Optical properties of stacked liquid crystal superstructures with opposite chirality [Invited]

Lin Zhu; Yiheng Zhang; Shijun Ge; Peng Chen; Yanqing Lu

doi:10.3788/COL202422.061601

Journals >Chinese Optics Letters >Volume 22 >Issue 6 >Page 061601 > Article

Chinese Optics Letters
Vol. 22, Issue 6, 061601 (2024)

Optical properties of stacked liquid crystal superstructures with opposite chirality [Invited] | Editors' Pick

Lin Zhu, Yiheng Zhang, Shijun Ge, Peng Chen^*, and Yanqing Lu

Author Affiliations

National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

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DOI: 10.3788/COL202422.061601 Cite this Article Set citation alerts

Lin Zhu, Yiheng Zhang, Shijun Ge, Peng Chen, Yanqing Lu, "Optical properties of stacked liquid crystal superstructures with opposite chirality [Invited]," Chin. Opt. Lett. 22, 061601 (2024) Copy Citation Text

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Abstract

Cholesteric liquid crystal (CLC) has been widely used in flat optical elements due to the Pancharatnam–Berry (PB) phase modulation. In order to achieve PB phase modulation for both circular polarizations, it is natural to come up with stacking CLCs with opposite chirality. Here, various optical properties of diverse CLC stacking structures are systematically investigated by numerical calculations. With the thickness of the CLC sublayers becoming smaller, the reflection bandgap splits into three main parts, and the rotatory dispersion gradually becomes negligible. Vector beams provide a more intuitive verification. These results provide theoretical guidance for future studies on stacked chiral anisotropic media.

Keywords

chirality cholesteric liquid crystals Pancharatnam–Berry phases vector beams

\begin{matrix} {\begin{matrix} ε_{R} (z) = [\begin{matrix} ε_{m} + ε_{m} δ \cos 2 (\frac{2 π}{p} z - α) & ε_{m} δ \sin 2 (\frac{2 π}{p} z - α) & 0 \\ ε_{m} δ \sin 2 (\frac{2 π}{p} z - α) & ε_{m} - ε_{m} δ \cos 2 (\frac{2 π}{p} z - α) & 0 \\ 0 & 0 & ε_{3} \end{matrix}], (k - 1) A \leq z < (k - \frac{1}{2}) A \\ ε_{L} (z) = [\begin{matrix} ε_{m} + ε_{m} δ \cos 2 (- \frac{2 π}{p} z - α) & ε_{m} δ \sin 2 (- \frac{2 π}{p} z - α) & 0 \\ ε_{m} δ \sin 2 (- \frac{2 π}{p} z - α) & ε_{m} - ε_{m} δ \cos 2 (- \frac{2 π}{p} z - α) & 0 \\ 0 & 0 & ε_{3} \end{matrix}], (k - \frac{1}{2}) A \leq z < k A \end{matrix} \end{matrix}, where k = 1, 2, \dots, D / A .

(1)

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f (z) = {[E_{x} (z), i H_{y} (z), E_{y} (z), - i H_{x} (z)]}^{T} .

(2)

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P (0, D) = P_{L} (D - \frac{A}{2}, \frac{A}{2}) P_{R} (D - A, \frac{A}{2}) \dots P_{L} (\frac{A}{2}, \frac{A}{2}) P_{R} (0, \frac{A}{2}) .

(3)

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| R ⟩ e^{+ i 2 α} + | L ⟩ e^{- i 2 α + i ψ} = (\hat{x} - i \hat{y}) e^{+ i 2 α} + (\hat{x} + i \hat{y}) e^{- i 2 α + i ψ} = 2 e^{i ψ / 2} [\hat{x} \cos (2 α - ψ / 2) + \hat{y} \sin (2 α - ψ / 2)],

(4)

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Lin Zhu, Yiheng Zhang, Shijun Ge, Peng Chen, Yanqing Lu, "Optical properties of stacked liquid crystal superstructures with opposite chirality [Invited]," Chin. Opt. Lett. 22, 061601 (2024)

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