the Q factor of the mode can be enhanced or degraded by the inclusion of a bottom reflector, which is discussed extensively in Ref. [@kim2006]. The data indicate that for the specific air gap separation of 925 nm, the Q is virtually unaffected when this bottom reflector is introduced; however, the collection efficiency changes significantly. This is partially due to the fact that the collection efficiency maximum is 50$\%$ for simulations without a bottom reflector, while it can be as high as 100$\%$ when the bottom relfector is taken into account. For the optimized $s/a=0.115$ device, we performed a series of simulations to optimize the air gap separation, with results shown in Fig. \[figair1\]. In this case, we consider the trade-off between Q and maximum coupling to a single mode fiber, noting that the fiber mode diameter for maximum coupling may be different for each device. Far-field radiation patterns for a selection of devices are shown in the bottom panel of Fig \[figair1\]. We find the best compromise air gap to be $L = 925$ nm, which corresponds to $L/\lambda=0.96$. The maximum coupling between this device and a fiber mode with a beam waist of 1.5 $\mu$m is 92$\%$. The 