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ABSTRACT: In this work, a technique to generate aspherical liquid crystal lenses with positive and negative optical power is experimentally demonstrated. The main enabling element is a micro-metric electrode with variable spatial size. This produces a decreasing resistance towards the lens centre that generates the desired voltage/phase profiles. Then, the voltage is homogeneously distributed across the active area of the lens by micro-metric concentric electrodes. As it is demonstrated, the phase shift can be controlled with voltages from 0 to 4.5 VRMS. As a result, parabolic profiles are obtained both for negative and positive optical powers. Furthermore, this approach avoids some disadvantages of previous techniques; parabolic profiles can be obtained with only one lithographic step and one or two voltage sources. Other complex aspherical profiles could be fabricated using the same technique, such as elliptical or hyperbolic ones. ; Funding: European Social Fund (NAWA PROM projekt nr POWR.03.03.00-00-PN13/18); Comunidad de Madrid and FEDER Program (S2018/NMT-4326); MCIN/ AEI/10.13039/501100011033 and European Union "Next generation EU"/PTR (PDC2021-121172-C21); MCIN/ AEI/10.13039/501100011033 and FEDER "A way to make Europe" (PID2019-107270RB-C21, PID2019-109072RB-C31, RTC-2017-6321-1).

There is an increasing need to control light phase with tailored precision via simple means in both fundamental science and industry. One of the best candidates to achieve this goal are electro-optical materials. In this work, a novel technique to modulate the spatial phase profle of a propagating light beam by means of liquid crystals (LC), electro-optically addressed by indium-tin oxide (ITO) grating microstructures, is proposed and experimentally demonstrated. A planar LC cell is assembled between two perpendicularly placed ITO gratings based on microstructured electrodes. By properly selecting only four voltage sources, we modulate the LC-induced phase profle such that non-difractive Bessel beams, laser stretching, beam steering, and 2D tunable difraction gratings are generated. In such a way, the proposed LC-tunable component performs as an all-in-one device with unprecedented characteristics and multiple functionalities. The operation voltages are very low and the aperture is large. Moreover, the device operates with a very simple voltage control scheme and it is lightweight and compact. Apart from the demonstrated functionalities, the proposed technique could open further venues of research in optical phase spatial modulation formats based on electro-optical materials. ; This work was supported by the Comunidad de Madrid and FEDER Program (S2018/NMT-4326), the Ministerio de Economía y Competitividad of Spain (TEC2013-47342-C2-2-R and TEC2016-76021-C2-2-R), the FEDER/Ministerio de Ciencia, Innovación y Universidades and Agencia Estatal de Investigación (RTC2017-6321-1, PID2019-109072RB-C31 and PID2019-107270RB-C21). The authors also acknowledge the support by the Ministry of National Defense of Poland (GBMON/13-995/2018/WAT), Military University of Technology (Grant no. 23-895).

Correction to: Scientific Reports https://doi.org/10.1038/s41598-020-70783-8, published online 14 August 2020 This Article contains a typographical error in the Acknowledgements section. "the Ministerio de Economía y Competitividad of Spain (TEC2013-47342-C2-2-R)" should read: "the Ministerio de Economía y Competitividad of Spain (TEC2016-77242-C3-1-R)" ; This work was supported by the Comunidad de Madrid and FEDER Program (S2018/NMT-4326), the Ministerio de Economía y Competitividad of Spain (TEC2013-47342-C2-2-R and TEC2016-76021-C2-2-R), the FEDER/Ministerio de Ciencia, Innovación y Universidades and Agencia Estatal de Investigación (RTC2017-6321-1, PID2019-109072RB-C31 and PID2019-107270RB-C21). The authors also acknowledge the support by the Ministry of National Defense of Poland (GBMON/13-995/2018/WAT), Military University of Technology (Grant no. 23-895).