# Photonic Crystal Cavity with a Thin Low-Index Layer for Silicon-Compatible Nanolight Source
## 4 Design of Photonic Crystal Cavity Mode  
We designed a 2D photonic crystal by placing cylinders with square lattices consisting of Si and a thin SiO\({}_{2}\) layer, where the total height (\(H\)) and SiO\({}_{2}\) thickness (\(t\)) of each cylinder were 1000 nm and 10 nm, respectively. The lattice constant (\(a\)) and radius (\(r\)) of the cylinder are set to 500 nm and 125 nm, respectively, to achieve a maximum photonic bandgap based on the 3D plane wave expansion (PWE) method. In the calculations of the bandgap, we used a superlattice of the stacked structure  
Figure 3: **(a)** Effective index of a thin SiO\({}_{2}\) layer embedded in a Si slab with a height (\(H\)) of 1000 nm as a function of the SiO\({}_{2}\) layer thickness. Here, 1550 nm is considered as the target wavelength; (**b**) Mode profiles of z-directional electric field intensity for the SiO\({}_{2}\) layer thickness (\(t\)) of 10 nm (left) and 50 nm (right); (**c**) Electric field intensity profiles for different SiO\({}_{2}\) layer thicknesses; (**d**) Confinement factor (black) and normalized confinement factor (blue) as functions of thin SiO\({}_{2}\) layer thickness. of air and a 2D rod-type photonic crystal layer. The photonic band diagram of Figure 4a shows that the target wavelength of 1550 nm (1216 THz) is positioned in the photonic bandgap of the proposed structure. The photonic band diagram was obtained by the 3D PWE method. The \(Q\) factor and electric field distributions of a cavity mode were obtained by using FDTD analysis. To induce a cavity mode, we reduced the radius of a cylinder at the center and obtained a fundamental cavity mode at wavelengths of 1549 nm, 1568 nm, and 1612 nm when the defect radius (\(r_{d}\)) was 80 nm, 85 nm, and 90 nm, respectively (Figure 4b-d). The highest quality factor (\(Q\) factor) is 4900 in the structure, with an \(r_{d}\) of 90 nm. To increase the \(Q\) factor further, we suppressed the vertical radiation loss of the cavity by shifting the four nearest neighborhood cylinders into the center defect and changing the mode profiles slightly [20], as shown in Figure 5a. As the nearest cylinders shift into the center and the distance changes from 10 nm to 100 nm, the resonant wavelength of the cavity mode blue-shifts 1568 nm to 1509 nm because of the decrease in the mode volume, as shown in Figure 5c. In contrast, the \(Q\) factor has the highest value of 15,000 when \(r_{d}\) and the shifted distance (d) are 90 nm and 60 nm, respectively, and the corresponding wavelength is 1537 nm. Figure 5b shows the horizontal and vertical mode profiles in the cavity with \(r_{d}\) = 90 nm and \(d\) = 60 nm. The mode is horizontally well confined in the defect cylinder by the photonic bandgap. As expected from the slot waveguide mode profile of Figure 3b, the electric field is strongly confined in the low-index thin SiO\({}_{2}\) layer, as shown in the inset of Figure 5b. Figure 4: (**a**) Photonic band diagram of the proposed structure for a cylinder height (\(H\)) of 1000 nm, thin SiO\({}_{2}\) layer thickness (\(t\)) of 10 nm, and cylinder radius (\(r\)) of 125 nm; (**b–d**) z-component electric field mode profiles of cavity modes with different defect radius (\(r_{d}\)); (**b**) \(r_{d}\) = 80 nm; resonant wavelength 1549 nm; total quality factor = 670; (**c**) \(r_{d}\) = 85 nm; wavelength = 1568 nm; total quality factor = 1000; (**d**) \(r_{d}\) = 90 nm; wavelength 1612 nm; total quality factor = 4900. The mode profiles are obtained at the vertical center of the cylinder. Figure 5: (**a**) Schematic of the modified cavity with a central defect cylinder and our shifted nearest neighbor cylinders. The four cylinders are shifted into the center over a distance of d; (**b**) XY and XZ mode profiles of the cavity mode when the defect cylinder radius \(r_{d}\) = 90 nm, the shift of the four nearest cylinders \(d\) = 60 nm, and the resonant wavelength is 1537 nm.