  The helical-flexo-electro-optic effect shows interesting in-plane
electro-optic switching behaviour due to flexoelectric coupling with applied
electric fields. Previous understanding of the behaviour has been generally
based on an analytic approach which makes certain assumptions about the
uniformity of the helical structure and the induced tilt angle under field
application. Here we remove these assumptions and develop a perturbative
approximation to describe the structure in more detail. We also use a numerical
method to investigate the behaviour in regimes where the perturbative approach
is inappropriate. The impact of variation in elastic constants and dielectric
anisotropy is investigated. We find that dielectric behaviour in particular can
lead to substantial differences between the tilt angle obtained here and those
obtained using previous analytic models.
