## 4 Discussion  
The mutual coupling between rods has a strong influence on the overall threshold pumping density of a PM, but not always in a positive trend. To design a low threshold PM that is also practical for actual devices, all rods in the PM have to be uniformly excited. An effective coupling with peripheral unexcited rods will only increase the threshold pumping density. Therefore, a well-coupled PM with a confined device footprint is more practical than a large-area two-dimensional rod array for practical implementation. Furthermore, the hexagons do not possess a full rotational symmetry like that of the microdisks or micro-rings. The relative orientation between adjacent rods also plays an important role in forming PMs in the monolithic wurtzite crystal. For example, Figure 5a-d showed four different kinds of supermode in a hexagon dimer. The rods in Figure 5a,b were aligned along the [100] direction (or a-axis) while those in Figure 5c,d were along the [110] direction, (or m-axis) in the wurtzite crystal. In each configuration, the evanescent interaction further split into two supermodes, forming optical bonds or node planes in the middle of two rods. For the sake of brevity, we coded the supermodes with three digits: The first letter illustrated the relative orientation among each cavity, which could be either corner-to-corner (C) or side-to-side (S); the second digit was the number of cavities in the photonic molecules; and the last digit described the type of evanescent field interaction between adjacent cavities, which could be either bond-like (B) or node-like (N). For example, the supermodes from Figure 5a-d were coded as C2B, C2N, S2B, and S2N, respectively. Figure 5e,f illustrate the \(\lambda\) and Q-factor response to the minimum distance d between two rods. Figure 5e is the summary for the dimer with C-configuration. When the hexagons were in a subwavelength proximity (D < 200 nm), the formation of optical-bonds caused a resonance wavelength redshift, while forming an optical node plane resulted in a blueshift to the reference of a singular hexagon. As d increased, the spectral splitting gradually decreased to zero and then the sign changed when d > 450 nm. As d further increased, both \(\lambda\)'s oscillated sinusoidally with a diminishing amplitude. This damped oscillation characteristic originated from the mutual interference of the evanescent fields. Figure 5: (**a**–**d**) show the intensity profiles of a two-rod PM with two relative orientations and two type mode interaction. The dependence of the Q-factor and resonant wavelength on the rod-to-rod spacing, (**d**) while two rods were aligned (**e**) corner-to-corner and (**f**) side-to-side. The black dashed line marked the reference value from a single rod. The strength of the interacting evanescent field became weak as d increased, resulting in a gradual decoherence in the space. A similar damped oscillation also occurred in the Q-factor. It is worth noting that forming a photonic molecule does not guarantee an enhanced Q-factor for a particular supermode. If the evanescent field \"outside\" the photonic molecule is strengthened under mutual resonance, the photons are actually more likely to be scattered. Fortunately, when the Q-factor of one supermode is beneath the reference under a given d, the other one will surpass it. Therefore, we can still say that forming a photonic molecule helps enhance the overall Q-factor. Figure 5f is the same summary as Figure 3a, but for the side-to-side configuration. The dependence of \(\lambda\) and the Q-factor on d were similar, but the oscillation amplitude was higher in Figure 3b. We attributed the stronger response in \(\lambda\) and Q-factor simply due to a higher overlap of the evanescent field from each cavity. The maximum Q-factor took place in mode S2N, which was 2.2 times higher than that of the single rod case. The comparison further justified the necessity of considering the relative orientations for photonic molecules in a monolithic wurtzite crystal.