BST$({\mathrm{Ba}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{TiO}}_3)/\mathrm{PZT}({\mathrm{Pb}}_{0.52}{\mathrm{Zr}}_{0.48}{\mathrm{TiO}}_3)$ photonic crystals were fabricated by magnetron sputtering and annealed at $620°\mathrm{C}\text{?}700°\mathrm{C}$. By controlling the crystallinity and the oxygen vacancies of the ferroelectric photonic crystals, the optically and electrically controllable terahertz wave modulations were realized. The variation in refractive index of the 680°C annealed sample showed the highest modulation to the optical pump and increased to 11.9 due to the highest absorption near 532 nm. In the optical pump, the electrons from ${\mathrm{Ti}}^{3}2{\mathrm{p}}_{3/2}$ ions could be stimulated and captured by ${\mathrm{Ti}}^{4}2{\mathrm{p}}_{3/2}$ ions, and the ratio of ${\mathrm{Ti}}^3/{\mathrm{Ti}}^4$ observed increased with the increasing annealing temperature, indicating the increasing oxygen vacancies concentration, which increased the 532 nm optical absorption and contributed to the improved optical modulation. The excess Pb migrating to the surface at higher annealing temperature might be one reason for the degradation of optical modulation. The increasing polarization and leakage current could contribute to the increasing permittivity and loss with the increasing annealing temperature. Two different results were observed on the sample annealed at 680°C when the order of applying external optical and electric fields was changed, due to the different migration mechanisms of excited carriers. This work provides a potentially effective approach to fabricate THz sensing, imaging, and communications devices with multi-function in the modulation of optical and electric multi-fields.