the resonant mode of wavelength $\lambda$ in the membrane; the downward propagating wave will eventually be redirected upward and will interfere with the upward propagating wave. If we consider radiation into an angle $\theta$, the phase change through the PhC slab, $\phi$, is given by $$\phi=(\frac{2\pi n_{eff}}{\lambda})d\cdot\sqrt{1-(1/n_{eff})^2 sin^2 \theta},$$ and the round trip phase in the air gap is $2\varphi$, where $$\varphi=(\frac{2\pi}{\lambda})L\cdot cos \theta.$$ Let $S$ be the sum of all waves detected upward which initially propagate downward. It can then be shown that[@kim2006] $$S=\frac{t_0^2e^{i\phi}}{(1-r_0^2e^{2i\phi})(r_0+e^{-2i\varphi}e^{-i\epsilon})-r_0t_0^2e^{2i\phi}},$$ where $\epsilon$ is the phase changes at the bottom reflector, and $r_0$ and $t_0$ are coefficients of amplitude reflection and transmission, respectively, for a single dielectric interface. An interference between $S$ and the wave initially propagating upward is characterized by $1+S$, and the resultant radiation intensity is given by $$W=|1+S|^2.$$ In Fig. \[figair2\], the intensity $W$ is plotted as a function of NA and $L/\lambda$ for the following parameters: $n_{eff}=2.8$, $\lambda=963$ nm, $d=130$ nm, and $\epsilon=\pi$.

![A plot of the total radiation intensity ($W=|S+1|^2$) as a function of NA, for different values of $L/\lambda$. The calculation is done for the following paramaters: $n_{eff}=2.8$, $\lambda=963$ nm, $d=130$ nm, and $\epsilon=\pi$. In the bottom panel, line cuts 