The linear electro-optic (EO) and electro-gyration (EG) effects are studied in an optically active material systems including Bi₁₂SiO₂₀ (BSO) oxide and bent-core liquid crystals. In an isotropic BSO sample, the breaking of intrinsic centro-symmetry allowed the EO modulation of the refractive index. In a mixture of bent-shaped liquid crystalline molecules having both optical activity and birefringence, the observed intensity modulation is investigated, which is related to the nonlinear optical responses of both the optical rotatory power and the birefringence. Both the linear EO and EG effects are understood in terms of the superposition principle of linear and circular birefringences.

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