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Abstract
Cholesteric liquid crystals form a right-angle helicoidal structure with the pitch in the submicrometer and micrometer range. Because of the periodic modulation of the refractive index, the structure is capable of Bragg and Raman-Nath diffraction and mirrorless lasing. An attractive feature of cholesterics for optical applications is that the pitch and thus the wavelength of diffraction respond to temperature or chemical composition changes. However, the most desired mode of pitch control, by electromagnetic fields, has so far been elusive. Synthesis of bent-shape flexible dimer molecules resulted in an experimental realization of a new cholesteric state with an oblique helicoidal structure, abbreviated as ChOH. The ChOH state forms when the material is acted upon by the electric or magnetic field and aligns its axis parallel to the field. The principal advantage of ChOH is that the field changes the pitch but preserves the single-harmonic heliconical structure. As a result, the material shows an extraordinarily broad range of electrically or magnetically tunable robust selective reflection of light, from ultraviolet to visible and infrared, and efficient tunable lasing. The ChOH structure also responds to molecular reorientation at bounding plates and optical torques. This brief review discusses the recently established features of ChOH electro-optics and problems to solve.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction: optics of cholesteric liquid crystals
Development of materials capable to dynamically control transmission and reflection of visible light, ultraviolet (UV) and near-infrared (IR) radiation is one of the most important directions of optical sciences with potential applications such as energy-saving smart windows, transparent displays, communication elements, lasers, optical and multispectral imaging. The most challenging problem is to formulate materials in which the transmission of light can be controlled dynamically and independently for different spectral bands, preferably by controlling reflection and transmission rather than by absorption. Among the best materials capable of selective reflection of light are liquid crystals of the cholesteric (Ch) type, formed by chiral elongated organic molecules in a certain temperature range between a solid crystal and an isotropic melt. The molecules pack into a periodic structure in which the director $\hat{{\mathbf n}}$, describing their local orientation, rotates around a helicoidal axis $\hat{{\mathbf h}}$, remaining everywhere perpendicular to it, Fig. 1(a). The structure can be abbreviated ChRA or Ch90, where the subscripts refer to the right-angle that the director makes with the helicoidal axis.
Fig. 1. Conventional right-angle helicoidal Ch90 with $\Delta \varepsilon = {\varepsilon _{||}} - {\varepsilon _ \bot } > 0$ in a planar cell. (a) In the absence of the electric field, Ch90 shows Bragg reflection for light propagating parallel to the helicoidal axis$\hat{{\mathbf h}}$; (b) realignment of $\hat{{\mathbf h}}$ and formation of the “fingerprint” light-scattering texture in the vertical electric field; because of positive dielectric anisotropy, the preferred orientation of the local director is parallel to the field. The schemes are not to scale as the experimental cell is typically 10-20 times thicker than the cholesteric pitch to enhance reflectivity.
The pitch ${P_0}$ of the resulting right-angle helicoid is typically in the range (0.1-10) $\mathrm{\mu }\textrm{m}$, being much larger than the molecular scale of 1 nm because rotations of molecules around their long axes mitigate chiral effects in the packing. If the molecules are not chiral (or form a racemic mixture), the pitch diverges, and the so-called uniaxial nematic is formed instead of the cholesteric. In the ground state of the nematic, the director points along a single direction $\hat{{\mathbf n}} = const$[1,2].
The cholesteric slab separates the light beam traveling along $\hat{{\mathbf h}}$ into two components, of a right-handed and left-handed circular polarization. One component, of the same handedness as the cholesteric, is reflected, and the other is transmitted. The selective reflection is observed in the spectral range $\Delta \lambda = ({{n_e} - {n_o}} ){P_0}$ determined by the pitch and the ordinary ${n_o}$ and extraordinary ${n_e}$ refractive indices [1,2]. The band is centered at ${\lambda _p} = \bar{n}{P_0}$, where $\bar{n} = ({{n_e} + {n_o}} )/2$ is the average refractive index. The selectively reflected colors are highly saturated; they add like colored lights and produce a color gamut greater than that obtained with inks, dyes, and pigments [3]. The cholesteric arrangements are known to produce structural colors of certain birds, beetles [4], and plants [5].
