Modeling of a converging gradient-index lens with variable focal length in a lanthanum-modified lead zirconate titanate ceramic cylinder with a lateral multielectrode structure.

A mathematical model is presented to characterize the performance of a lanthanum-modified lead zirconate titanate electro-optical cylindrical structure with an arbitrary number N of lateral electrodes switched with a series of voltages V(0) and V(0) + DV. The method yields a solution that can be written as a sum of numerical and analytical components, and the contribution of numerical components becomes increasingly smaller as the electrode wrapping angle is decreasing below pi/3N. The effects of the electrode wrapping angle and the switching voltages on the induced refractive-index distribution and electrode capacitance are analyzed. It is shown that the design offers a simple and compact structure that performs dynamic light diverging with a focal length that can be controlled by the applied voltage. The possibility of light steering is considered for a two-electrode structure.