photoluminescence emission at the back focal plane of the objective onto an intensified CCD[@bonato2012]. We use a $2f - 2f$ imaging setup, where $f=40$ cm is the focal length of the imaging lens; our objective has an NA of 0.8. Using a CCD exposure time of 30 to 120 seconds, spectrally filtered images were collected of the far-field radiation pattern. A background image, taken with a slightly tilted interference filter, was subtracted to improve the signal-to-noise ratio.

Figure \[figshcomp\] shows simulated and experimental k-space far-field profiles of the H dipole mode for different outward shift values. For small $s/a$ values, the radiation intensity is spread over a large range of angles; as $s/a$ is increased, the emitted light becomes more intense in the central region of the light cone. It is clear that the bottom reflector (middle row of Fig. \[figshcomp\]) modifies the far-field profiles significantly and shows much better agreement with the experimental results than the simulations of the membrane only (top row of Fig. \[figshcomp\]). As demonstrated in Sec. \[sims\], it is sufficient to approximate the DBR below the air gap as a simple dielectric of constant refractive index for determining the ideal fabrication parameters for collection efficiency 