temporal coupled-mode theory. (a) Representation of the PhC cavity, with two input/output ports. (b) Schematic of the full structure, including the PhC membrane, the air gap, the DBR mirror, and the substrate.[]{data-label="figmodel"}](fig7.eps){width="55.00000%"}

However, our system is complicated by the presence of a DBR, placed at a distance $L$ from the bottom of the photonic crystal membrane (see Fig. \[figmodel\](b)). The DBR couples the input and output channels for port-2: $$E_2 = r_{DBR} e^{2i\omega L/c} E'_2$$ where $r_{DBR}$ is the Fresnel coefficient of the DBR stack. Combining with $E'_2 = \Sigma_{21} E_1 + \Sigma_{22} E_2$, we get a relation between $E_2$ and $E_1$: $$E_2 = \frac{r_{DBR} e^{2i\omega L/c} \Sigma_{21} (\omega)}{1-r_{DBR} e^{2i\omega L/c} \Sigma_{22} (\omega)} E_1$$ and we can reduce the system to a one-port device with a reflectivity $|E_1'/E_1|^2$. The effective reflectivity is: $$R_{eff} (\omega) = \left|
\Sigma_{11} (\omega)+
\frac{r_{DBR} e^{2i\omega L/c} \Sigma_{21} (\omega) \Sigma_{12} (\omega)}{1-r_{DBR} e^{2i\omega L/c} \Sigma_{22} (\omega)}
\right|^2$$ The predicted reflection spectra for our experimental parameters are plotted with our data in Fig. \[figfano\], with the only free parameter being the mode-matching. The predicted asymmetric reflection dips match well with our experimental observations.

Conclusion {#conclude}
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In conclusion, we have performed extensive simulations to optimize the far-field emission 