.
