Calculation of gyrotropy coefficients in media with low-pitch helical structures

Chiral smectic liquid crystals are known for their huge optical activity due to the precession of the anisotropic dielectric tensor around the helicoidal axis. For an oblique direction of the propagating wave, the helix acts as a grating which splits an incident beam in different directions as long as the pitch is not too small with respect to the light wavelength. When the pitch of the helix is smaller than the wavelength, the effect of the helix is a renormalization of the gyrotropic coefficients (g_{⊥} and g_{∥}) of the resulting uniaxial medium. We report here on a method to compute these coefficients in that limit. Resolution of the Maxwell equations, using a perturbative approach, gives expressions for g_{⊥} and g_{∥} as a power development of the ratio (p/λ). The various terms of these developments coincide with the approximate expressions of these coefficients known in the literature.