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's 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. This work provides theoretical guidance for future studies on stacked chiral anisotropic media.
Liquid crystal is known for the combination of the fluidity of liquid and the dielectric anisotropy of crystals. Cholesteric liquid crystal (CLC) is a typical liquid crystalline phase with the helical ordering of anisotropic molecules. The CLC exhibits a striking feature – Bragg reflection. Light propagating along the helix axis with appropriate wavelength (from nop to nep) can be reflected, where ne and no represent extraordinary and ordinary refractive indices, respectively. Moreover, the chiral structure of the CLC endows the Bragg reflection with the spin-selectivity, therein, only light with the same circular polarization chirality as the CLC can be reflected, while the opposite one is transmitted.
In 2016, researchers found light reflected from CLC is endowed with geometric phase, which is determined by the orientation angle of the CLC director at the front surface. Thanks to the digital micromirror device (DMD) with high resolution, arbitrary PB phase design makes patterned CLCs compelling in flat optics. However, PB phase only exists in reflected light and the transmitted light remain untailored. Stacking CLC layers with right-handedness and left-handedness together makes conjugated PB phase modulation achievable. Up to now, the cascade of a right-handed and a left-handed CLC devices, and a single device consisting of both handedness, have been demonstrated in experiments. For diverse types of CLC stacks, there still lacks a comprehensive model on their optical properties, especially the PB phase, which is very important for taking more profound insight into those observed phenomena and predicting more intriguing properties in some unexplored structures.
The research group led by Prof. Yanqing Lu and Assoc. Prof. Peng Chen from Nanjing University proposed the theoretical models of the opposite-chirality CLC stacked superstructures and develop a 4 × 4 matrix solver for simulating corresponding optical properties. This work gives deeper understanding of opposite-chirality CLC stacks, and promisingly offers theoretical directions for complex chiral anisotropic structures. The research results are published in Chinese Optics Letters, Vol. 22, Issue 6, 2024: Lin Zhu, Yiheng Zhang, Shijun Ge, Peng Chen, Yanqing Lu. Optical properties of stacked liquid crystal superstructures with opposite chirality [Invited]. Chinese Optics Letters, 2024, 22(6): 061601
In this work, the researchers systematically investigate the optical properties of various stacked liquid crystal superstructures with opposite chirality. A consistent framework is proposed to describe the trivial cascade of two CLC structures with opposite chirality, the opposite-chirality-coexisted superstructures, and other intermediate configurations. Through numerical simulations, the reflections from different stacked structures are compared under normal and linearly polarized incidence. Both circular polarizations can be reflected in these opposite-chirality stacks, and particularly, the Bragg bandgap splits when the structural repeating units become thin enough (Fig. 1(e-h)). The researchers also study the reflective PB phase, and clarify how the CLC director orientation determines the linear polarization angle of the reflected light. Specifically, the reflected linear polarization also depends on the incident wavelength, attributing to the propagation phase difference between orthogonal circular polarization components. Such rotatory dispersion can be wholly suppressed in the opposite-chirality-coexisted superstructures (Fig. 1(i-l)).
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Fig. 1. (a-d) Schematics of four stacked CLC models. (e-h) Reflectance spectra and (i-l) polarization of the light reflected from four stacked CLC models.
In addition to uniformly alignment, the researchers further imprint an azimuthally gradient pattern on the CLC stacks, and verify the capability of vector beam generation, indicating the broadband and dispersion-free manipulation of structured light. Two representative incident wavelengths (633 nm and 650 nm) are compared within the central Bragg bandgap. As indicated by Fig. 2(a,b), at these two incident wavelengths, the vector beams exhibit different polarization distributions and different orientations of the analyzed intensity profile, which attributes to the evident rotatory dispersion in the two-layer model. When it comes to the case of multi-layer model, the polarization variance between the vector beams becomes smaller (Fig. 2(c,d)), and finally such variance vanishes in the limiting case of coexisted model (Fig. 2(e,f)). This phenomenon again proves that the reflective rotatory dispersion become weaker as the thickness of each sublayer becomes smaller. Importantly, the rotatory dispersion is fully suppressed in the opposite-chirality-coexisted CLC model, owing to the negligible dynamic phase difference between the right-handed and the left-handed circular polarized components. Above results of the generated vector beams offer a vivid illustration of the PB phase and the rotatory dispersion in the patterned CLC stacks. This implies a promising strategy for broadband and dispersion-free structured light manipulation.
Fig. 2. The polarization distribution and the diffracted optical fields with/without analyzer for the generated vector beams at (a, c, e) 633 nm and (b, d, f) 650 nm, respectively.
In all, this work provides a full insight into the optical physics of opposite-chirality CLC superstructures, and offers a theoretical guidance on their designs and applications.
