Analysis of optical polarization modulation systems through the Pancharatnam connection

We present a geometrical analysis on the Poincaré sphere of the complex (amplitude and phase) response of polarization modulation systems. The proposed method can be applied to analyze non-cyclic polarization changes and, in particular, the phase is evaluated through the geometric Pancharatnam-Berry phase and the Pancharatnam connection between the initial and the final state. The method can be very useful to analyze and intuitively understand the complex modulation mechanism in polarization modulation devices such as liquid crystal displays.