Patterning Liquid-Crystal Alignment for Ultrathin Flat Optics.

Liquid-crystal (LC)-based ultrathin flat optical elements (FOEs) exhibit several attractive properties, such as a high degree of optical tunability, strong polarization selectivity, nearly 100% diffraction efficiency, and a simple fabrication process. Investigating the alignment patterning of LC-FOEs to diversify their performance has attracted broad interest in the optics field. In this mini-review, we start from the photoalignment (PA) process and then dive into device structures and performances. By generating and recording the desired polarization fields on the PA layer, the LC molecules will follow the recorded patterns and establish the phase profiles for different functionalities, such as gratings and lenses. Because of the polarization dependency, LC-FOEs have found useful applications in near-eye displays. Understanding the interactions between the PA mechanism and LC molecules helps to optimize the device performance for novel optical systems.

Introduction

Different from conventional refractive optics that use the optical path difference to produce phase patterns, liquid-crystal-based flat optical elements (LC-FOEs) generate the desired phase profile by spatially varying the LC orientations, which is controlled through the alignment patterning on the bottom surface.[1,2] Due to the distinct optical properties, such as a flat surface, ultrathin form factor, high diffraction efficiency, strong polarization dependency, and high optical quality, LC-FOEs have been successfully integrated into various optical systems to satisfy the increasing demands from near-eye displays[3,4] and head-up displays.[5]

The working principle of these planar optics is based on the modulation of the LC material’s refractive index, which is established and controlled by the alignment patterning and the self-organization of LC molecules.[2] Among various approaches to obtain the desired surface alignment, including mechanical rubbing[6] and nanoimprinting lithography (NIL),[7] photoalignment (PA) has the advantages of high resolution, a simple and quick fabrication process, and low cost.[8] Compared to the novel method such as NIL, PA has been studied for decades. The origin can be traced back to the 1970s.[9] Then in 1988,[10] the first publication about LC PA appeared, which proposed the photoinduced alignment of a reversible transformation of azobenzene molecular layers. The LC alignment was induced by controlling the wavelength of an unpolarized light beam. Subsequently, Gibbons et al. reported the surface-mediated alignment of nematic LCs with a polarized light in 1991.[11] The LC alignment is induced by exposing a dye-doped polymer layer to the polarized light. The LC molecules in contact with the illuminated area were homogeneously aligned perpendicular to the laser polarization direction and remained aligned after the laser beam was turned off. Since 1992, the cinnamoyl side-chain polymers and polyimide aligning agents have been used for LC alignment.[12] Nowadays, the class of azo dyes is widely used for recording alignment patterns of LC-based optics. Through controlling the alignment, LC-FOEs can exhibit various functional properties,[13,14] which is not only scientifically interesting but also practically useful.

Liquid-Crystal Photoalignment

Mechanism of Photoalignment

The LC molecular orientation results from photoinduced absorption in an amorphous film (PA layer) formed by anisotropic absorbing molecular units (PA materials).[8] This process can generally be divided into two types: reversible transformation[15,16] and irreversible transformation.[12,17] For each type, it can also be further classified based on different chemical reactions and molecular motions. Compared to the irreversible photochemical changes, the reversible type involving azo dyes shows a higher purity of alignment layer, which is favorable for numerous LC-based applications including flat optics.

The PA mechanism in the proposed LC-FOEs belongs to the reversible type, and this process can be described by the diffusion model of azo dye chromophore molecules or azo dye molecular solutes. As Figure a depicts, the azo dye molecules are exposed under a polarized UV light. The angle between the absorption oscillator of the molecule and the polarization direction is defined as θ. For each azo dye molecule, the probability to absorb light energy is proportional to cos2 θ.[8] When the molecule is parallel to the polarization direction, the probability is the highest; that is, it is most likely to obtain increased internal energy through absorption. This increased energy leads to a more active rotational motion until the absorption oscillator is perpendicular to the polarization direction, as shown in Figure b. Therefore, all or most of the azo dye molecules are tempting to rotate and align the long axes perpendicular to the polarization direction of the UV light. After orientation, the force between the molecules will fix the position and the molecules will not move even if light is absent (Figure c). Thus, the orientation of azo dyes produced by the linear polarization is complete.

Figure 1

Mechanism of the PA process. (a) Azo dyes are exposed to a linearly polarized UV light, (b) reorientation occurs, and (c) mechanism is locked by the intermolecular forces.

Polarization Absorption of Photoalignment Materials

Brilliant yellow (BY), a commercially available azo dye, has been widely applied to LC-FOEs as PA agents.[1−5] The chemical structure of BY is shown in Figure a. In experiment, the BY was diluted in 0.5 wt % dimethylformamide (Sigma-Aldrich, 99%, water content ⩽0.5%) and then spin-coated on a clean glass substrate at 1500 rpm for 30 s. We measured the polarized absorption spectra at room temperature under different conditions: exposure energy (linearly polarized UV light (λ ≈ 365 nm) at 0.4, 1.0, and 2.5 J/cm2), with or without soft baking (90 °C for 20 min); the measured beam is parallel (Apara) or perpendicular (Aperp) to the molecular orientation direction.

