jumps and shot noise should be detectable. Notwithstanding these developments in Si$_{3}$N$_{4}$, we note that the results presented here can be used for device design in any low-loss material with a similar index of refraction, such as diamond [@Mouradian:17].

Photonic crystal nanocavity design
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![(a) Schematic of the Si$_{3}$N$_{4}$ photonic crystal dielectric patterning with the cavity section shown enlarged and dotted line denoting the cavity centre. Dimensions: width $w$, lattice constant $a$, semi-minor and -major axes ($R_x,R_y$). (b) The TE-polarization bandstructure for the centre hole unit cell of the device in (a) for varying nanobeam thicknesses. The air (dielectric) modes are denoted with solid (dotted) lines, and the bandgaps (bg’s) of the mirror holes for the respective coloured bands are shown to the right of the plot area. (c) The quality factor $Q_o$ of the PCC’s symmetric fundamental mode determined from 3D FDTD simulations for thickness $t$. (d) The 3D FDTD electric field $E_y$ mode profile for a 500 nm thick device.[]{data-label="figureOne"}](figure1v6.pdf){width="12cm"}

We begin by discussing the design of the Si$_{3}$N$_{4}$ air-mode PCC shown in Fig. \[figureOne\](a). The hole dimensions and tapering were calculated with the deterministic design recipe in Refs. [@Quan10; @Quan11], as discussed below. We set the nanobeam 