Topological Protection and Slow-Light Coupling: mathematical and structural walkthrough

Section role: supports Section 3 during the teacher's synthesis of student findings and formalization of the mathematical framework of Zak phases and Delay-Bandwidth Products. Slides: (1) Title — 'Formalizing Topological Protection and Slow-Light Coupling'; (2) Zak Phase Formulation — bullets: mathematical definition using the Berry connection integral, interface between PC1 and PC2, formation of topological edge states (TESs); (3) Delay-Bandwidth Product (DBP) — bullets: formula C = Tg * (delta f / 2), buffering capacity metric; (4) Concrete DBP Data Point — bullets: L = 20a (10 um), delta f = 20.343 THz, delay time 0.24091 ps yielding C = 2.45 bits; (5) Robustness to Waveguide Bends — bullets: navigating U-shaped, H-shaped, 90-degree, and 45-degree bends without backscattering, comparison to traditional structures; (6) Fabrication Techniques — bullets: electron beam lithography (EBL), hydrofluoric acid (HF) etching; (7) Closing slide — 'How does the Zak phase difference directly dictate the energy confinement in topological edge states?' — bridges back to the gradient lattice design in Section 2 and sets up the DBP calculations in Section 4.

Lara from Teachy