Design of Tunable Liquid Crystal Lenses with a Parabolic Phase Profile

Abstract

An electrode pattern design generating a parabolic voltage distribution, in combination with usage of the linear response range of the liquid crystal (LC) material, has been recently proposed to obtain nearly ideal phase profiles for LC lenses. This technique features low driving voltages, simple structure, compact design, and the absence of high-resistivity (HR) layers. In this work, the universal design principle is discussed in detail, which is applicable not only to LC lens design, but also to other LC devices with any phase profile. Several electrode patterns are presented to form a parabolic voltage distribution. An equivalent electric circuit of the LC lens based on the design principle is developed, and the simulation results are given. In the experiments, an LC lens using the feasible parameters is prepared, and its high-quality performance is demonstrated.

Photoaligned Tunable Liquid Crystal Lenses with Parabolic Phase Profile

“…The fluid nature of the director field in liquid crystals (LC), combined with their high sensitivity to external stimuli, enables lenses based on liquid crystalline materials to fulfill the above requirements. The focal length of LC lenses is typically electrically tunable, and since the first report dated back to 1979 [1], several different structures have been proposed, mainly based on patterned electrodes [2][3][4][5][6][7]. In these systems, a lens-like refractive index profile is realized by pixelated electrodes with a proper distribution.…”

“…It should be noted that LC lenses with parabolic phase profiles have recently been proposed [7]. In the study, a parabolic profile was obtained using a proper electrode pattern that gave rise to a parabolic distribution of the applied voltage.…”

“…(𝐾 𝑠𝑖𝑛 𝜃 + 𝐾 𝑐𝑜𝑠 𝜃)𝜃 | − 𝑊(𝑥) sin(𝜃(0) − 𝜃 ) cos 𝜃(0) − 𝜃 = 0, 𝜃(𝑧 = 𝐿) = 𝜃 (7) Equations ( 6) and ( 7) should be accompanied by the Poisson equation for the electric field potential U, defined by the relation 𝑬 = −𝜵𝑈 [18] ∇ 𝜀ε 𝜵 𝑈(𝑥, 𝑧) = 0, (8) where 𝜀ε 0 = 𝜀ε 0 + 𝑖 , with 𝜀̃ as the permittivity tensor, 𝜔 as the AC electric field frequency, 𝜎 as the LC electric conductivity, and 𝜀̂ as the LC dielectric tensor. In our case, the latter has the following form: 𝜀̂= 𝜀 + 𝜀 cos 𝜃 0 𝜀 sin 𝜃 cos 𝜃 0 𝜀 0 𝜀 sin 𝜃 cos 𝜃 0 𝜀 + 𝜀 sin 𝜃 , (9) The electric field potential U(𝑥, 𝑧) obeys the following boundary conditions:…”

Photoaligned Tunable Liquid Crystal Lenses with Parabolic Phase Profile

“…The fluid nature of the director field in liquid crystals (LC), combined with their high sensitivity to external stimuli, makes lenses based on liquid crystalline materials able to fulfill the above requirements. The focal length of LC lenses is typically electrically tunable and since the first report dated back to 1979 [1], several different structures have been proposed mainly based on patterned electrodes [2][3][4][5][6][7]. LC cells with pixel-free electrodes, have also been proposed [8].…”

“…Noteworthy, LC lens with a parabolic phase profile have recently been proposed [7]. In that work the parabolic profile was obtained by a proper electrode pattern that gave rise to a parabolic distribution of the applied voltage.…”