The pitch ${P_0}$ and thus the wavelength ${\lambda _p}$ of reflected light in Bragg geometry respond to a variety of stimuli [6], thus enabling applications such as temperature indicators and sensors of minute quantities of gases [7]. However, the most desirable mode of electromagnetic control of the transmitted and reflective light has been elusive till recently. The reason for poor tunability of the structure by an electric field is illustrated in Fig. 1 for a dielectrically positive cholesteric, in which the dielectric permittivity ${\varepsilon _{||}}$ parallel to $\hat{{\mathbf n}}$ is higher than the permittivity ${\varepsilon _ \bot }$ in the perpendicular direction, $\Delta \varepsilon = {\varepsilon _{||}} - {\varepsilon _ \bot } > 0$. When the field is applied along $\hat{{\mathbf h}}$, it rotates the helicoid axis perpendicularly to itself, as dictated by the positive dielectric anisotropy, causing a light scattering “fingerprint” texture, Fig. 1(b). If the field is applied perpendicularly to $\hat{{\mathbf h}}$, it introduces wide regions in which the molecules are parallel to the field, separated by narrow regions with a rapid twist of the director by 180°; the single-harmonic character of helicoidal modulation is thus destroyed. Although this field-distorted helicoid shows the field-dependent pitch [8–10], it is not very useful for practical applications. For a cholesteric with $\Delta \varepsilon < 0$, the field applied parallel to $\hat{{\mathbf h}}$ would cause no realignment, while the field perpendicular to $\hat{{\mathbf h}}$ would destroy the single-harmonic structure. Because of these intrinsic difficulties, cholesterics so far have not found widespread applications as electrically tunable color filters; most of their current electro-optic applications employ the transparent-to-light scattering transition [11], illustrated in Fig. 1.
2. Theoretical prediction of ChOH
In 1968, two independent papers by P.G. de Gennes [12] and R.B. Meyer [13] predicted a distinct response of a Ch to an applied field in which the molecules realign from being orthogonal to the helicoidal axis, $\theta = \pi /2$, to being titled by some angle $\theta < \pi /2$, Fig. 2:
where $\varphi (z )= 2\pi z/P$ is the angle of homogeneous azimuthal rotation and P is the pitch inversely proportional to the field E [13]: with ${K_3}$ being the bend elastic constant. The new state, which can be called either oblique helicoidal, abbreviated ChOH, or heliconical, could be realized only when ${K_3} < {K_2}$, where ${K_2}$ is the twist elastic constant. The reason can be understood by observing that the ChOH structure contains both twists and bends, Fig. 2. In conventional cholesteric materials formed by rod-like molecules, bend is more difficult than twist, ${K_3} > {K_2}$, thus these materials do not show the predicted behavior and exists only in the Ch90 state.Fig. 2. Field-induced oblique helicoidal structure ChOH; ${K_3} < {K_2}$; as the electric field increases, the pitch and the conical angle both decrease. The schemes are not to scale as the cell is typically 10-20 times thicker than the pitch to enhance reflectivity.
3. Experimental realization of ChOH, potential applications, future research
As often happens, new chemistry brings new material properties and new physics. Figure 3 shows a so-called flexible dimer mesogen. At first sight, it is not much different from a conventional liquid crystal molecule, as the dimer is nothing else but two molecules, each with a rod-like “head” and an aliphatic tail, covalently bound into a pair. An important feature emerges when the number of methylene groups CH2 in the flexible connection is odd. Since the hydrogen pairs of each methylene group tend to maximally separate from the neighboring hydrogen pairs, the aliphatic spacer adopts a zigzag geometry, Fig. 3. An odd number of methylene groups results in a bent shape of the molecule, with two rigid segments forming a substantial angle with each other. The bend conformation brings about dramatic consequences for the supramolecular organization in liquid crystals, as reviewed by Mandle [14] and Jákli et al [15]. In particular, the uniaxial nematic phase formed by such flexible dimers easily adopts bend deformations. ${K_3}$ in the flexible dimer nematics is 5-15 times smaller than the constants ${K_2}$ of twist and ${K_1}$ of splay [16,17]. ${K_3}$ remains small when the nematic is transformed into a cholesteric by adding chiral molecules [18].
