and Q factor. However, here we simulate the full 10-layer DBR structure to provide the best possible comparison with the experimental results. Small discrepancies between the experimental and simulated far-field patterns could be due to fabrication imperfections or the finite grid size of the numerical simulations. For devices with increasing outward shift values, the experimental far-field measurements show that more of the light is emitted at small angles, in good agreement with simulations.

![Top row: FDTD simulated far-field profiles, considering the membrane only, for different values of $s/a$. The profiles are cut off at NA $=$ 0.8 to allow for better comparison with experimental results. Middle row: FDTD simulations, including the air gap and DBR, for the same $s/a$ values as above. For increasing shift values, the vertical beaming of the radiation clearly improves. Bottom row: Experimental far-field profiles, for one row of devices, showing a nice comparison with simulation results.[]{data-label="figshcomp"}](fig5.eps){width="80.00000%"}

Resonant reflection spectroscopy measurements
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By modifying the far-field profiles to become Gaussian-like, the cavity modes are expected to be better mode-matched to an external input field using a microscope objective of reasonable numerical aperture. This is important in c-QED applications based on the interference between the input field 