# Impact of Cubic Symmetry on Optical Activity of Dielectric 8-srs Networks
## 3 Results and Discussion
### Impact of Cubic Symmetry on Optical Activity  
To understand and quantify the effect of cubic symmetry on transmission properties of 8-srs PhCs, we simulated transmission spectra for structures with different aspect ratios, corresponding to the different radius, R, of the galvo-dithered (GD) correction. In a perfectly symmetric case, the focal spot of the writing laser beam is spherical and this is reflected into the model by utilizing an aspect ratio of e = 1. In other cases, the non-spherical focal spot has an elliptical shape and is implemented in the model by utilizing an aspect ratio e \(\
eq\) 1, as shown in inserts in Figure 4. If the radius of the GD correction is smaller than elongation of the focal spot (under-correction case), we have elongated features with an aspect ratio e > 1 (axial dimension being greater than lateral dimension). If the radius of the GD correction is larger than the elongation (over-correction), the aspect ratio is e < 1.  
Figure 3: Fabrication results. SEM images of focused ion beam cut polymer achiral 2-srs networks fabricated with (**a**) traditional direct laser writing (DLW) method and (**b**) GD-DLW showing a transition from elliptical to circular cross section respectively. In the inserts, cross sections are highlighted in green. (**c**) Top view of 8-srs PhCs fabricated using both DLW and GD-DLW. (**d**) Top view of an optimized 8-srs PhC.  
Transmission spectra were obtained by a well-established finite element method approach (see Materials and Methods section) and simulation inputs were the geometric parameters measured from SEM images; a unit cell size of 3.5 \(\upmu\)m and rod diameter of 550 nm. Numerical simulations in Figure 4a shows that position, intensity, and width of photonic stop bands (PSB) are strongly related to the aspect ratio. In the perfectly symmetric case (e = 1) PSB is 200 nm wide and centred at 3.6 \(\upmu\)m. When cubic symmetry is broken and e > 1, PSB undergoes a redshift, broadening, and a drop-in strength. For e = 3, PSB is redshifted by 200 nm, increases in strength by 40%, and width is increased by 50% compared to the perfectly symmetric case (e = 1). When e < 1 PBS intensity does not change, but in this case PSB undergoes a blueshift of 50 nm and PSB bandwidth decreases by approximately 50%.  
Since 8-srs PhCs belong to the I432 symmetry group, they possess remarkable chiral-optical properties [13], in particular OA. To quantify OA numerically, finite element simulations were conducted to evaluate the level of linear polarization rotation. The 8-srs networks were excited with a single linearly polarized plane wave oriented along the \(x\)-axis and transmission coefficients of both unconverted (\(T_{xx}\)) and converted (\(T_{xy}\)) polarization components were recorded. The level of OA for networks was then calculated according to equation [13]:  
\[\text{OA}=2\cdot\cos^{-1}\ \sqrt{\frac{T_{xx}}{T_{xx}+T_{xy}}} \tag{1}\]  
\[\text{or OA}=2\cdot\sin^{-1}\ \sqrt{\frac{T_{xy}}{T_{xx}+T_{xy}}} \tag{2}\]  
The calculated OA for different values of aspect ratio are reported in Figure 4b.  
In the symmetric case (e = 1) OA is centred at 3.6 \(\upmu\)m and 200 nm wide. When cubic symmetry is broken and e < 1, we observe a drop in OA of more than 60% and a blueshift of 50 nm compared to the e = 1 case. However, when e is increased and assumes values > 1, OA intens  
Figure 4: Simulation of transmission and optical activity (OA). (**a**) 8-srs transmission as a function of aspect ratio, e. (**b**) 8-srs OA as a function of aspect ratio, e.  
undergoes a redshift and broadening. Simulation for e = 3, for example, shows a redshift of 200 nm and bandwidth of OA is more than tripled. When cubic symmetry is broken (e > or e < 1), we observe redshift or blueshift in transmission dips respectively and a drop in transmission intensity.