  Electric field-induced modulation of the optical properties is crucial for
amplitude and phase modulators used in photonic devices. Here, we present a
comprehensive study of the band geometry-induced electro-optic effect,
specifically focusing on the Fermi surface and disorder-induced contributions.
These contributions are crucial for metallic and semimetallic systems and for
optical frequencies comparable to or smaller than the scattering rates. We
highlight the importance of the quantum metric and metric connection in
generating the electro-optic effect in parity-time reversal ($\mathcal{PT}$)
symmetric systems such as CuMnAs. Our findings establish the electro-optic
effect as a novel tool to probe band geometric effects and open new avenues to
design electrically controlled efficient amplitude and phase modulators for
photonic applications.
