Tunable liquid-crystal focusing device. 1. Theory

A theoretical model for a modal liquid-crystal focusing device is developed. The solutions to the system of equations are investigated in the approximation of a small modal parameter. The necessary relations between the control harmonic potentials for implementing a phase delay profile in the form of a circular truncated cone with a controlled position of the base centre and in the form of an elliptical truncated cone with a controlled centre position and fixed directions of the major axes of the ellipse (which are parallel to the aperture edges) are found.