We have reported light beam steering demonstration by using a liquid-crystal-loaded metasurface (LC-MS), which was based on voltage-controlled refractive index distribution on the metasurface. We can upgrade a beam steering device to a variable-focal-length lens by introducing parabolic refractive index distribution on LC-MS. Moreover, the focal length is controllable by voltage across the liquid crystal. We show the design method of the variable-focal-length lens and their numeric demonstrations in this paper.

The proposed lens model is one-dimensional and has parabolic refractive index distribution. In designing the device, we employed two procedures of theoretical far-field pattern (FFP) calculation and computer-based electromagnetic near-field pattern (NFP) simulation. The FFP calculation was carried out by means of phase calculation on the basis of classic optics. The results indicated the estimation of the lens effect although the preciseness of the focal length was not assured since the number of pixelated LC-MS was too small to evaluate the phases and steering direction of light beams. Then, our next strategy is electromagnetic field (EMF) simulation using the COMSOL simulator that can calculate EMF near the pixelated LC-MS. The simulation results improve by repeating these two processes. As a result, we found that LC-MS functions as a lens and the focal length is variable. The focal length was controllable within approximately 2.2 times, assuming a maximum refractive index change of 0.1, a pixel number of 11, and a wavelength of 600 nm.

To conclude, we established a design method of a variable-focal-length lens that employs LC-MS. The controllability of the focal length and the lens function were numerically demonstrated. This kind of LC-MS device does not require high voltages in general. Experimental demonstrations would be our next study.