Fig. 3. Flexible dimer 1,7-bis(4-cyanobiphenyl-4’-yl)heptane (CB7CB) tends to bend because of the odd number of the methylene groups in the aliphatic chain connecting two rigid rod-like cyanobiphenyl groups.
By adding chiral dopants to flexible dimers, Xiang et al. demonstrated the oblique helicoidal ChOH state and its electrically-tunable pitch and conical angle, first in the regime of Raman-Nath diffraction [19] and then in the Bragg diffraction geometry [20]. In the first case, the heliconical axis and the electric field are both in the plane of the cell. In the second case, they both are perpendicular to the bounding plates, as in Fig. 2. The ChOH state exhibits selective Bragg reflection of light with the peak’s wavelength electrically tunable from UV to IR, swiping the entire visible range [19–21], Fig. 4. As the field E increases, the pitch P decreases, according to Eq. (1). Importantly, the field preserves the single-harmonic character of the structure, thus yielding an excellent efficiency of reflection in the entire range of tunable wavelengths. The cone angle $\theta $ also decreases as the field increases [19],
Fig. 4. Electric field-controlled structural colors of a ChOH cell shown as (a) polarizing optical microscope textures and (b) reflection spectra. Incident light is unpolarized. The figures indicate the RMS amplitude of the field. Mixture CB7CB∶CB11CB∶5CB∶S811 in the weight proportion 49.8∶30∶16∶4.2. Temperature 27.5 °C. Data collected in a planar cell by Olena Iadlovska, Advanced Materials and Liquid Crystal Institute, Kent State University.
Although light propagation along the helicoidal axis is similar in ChOH and conventional Ch90, there are also differences. Bregar et al [23] demonstrated by numerical simulations an existence of a non-vanishing electric component of the light wave along the propagation direction. This nonzero component produces a spatially varying Poynting vector that can be tuned by the electric field, thus opening the door for a novel route for controlling the flow of light.
When the electric field decreases below [19]
Xiang et al. demonstrated that a single ChOH cell can tune the wavelength of selective Bragg reflection from 360 nm to 1520 nm [20], according to the relationship $\lambda = {\bar{n}_{eff}}P$, where ${\bar{n}_{eff}} = ({{n_{e,eff}} - {n_o}} )/2$, ${n_{e,eff}} = {n_e}{n_o}/\sqrt {n_e^2{{\cos }^2}\theta + n_o^2{{\sin }^2}\theta } $ is the effective extraordinary refractive index, and P is the field-dependent pitch in Eq.(1). As clear from Fig. 4, the electric field changes not only the peak wavelength of reflection but also the spectral width $\Delta \lambda $ of reflection, which narrows at higher fields. The reason is that $\theta $, ${n_{e,eff}}$, and the effective birefringence $\Delta {n_{eff}} = {n_{e,eff}} - {n_o}$ all decrease as the field increases. As a result, the spectral range $\Delta \lambda = \Delta {n_{eff}}P$ of the Bragg reflection narrows at higher fields [21]:
The ChOH structure is susceptible to the surface interactions at the bounding plates [22]. The same material in a cell of the same thickness acted upon by the same electric field shows a different wavelength of Bragg reflection for different director alignments at the bounding plates. Namely, planar alignment yields a peak that is red-shifted from the peak in a cell with perpendicular (homeotropic) alignment [22], Fig. 5. The effect can be used in sensing devices that recognize molecular interactions through surface anchoring of liquid crystals [24].
