the other half being lost out the bottom of the membrane. In the case with the bottom reflector, however, all light can be collected above the membrane, so the maximum collection efficiency is 100$\%$. We find the single-mode fiber coupling by calculating the mode overlap of the far-field PhC mode with a Gaussian of specified mode diameter, which is the guided mode of the fiber.

The simulated quality factor and collection efficiency for cavities with different outward shift values are plotted in Fig. \[figQsh\], indicating the trade-off between these figures of merit. As the collection efficiency is improved, the Q is expected to decrease as more light is being coupled to radiation modes rather than remaining confined in the dielectric slab. The collection efficiency increases for large outward shifts ($s/a$ greater than 0.1), but the Q reaches a maximum for $s/a = 0.085$. We find that $s/a=0.115$ gives a good compromise value, demonstrating an improved collection efficiency of $80\%$ for NA $= 0.8$ while still maintaining a high Q of 15,000.

Figure \[figQsh\] compares simulations without a bottom reflector (labeled ‘no R’) and with a bottom reflector separated by an air gap of $L=925$ nm (labeled ‘with R’). In general, 