Band geometry induced electro-optic effect and polarization rotation

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 phenomenon in parity-time reversal ($\mathrm{PT}$) symmetric systems such as CuMnAs. Our findings establish the electro-optic effect as a tool to probe band geometric effects and open different avenues to design electrically controlled efficient amplitude and phase modulators for photonic applications.