The ChOH structure resembles the chiral smectic C (SmC*). There is an important difference, however, that makes ChOH much better suited for the practical applications of the tunable pitch. In SmC*, the oblique helicoidal director coexists with nanoscale density modulation. Nanoscale layering makes SmC* hard to align and prone to mechanical instabilities, such as a formation of chevron defects caused by the change of the layers’ thickness [25]. The field-induced change of the tilt angle $\theta$ causes the layers’ thickness to vary, which results in defects and undulations. In contrast, ChOH is a fluid with density homogeneous in space. As a result, ChOH is easy to align uniformly and to tune without triggering undulations or chevron defects.
Fig. 5. Electric field-controlled selective reflection in ChOH cells with homeotropic (blue) and planar (red) surface alignment. Note the different wavelengths of light reflection for the two types of surface anchoring. Modified from Ref. [22].
The ChOH structural colors are also tunable by the magnetic field [26], since the liquid crystals are anisotropic diamagnetics. Recently, L. Lucchetti and F. Simoni groups [27] demonstrated a spectacular effect of optical control of the heliconical pitch and structural colors of ChOH. In these experiments, the electric field of the optical wave is perpendicular to the low-frequency (static) electric field and to the heliconical axis. The optical torque imposed onto the local director is opposite to the static field torque and tends to increase the director tilt $\theta $ [27]. For a fixed E, light irradiation changes the ChOH colors.
The oblique helicoidal ChOH allows one to realize an electrically tunable laser [28], as experimentally demonstrated by Xiang et al [29], Fig. 6. The wavelength of lasing shifts by more than 100 nm in the visible spectrum under the applied field [29]. The single-harmonic character of ChOH preserves itself in the electric field and thus ensures the efficiency of lasing in the entire tunable range of emission.
Fig. 6. Electric field dependence of the lasing wavelength for ChOH cells of thickness $50\;\mathrm{\mu }\textrm{m}$ doped with laser dyes DCM and LD688. Modified from Ref. [29].
Electrically tunable ChOH is an excellent candidate for applications in optical imaging (OI) in general and multispectral imaging (MSI) in particular. OI and MSI are widely used in biomedical and chemical analysis, food and agriculture, aerospace, and defense [30–34]. By visualizing information simultaneously at different wavelengths, usually from UV through visible to IR, MSI unveils details that are simply not accessible to a human eye. MSI can inform farmers about the state of plant vegetation, help doctors to diagnose deceases, help astronomers, and ecologists to understand our Universe and the state of our planet.
The requirement of using different spectral bands to image the same object poses challenges associated with the overall size of devices, weight, complexity, mechanical operation, and cost. The wavelength selection is usually achieved by mechanically replaceable filters or by sets of instruments that are sensitive to particular wavelengths. Some applications, such as hyperspectral imaging, require hundreds of spectral bands, which makes filter replacement not practical. Another difficulty arises when multiple apertures are used for simultaneous imaging at different wavelengths since they make the system larger and require co-localization. The current challenge in MSI reduces to a two-fold task: (1) to find the means to easily select and adjust the spectral band parameters such as peak wavelength and bandwidth and (2) to make the spectral imaging compact and affordable. ChOH is an attractive candidate to satisfy both requirements, as a single-aperture single-cell homogeneous layer of ChOH placed between two transparent electrodes is a ready-to-use electrically controlled filter [19,20,26]. ChOH optical filters are simpler in construction than tunable filters based on stacks of multiple tunable-retardation liquid crystal slabs and holographically formed polymer dispersed liquid crystals reviewed in Ref. [34]. As already stressed, the critical advantage of ChOH filters is that the external field, while changing the period, preserves the single-mode character of refractive index variation, thus maintaining the efficiency of reflection and diffraction in a broad spectral range. Another attractive feature is the absence of light absorption in the operational principle. Since the ChOH cells are low in cost and power consumption, their potential applications might be very broad, from sensing, lasing, and imaging to miniature “lab-on-a-chip” devices.
