Title: Electrically tunable total reflection of light by oblique helicoidal cholesteric

Abstract

An oblique helicoidal state of a cholesteric liquid crystal (Ch_{OH}) is capable of continuous change of the pitch$$P$$$P$in response to an applied electric field. Such a structure reflects 50% of the unpolarized light incident along the Ch_{OH}axis in the electrically tunable band determined by$$P$$$P$/2. Here, we demonstrate that at an oblique incidence of light, Ch_{OH}reflects 100% of light of any polarization. This singlet band of total reflection is associated with the full pitch$$P$$$P$. We also describe the satellite$$P/2$$$P/2$,$$P/3$$$P/3$, and$$P/4$$$P/4$bands. The$$P/2$$$P/2$and$$P/4$$$P/4$bands are triplets, whereas$$P/3$$$P/3$band is a singlet caused by multiple scatterings at$$P$$$P$and$$P/2$$$P/2$. A single Ch_{OH}cell acted upon by an electric field tunes all these bands in a very broad spectral range, from ultraviolet to infrared and beyond, thus representing a structural color device with enormous potential for optical and photonic applications.

Impact statement

Pigments, inks, and dyes produce colors by partially consuming the energy of light. In contrast, structural colors caused by interference and diffraction of light scattered at submicrometer length scales do not involve energy losses, which explains their widespread in Nature and the interest of researchers to develop mimicking materials. The grand challenge is to produce materials in which the structural colors could be dynamically tuned. Among the oldest known materials producing structural colors are cholesteric liquid crystals. Light causes coloration by selective Bragg reflection at the periodic helicoidal structure formed by cholesteric molecules. The cholesteric pitch and thus the color can be altered by chemical composition or by temperature, but, unfortunately, dynamic tuning by electromagnetic field has been elusive. Here, we demonstrate that a cholesteric material in a new oblique helicoidal Ch_{OH}state could produce total reflection of an obliquely incident light of any polarization. The material reflects 100% of light within a band that is continuously tunable by the electric field through the entire visible spectrum while preserving its maximum efficiency. Broad electric tunability of total reflection makes the Ch_{OH}material suitable for applications in energy-saving smart windows, transparent displays, communications, lasers, multispectral imaging, and virtual and augmented reality.

The characterization of normal mode (CNM) procedure coupled with an adiabatic connection scheme (ACS) between local and normal vibrational modes, both being a part of the Local Vibrational Mode theory developed in our group, can identify spectral changes as structural fingerprints that monitor symmetry alterations, such as those caused by Jahn-Teller (JT) distortions. Employing the PBE0/Def2-TZVP level of theory, we investigated in this proof-of-concept study the hexaaquachromium cation case,$$\mathrm {[Cr{(OH_2)}_6]^{3+}}$$${\left[\mathrm{Cr}{\left({\mathrm{OH}}_{2}\right)}_{6}\right]}^{3+}$/$$\mathrm {[Cr{(OH_2)}_6]^{2+}}$$${\left[\mathrm{Cr}{\left({\mathrm{OH}}_{2}\right)}_{6}\right]}^{2+}$, as a commonly known example for a JT distortion, followed by the more difficult ferrous and ferric hexacyanide anion case,$$\mathrm {[Fe{(CN)}_6]^{4-}}$$${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_{6}\right]}^{4-}$/$$\mathrm {[Fe{(CN)}_6]^{3-}}$$${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_{6}\right]}^{3-}$. We found that in both cases CNM of the characteristic normal vibrational modes reflects delocalization consistent with high symmetry and ACS confirms symmetry breaking, as evidenced by the separation of axial and equatorial group frequencies. As underlined by the Cremer-Kraka criterion for covalent bonding, from$$\mathrm {[Cr{(OH_2)}_6]^{3+}}$$${\left[\mathrm{Cr}{\left({\mathrm{OH}}_{2}\right)}_{6}\right]}^{3+}$to$$\mathrm {[Cr{(OH_2)}_6]^{2+}}$$${\left[\mathrm{Cr}{\left({\mathrm{OH}}_{2}\right)}_{6}\right]}^{2+}$there is an increase in axial covalency whereas the equatorial bonds shift toward electrostatic character. From$$\mathrm {[Fe{(CN)}_6]^{4-}}$$${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_{6}\right]}^{4-}$to$$\mathrm {[Fe{(CN)}_6]^{3-}}$$${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_{6}\right]}^{3-}$we observed an increase in covalency without altering the bond nature. Distinct$$\pi $$$\pi $back-donation disparity could be confirmed by comparison with the isolated CN$$^-$$${}^{-}$system. In summary, our study positions the CNM/ACS protocol as a robust tool for investigating less-explored JT distortions, paving the way for future applications.