Figure 2

(a) Chemical structure of brilliant yellow. (b) Measured DR and absorption spectra at 2.5 J/cm2 (c) with and (d) without soft baking.

Figure b–d depicts the experimental results. As expected, higher exposure energy gives a larger dichroic ratio (DR = Apara/Aperp). Interestingly, we find that the DR of the nonbaking sample is higher than that of the baked one, as Figure b shows. Figure c,d shows the detailed absorption spectra with and without baking at 2.5 J/cm2 exposure. Before UV exposure, the absorption of BY is polarization-independent (black lines). After exposure to a linearly polarized light, the redirected azo dye molecules have different absorption responses to the measurement beam whose polarization direction is perpendicular or parallel to the absorption oscillator. When the polarization direction of the measurement beam is perpendicular to the redirected absorption oscillator, the absorption decreases (blue lines). On the contrary, when they are parallel, the absorption is stronger (red lines). Because of this unique polarized absorption behavior, azo dyes have been commonly used for PA applications, especially for LC-based photonic devices.

Application of Photoalignment for Ultrathin Flat Optics

Polarization Field Generation

As mentioned above, the azo dyes respond to and record the polarized light fields. After exposure, the patterned PA layer will replicate the alignment patterns to the LC monomer lying on top. Commonly utilized approaches to generate polarization fields for LC-FOEs can be categorized into two types: interferometry and noninterferometry.

The most widely used exposure setups are two-beam interferometry[18] and Mach–Zehnder[1] interferometry, as illustrated in Figure a,b. The linearly polarized beam from the laser is split into two arms and then converted to circular polarization (CP). When two CP beams with opposite handedness interfere at the sample position, the electric field on the sample plane exhibits a sinusoidal linear polarization pattern, which is recorded by the PA layer. This simple setup with a large interference angle is suitable for fabricating optical elements with a small periodicity, such as gratings or lenses whose period is several hundreds of nanometers.[14] Different from the two-beam method, the Mach–Zehnder interferometry limits the interference to a small angle. This is suitable for fabricating large period optical elements, such as gratings or lenses with a period up to several tens of micrometers.[1] In addition, Sagnac interferometry (Figure c) with high stability[1] and standing wave interferometry (Figure d) with doubled efficiency[19] has also been demonstrated recently.

Figure 3

Experimental setups of the exposure pattern generation. Interferometry types: (a) two-beam, (b) Mach–Zehnder, (c) Sagnac, and (d) standing wave. Noninterferometry types: (e) polarization holography by a SLM and (f) polarization direct-write (BS, beam splitter; M, mirror; QWP, quarter-wave plate; TO, template optics; S, sample; PBS, polarizing beam splitter; PM, polarization modulator; TS, translation stage).

In the noninterferometry approach, the desired polarization fields can be generated by a spatial light modulator (SLM) or direct writing, as illustrated in Figure e,f, respectively. An important advantage of using SLM is its convenience to provide a one-shot arbitrary pattern without complex interference.[20] In contrast to SLM, direct writing generates a designed pattern by scanning a focused laser beam to a sample placed on a translation stage.[21]

LC Orientation and Dynamics

Different exposure patterns would generate different LC-FOEs, including but not limited to gratings, lenses, lens array, vortex retarders, and other complex optics. Among them, LC-based gratings and lenses have been widely investigated and utilized in near-eye display systems. Figure a,b depicts the polarized optical microscopy images of the LC grating and lens, respectively. If we zoom into a small area, as the insets in Figure a,b show, the LC director orientation is periodically and continuously rotated according to the sinusoidal PA patterns in the x–y plane.

Figure 4

Polarizing optical microscope images of LC-based flat optics: (a) grating and (b) lens. The scale bar is 50 μm, and the insets are the local LC molecular directions. (c) Formation of in-plane sinusoidal structure. (d) Distortion of sinusoidal structure. (e) CLC helical structure and (f) tilted CLC structure.

When a nematic LC is placed on top of the sinusoidal photoalignment pattern, the bottom LC molecules tend to follow the pattern and then transfer the pattern to the bulk along z direction. This whole process can be described by the Oseen–Frank model,[22] where the total free energy for surface and bulk interactions is minimized. When the sample thickness (d) is smaller than the pattern period, the bulk LC molecules can maintain the in-plane sinusoidal pattern, as shown in Figure c. As d gets larger or the grating period becomes smaller, the bulk LC will deviate from the planar alignment and start to orient toward the substrate normal,[23,24] as Figure d shows. This behavior can be intuitively understood by the fact that the most relaxed state for nematic LC is the uniform distribution, which corresponds to the zero free energy. The sinusoidal in-plane LC orientation is a distorted state and has a higher free energy. As the thickness increases, the confining power of the bottom pattern becomes weaker and the upper LC molecules tend to relax to the uniform state. If an electric field is applied to the bulk LC, the total free energy would include the term responding to the field–molecule interaction. The LC molecules will tend to align along or perpendicular to the electric field, depending on the dielectric anisotropy of the employed LC. As the voltage keeps increasing, the bulk LC molecules will be eventually reoriented by the electric field. As a result, the grating pattern and the associated diffraction behavior disappears. This dynamic switching behavior of diffraction has found useful applications in imaging and display devices.