There are still many aspects of the ChOH electro-optics that require further studies. Among them is a continuous vs. step-wise tunability of the pitch and the response time of the pitch adjustments. Surface anchoring, as already indicated, brings about a dramatic change in the director structure and Bragg reflection wavelength, Fig. 5. Besides the difference in spectral positions of the Bragg peaks [22], the homeotropic and planar anchoring should impart differently on the dynamics of structural transformations under the electric or magnetic field. When the director is perpendicular to the bounding surfaces, the in-plane realignments are free. The homeotropic cells thus allow a continuous change of the pitch. In contrast, planar anchoring controls both the polar and azimuthal director angles at the substrates. Imagine that both the top and bottom plates impose a strong in-plane anchoring. For a cell of finite thickness, the number of ChOH pseudolayers should be quantized. As the field changes the pitch, the number of pseudolayers should change, which implies an introduction of edge dislocations. The field-induced tuning of the pitch would result in step-wise changes in the reflection wavelength. One should also bear in mind that the dynamics of edge dislocations in Ch90 [35] and ChOH [19] is slow. However, if the azimuthal surface anchoring is weak, the edge dislocations are expelled [36], and their influence mitigated. The dynamic and spectral properties of planar and homeotropic optical filters should be very different. A whole new dimension of research and applications is expected in surface-patterned ChOH, which would allow one to combine the electromagnetically tunable diffractive Bragg effect with the Pancharatnam-Berry phase control.
Another interesting direction of future research is the regime of oblique incidence of light. So far, the optical properties of ChOH have been analyzed mostly for normal incidence, in which the Bragg reflection $\lambda = \bar{n}P$ is caused by the $P/2$ periodicity and reaches its theoretical maximum of 50% for non-polarized light. The true periodicity of ChOH is P rather than $P/2$ because of the molecular tilt. In ChOH, one also observes a reflection at $\Lambda = 2\bar{n}P$ in addition to $\lambda = \bar{n}P$ [20]. Numerical simulations by Berreman [37] of reflection spectra of SmC* indicate that the oblique incidence might enhance the reflection efficiency up to 100% for non-polarized light, for both $P$- and $P/2$- reflection peaks. The angle of incidence would also affect the reflection wavelength [38].
4. Summary
The bent-shaped flexible dimers bring about a new structural organization in the cholesteric phase. This review describes a peculiar oblique helicoidal ChOH structure that is formed by a cholesteric liquid crystal in the presence of an electric or magnetic field. The field changes the ChOH pitch and cone angle but does not alter a single-harmonic modulation of the director. As a result, ChOH shows spectacular effects such as electrically or magnetically tunable structural colors and lasing. The tunable range is exceptionally broad, as the wavelength of selective reflection by a single cell can swipe from UV to visible and then to IR. Research so far focused on the geometry of Bragg diffraction in uniformly aligned cells and normal incidence, but other geometries, for example, patterned cells and oblique incidence, would be of interest to explore. The ChOH cells can also serve as non-reflective optical elements, such as tunable polarization rotators. Doping ChOH with photosensitive and light-absorbing dyes might lead to interesting opto-optical effects. Beam-steering applications could employ the Raman-Nath diffraction at ChOH with the helicoidal axis perpendicular to the propagation direction of light, driven by the in-plane electric field. There is little doubt that the exploration of the scientific and practical aspects of electromagnetically tuned optical properties of this new ChOH state will flourish in years to come.
Funding
NSF Directorate for Engineering (ECCS-1906104).
Acknowledgments
The studies of ChOH in the author’s group became possible thanks to the contributions of the former and current graduate students J. Xiang, O. Iadlovska, G. Babakhanova, K. Thapa; undergraduate G. R. Maxwell; visiting scientists M. Mrukiewicz and D.A. Paterson; the supply of materials by C. T. Imrie, Q. Li, G. H. Mehl, and T. White; collaboration with J.T. Gleeson, A. Jákli, L. Lucchetti, J. V. Selinger, S. V. Shiyanovskii, S. Siemianowski, F. Simoni, S. Sprunt, P. Palffy-Muhoray, and A. Varanytsia. I acknowledge the help of V. Borshch, O. Iadlovska, A. Varanytsia, and J. Xiang in the preparation of illustrations. I am thankful to the reviewers of the manuscript for helpful suggestions. The work is supported by NSF grant ECCS-1906104.
Disclosures
The author declares no conflicts of interest.
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