Geometric phase and o-mode blue shift in a chiral anisotropic medium inside a Fabry-P\'erot cavity

Anomalous spectral shift of transmission peaks is observed in a Fabry--P\'erot cavity filled with a chiral anisotropic medium. The effective refractive index value resides out of the interval between the ordinary and the extraordinary refractive indices. The spectral shift is explained by contribution of a geometric phase. The problem is solved analytically using the approximate Jones matrix method, numerically using the accurate Berreman method and geometrically using the generalized Mauguin--Poincar\'e rolling cone method. The $o$-mode blue shift is measured for a 4-methoxybenzylidene-4'-$n$-butylaniline twisted--nematic layer inside the Fabry--P\'erot cavity. The twist is electrically induced due to the homeoplanar--twisted configuration transition in an ionic-surfactant-doped liquid crystal layer. Experimental evidence confirms the validity of the theoretical model.