Aside from nematic, we can also use cholesteric liquid crystal (CLC), which can be formulated by doping some chiral agents to a nematic host. The most relaxed state of an CLC is the helical structure depicted in Figure e, whose pitch P is determined by the chiral concentration and helical twisting power. If a CLC is placed on the sinusoidal pattern instead, the situation becomes more complicated. On one hand, the bottom LC in contact with the photoalignment layer still tends to follow the pattern. On the other hand, the bulk LCs tend to maintain an ideal helical structure to minimize the free energy. The only way to satisfy both conditions is to tilt the bulk helical structure to match the k-vector of the bottom pattern,[22] as shown in Figure f. This indicates the tilt angle α should satisfy P = Λ cos α, where Λ is the horizontal period. The tilted structure brings a transitional region where the LC molecules transit from the bottom in-plane orientation to the tilted helical structure. The thickness of the transition region is usually tens of nanometers, so the contribution of this region to the total energy is very small. Here, we make a presumption that the CLC pitch is smaller than the pattern period. Otherwise, no matter how the CLC is tilted, the matching of the bottom wave-vector cannot happen. If an electric field is applied to the tilted CLC structure, the tilt angle will begin to increase.[24] As the voltage increases, the CLC helical axis will be reoriented to be parallel to the substrate surface. This structure is known as uniform lying helix (ULH). As the voltage keeps increasing, the ULH will be distorted toward the field direction until the helical structure is completely unwound by the electric field.

Optical Properties

Due to different LC orientations inside the volume, LC-FOEs are usually divided into transmissive type (patterned nematic LC) and reflective type (patterned CLC). The operation principle of transmissive LC flat optics can be simply explained by Jones calculus:where J is the Jones vectors of circularly polarized light, R is the rotation matrix, W is the half-wave retardation Jones matrix, and ψ is the local LC director orientation angle. The subscripted ± signs indicate the left- and right-handed circular polarization (LCP and RCP) states. From eq , the accumulated phase is opposite for LCP and RCP lights. As depicted in Figure a,b, a transmissive LC grating will deflect RCP and LCP to opposite directions, and a lens will focus RCP but defocus LCP light.[25]

Figure 5

Illustration and photos of LC optics. Transmissive type: (a) a grating diffracts RCP light to +1 order and LCP light to −1 order; (b) a lens diverges the input LCP light but converges the RCP light. Reflective type: (c) a grating diffracts LCP light and transmits RCP light; (d) a lens reflects and converges the incident LCP light but transmits the RCP. Photograph courtesy of Kun Yin. Copyright 2020. The image is free domain.

The reflective LC-FOEs work under Bragg condition. It enables tunable spectral bandwidth and manifests more sensitive spectral and angular responses than the transmissive type. A typical CLC device can be realized by self-organized molecules to form a helical structure. If the incident circularly polarized light (e.g., LCP) has the same handedness as the helical twist, then it will experience Bragg reflection at normal incidence over the spectral range 2noP < λ < 2neP, where no and ne are the ordinary and extraordinary refractive indices. Meanwhile, the RCP will pass through the CLC layer. Therefore, unlike transmissive LC flat optics, ordinary reflective LC flat optics only works for one polarization handedness, and the other will be transmitted without changing its polarization state (Figure c,d).

It is worth mentioning that both transmissive and reflective LC-FOEs can achieve nearly 100% diffraction efficiency. The thickness of each element can be controlled between several hundreds of nanometers and several microns, depending on the working type. By applying more complex structures, such as multilayers and gradient pitch, we can obtain LC flat optics with a wide viewing angle and broadband while maintaining a high efficiency and ultrathin form factor.

Conclusions

In this mini-review, we briefly summarize the mechanism of PA and optical properties of LC-FOEs. To understand the PA mechanism of azo dyes, we use the diffusion model to explain the photoinduced process and take brilliant yellow as an example to investigate the dichroic ratio under different conditions. Based on the polarized response of azo dyes, it is feasible to record various patterns through appropriate exposure methods. The LC molecules follow the recorded pattern and precisely organize the vertical structures for building planar optical elements. Due to the unique molecular dynamics and polarization selectivity, LC-FOEs with ultrathin form factor have found widespread applications in novel optical systems, particularly virtual/augmented/mixed reality displays and head-up displays.