The incorporation of the Pockels effect in structurally chiral materials (SCMs) engenders new modalities for
control manipulation of the circular Bragg phenomenon (CBP). The boundary-value problem of the reflection
and transmission of a plane wave due to a slab of an electro-optic SCM is formulated in terms of a 4×4
matrix ordinary dfferential equation. The SCM slab can be locally endowed with one of 20 classes of point
group symmetry, and is subjected to a dc voltage across its thickness. The enhancement (and, in some cases,
the production) of the CBP by the application of a dc electric field across the thickness of the SCM slab has
switching and circular-polarization-rejection applications in optics.