Graphical abstract

The adiabatic connection scheme relates local to normal modes, with symmetry breaking giving rise to axial and equatorial group local frequencies

Deary, J; Scheck, M; Schwengner, R; O’Donnell, D; Bemmerer, D; Beyer, R; Hensel, Th; Junghans, A R; Kögler, T; Müller, S E; et al(
, The European Physical Journal A)

Abstract

The electricE1 and magneticM1 dipole responses of the$$N=Z$$$N=Z$nucleus$$^{24}$$${}^{24}$Mg were investigated in an inelastic photon scattering experiment. The 13.0 MeV electrons, which were used to produce the unpolarised bremsstrahlung in the entrance channel of the$$^{24}$$${}^{24}$Mg($$\gamma ,\gamma ^{\prime }$$$\gamma ,{\gamma}^{\prime}$) reaction, were delivered by the ELBE accelerator of the Helmholtz-Zentrum Dresden-Rossendorf. The collimated bremsstrahlung photons excited one$$J^{\pi }=1^-$$${J}^{\pi}={1}^{-}$, four$$J^{\pi }=1^+$$${J}^{\pi}={1}^{+}$, and six$$J^{\pi }=2^+$$${J}^{\pi}={2}^{+}$states in$$^{24}$$${}^{24}$Mg. De-excitation$$\gamma $$$\gamma $rays were detected using the four high-purity germanium detectors of the$$\gamma $$$\gamma $ELBE setup, which is dedicated to nuclear resonance fluorescence experiments. In the energy region up to 13.0 MeV a total$$B(M1)\uparrow = 2.7(3)~\mu _N^2$$$B\left(M1\right)\uparrow =2.7\left(3\right)\phantom{\rule{0ex}{0ex}}{\mu}_{N}^{2}$is observed, but this$$N=Z$$$N=Z$nucleus exhibits only marginalE1 strength of less than$$\sum B(E1)\uparrow \le 0.61 \times 10^{-3}$$$\sum B\left(E1\right)\uparrow \le 0.61\times {10}^{-3}$ e$$^2 \, $$${}^{2}\phantom{\rule{0ex}{0ex}}$fm$$^2$$${}^{2}$. The$$B(\varPi 1, 1^{\pi }_i \rightarrow 2^+_1)/B(\varPi 1, 1^{\pi }_i \rightarrow 0^+_{gs})$$$B(\Pi 1,{1}_{i}^{\pi}\to {2}_{1}^{+})/B(\Pi 1,{1}_{i}^{\pi}\to {0}_{\mathrm{gs}}^{+})$branching ratios in combination with the expected results from the Alaga rules demonstrate thatKis a good approximative quantum number for$$^{24}$$${}^{24}$Mg. The use of the known$$\rho ^2(E0, 0^+_2 \rightarrow 0^+_{gs})$$${\rho}^{2}(E0,{0}_{2}^{+}\to {0}_{\mathrm{gs}}^{+})$strength and the measured$$B(M1, 1^+ \rightarrow 0^+_2)/B(M1, 1^+ \rightarrow 0^+_{gs})$$$B(M1,{1}^{+}\to {0}_{2}^{+})/B(M1,{1}^{+}\to {0}_{\mathrm{gs}}^{+})$branching ratio of the 10.712 MeV$$1^+$$${1}^{+}$level allows, in a two-state mixing model, an extraction of the difference$$\varDelta \beta _2^2$$$\Delta {\beta}_{2}^{2}$between the prolate ground-state structure and shape-coexisting superdeformed structure built upon the 6432-keV$$0^+_2$$${0}_{2}^{+}$level.

Gazaki, Evangelia; Love, Jonathan(
, Research in Number Theory)

Abstract

For a smooth projective varietyXover an algebraic number fieldka conjecture of Bloch and Beilinson predicts that the kernel of the Albanese map ofXis a torsion group. In this article we consider a product$$X=C_1\times \cdots \times C_d$$$X={C}_{1}\times \cdots \times {C}_{d}$of smooth projective curves and show that if the conjecture is true for any subproduct of two curves, then it is true forX. For a product$$X=C_1\times C_2$$$X={C}_{1}\times {C}_{2}$of two curves over$$\mathbb {Q} $$$Q$with positive genus we construct many nontrivial examples that satisfy the weaker property that the image of the natural map$$J_1(\mathbb {Q})\otimes J_2(\mathbb {Q})\xrightarrow {\varepsilon }{{\,\textrm{CH}\,}}_0(C_1\times C_2)$$${J}_{1}\left(Q\right)\otimes {J}_{2}\left(Q\right)\stackrel{\epsilon}{\to}{\phantom{\rule{0ex}{0ex}}\text{CH}\phantom{\rule{0ex}{0ex}}}_{0}({C}_{1}\times {C}_{2})$is finite, where$$J_i$$${J}_{i}$is the Jacobian variety of$$C_i$$${C}_{i}$. Our constructions include many new examples of non-isogenous pairs of elliptic curves$$E_1, E_2$$${E}_{1},{E}_{2}$with positive rank, including the first known examples of rank greater than 1. Combining these constructions with our previous result, we obtain infinitely many nontrivial products$$X=C_1\times \cdots \times C_d$$$X={C}_{1}\times \cdots \times {C}_{d}$for which the analogous map$$\varepsilon $$$\epsilon $has finite image.

