Spatial distribution of the real part of the Poynting vector (top row) and the corresponding in-plane Poynting vector field (bottom row) for the optimized 4 × 4 symmetric geometry. The colormap illustrates the magnitude and sign of the power flow, while the arrow plots indicate the local energy propagation direction across the unit cell. The results highlight the symmetry-induced field distribution and energy transport characteristics of the structure. (k _Γ-M  = 125 × 10⁻³, band: 1; k _Γ-M  = 5.00 × 10⁻³, band:3; k _Γ-M  = 125 × 10⁻³, band: 3.