Nonlinear optimization approach to determine optical dispersion in liquid crystals

We report the method of calculating optical dispersion of selected nematic liquid crystals using maxima positions of a transmittance filled Fabry–Pérot filter. Additionally, the profiles of a dispersive phase of reflection have been calculated. The transmittance of Fabry–Pérot filter was described as a form of a modified Airy formulae (with parameters dependence on wavelength and phase of reflection). To correctly use this function, additionally the phase of reflection is defined, taking into account the problem of a beam penetrating the mirror structure. The authors of this work assume that the point where the beam is reflected is not created strictly on the boundary of media, but it is moved into the mirror structure. The depth of the penetration changes the optical way of the wave and in consequence – the optical width of the Fabry–Pérot filter cavity. The parameter describing this phenomenon was named as a phase of reflection. This work presents how to calculate: the phase of reflection, one of refractive indices of birefringent medium inside Fabry–Pérot filter and the cavity width at the same time with the use of composed nonlinear optimization methods. The proposed method is an alternative for a reverse task solution which is hard to define properly here.