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Application of liquid crystal (LC) photoalignment for spatial modulation of geometrical phase is a unique tool for fabrication of arbitrary shape flat optical elements. The liquid crystal devices (LCD) technologies are currently one of the most perspective and cost effective solutions for fabrication of switchable flat optical elements. Laser based photoalignment enables linear polarization orientation pattern recording into photoalignment layer by phase interference exposure for initializing surface orientation (alignment) of LC. Exposure of photoalignment layer to light patterns of two circular-polarized interfering laser beams, known as holographic recording, allows formation of LC geometrical phase distributions. This technology allows constructing low-voltage electrically controlled flat LC lenses with ON-OFF switchable distribution of geometrical phase. However, it is the switching between ‘lens’ and ‘no lens’ states only, while electrical switching between two different focuses is not common known. Since the focus of a LC polarization hologram lens is subject to geometry phase distribution, predetermined by the pattern of LC cell alignment, electrical change of the shape of geometrical phase surface is highly desired. In the present work we consider this question and suggest a possible solution. Classical LCDs use voltage to control the liquid crystal reorientation. We applied model of electrically changing liquid crystal distribution to observe geometrical phase modification and made calculations of this process. We were able to derive conditions when specially designed LC polarization hologram lens system has two different focuses F1 and F2 at two different voltage levels V1 and V2, correspondingly. Both states have different LC director and geometrical phase distributions, but same LC alignment patterns. The F1 and F2 are dependent, and we obtained the next formula: 𝐹2 = (5𝐹2 ± 3√𝐹22 + 𝑅2)/4, where R is the lens radius. The sign ‘+’ or ‘–’ depends on the choice of states notation for F1 and F2. The designed flat lens has low complexity of LC cell with single uniform electrode and can be electrically switched between 3 different states: ON1 (F1, V1), ON2 (F2, V2) and OFF (F3 = ∞, V3). The lightweight electrically switchable flat lens is perspective for various applications in photonics, lighting and information display devices.
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