Hashemi, Aref; Gilman, Edward T.; Khair, Aditya S.(
, The European Physical Journal E)

Abstract

We develop a two-timing perturbation analysis to provide quantitative insights on the existence of temporal ratchets in an exemplary system of a particle moving in a tank of fluid in response to an external vibration of the tank. We consider two-mode vibrations with angular frequencies$$\omega $$$\omega $and$$\alpha \omega $$$\alpha \omega $, where$$\alpha $$$\alpha $is a rational number. If$$\alpha $$$\alpha $is a ratio of odd and even integers (e.g.,$$\tfrac{2}{1},\,\tfrac{3}{2},\,\tfrac{4}{3}$$$\frac{2}{1},\phantom{\rule{0ex}{0ex}}\frac{3}{2},\phantom{\rule{0ex}{0ex}}\frac{4}{3}$), the system yields a net response: here, a nonzero time-average particle velocity. Our first-order perturbation solution predicts the existence of temporal ratchets for$$\alpha =2$$$\alpha =2$. Furthermore, we demonstrate, for a reduced model, that the temporal ratcheting effect for$$\alpha =\tfrac{3}{2}$$$\alpha =\frac{3}{2}$and$$\tfrac{4}{3}$$$\frac{4}{3}$appears at the third-order perturbation solution. More importantly, we find closed-form formulas for the magnitude and direction of the induced net velocities for these$$\alpha $$$\alpha $values. On a broader scale, our methodology offers a new mathematical approach to study the complicated nature of temporal ratchets in physical systems.

Du, Hongmin_W; Li, Xiang; Wang, Guanghua(
, Journal of Combinatorial Optimization)

Abstract

Given a monotone submodular set function with a knapsack constraint, its maximization problem has two types of approximation algorithms with running time$$O(n^2)$$$O\left({n}^{2}\right)$and$$O(n^5)$$$O\left({n}^{5}\right)$, respectively. With running time$$O(n^5)$$$O\left({n}^{5}\right)$, the best performance ratio is$$1-1/e$$$1-1/e$. With running time$$O(n^2)$$$O\left({n}^{2}\right)$, the well-known performance ratio is$$(1-1/e)/2$$$(1-1/e)/2$and an improved one is claimed to be$$(1-1/e^2)/2$$$(1-1/{e}^{2})/2$recently. In this paper, we design an algorithm with running$$O(n^2)$$$O\left({n}^{2}\right)$and performance ratio$$1-1/e^{2/3}$$$1-1/{e}^{2/3}$, and an algorithm with running time$$O(n^3)$$$O\left({n}^{3}\right)$and performance ratio 1/2.

@article{osti_10518191,
place = {Country unknown/Code not available},
title = {Electrically tunable total reflection of light by oblique helicoidal cholesteric},
url = {https://par.nsf.gov/biblio/10518191},
DOI = {10.1557/s43577-024-00723-8},
abstractNote = {AbstractAn oblique helicoidal state of a cholesteric liquid crystal (ChOH) is capable of continuous change of the pitch$$P$$Pin response to an applied electric field. Such a structure reflects 50% of the unpolarized light incident along the ChOHaxis in the electrically tunable band determined by$$P$$P/2. Here, we demonstrate that at an oblique incidence of light, ChOHreflects 100% of light of any polarization. This singlet band of total reflection is associated with the full pitch$$P$$P. We also describe the satellite$$P/2$$P/2,$$P/3$$P/3, and$$P/4$$P/4bands. The$$P/2$$P/2and$$P/4$$P/4bands are triplets, whereas$$P/3$$P/3band is a singlet caused by multiple scatterings at$$P$$Pand$$P/2$$P/2. A single ChOHcell acted upon by an electric field tunes all these bands in a very broad spectral range, from ultraviolet to infrared and beyond, thus representing a structural color device with enormous potential for optical and photonic applications. Impact statementPigments, inks, and dyes produce colors by partially consuming the energy of light. In contrast, structural colors caused by interference and diffraction of light scattered at submicrometer length scales do not involve energy losses, which explains their widespread in Nature and the interest of researchers to develop mimicking materials. The grand challenge is to produce materials in which the structural colors could be dynamically tuned. Among the oldest known materials producing structural colors are cholesteric liquid crystals. Light causes coloration by selective Bragg reflection at the periodic helicoidal structure formed by cholesteric molecules. The cholesteric pitch and thus the color can be altered by chemical composition or by temperature, but, unfortunately, dynamic tuning by electromagnetic field has been elusive. Here, we demonstrate that a cholesteric material in a new oblique helicoidal ChOHstate could produce total reflection of an obliquely incident light of any polarization. The material reflects 100% of light within a band that is continuously tunable by the electric field through the entire visible spectrum while preserving its maximum efficiency. Broad electric tunability of total reflection makes the ChOHmaterial suitable for applications in energy-saving smart windows, transparent displays, communications, lasers, multispectral imaging, and virtual and augmented reality. Graphical Abstract},
journal = {MRS Bulletin},
volume = {49},
number = {9},
publisher = {Cambridge University Press (CUP)},
author = {Iadlovska, Olena_S and Thapa, Kamal and Rajabi, Mojtaba and Mrukiewicz, Mateusz and Shiyanovskii, Sergij_V and Lavrentovich, Oleg_D},
}

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