1. Introduction

Augmented reality (AR) is an exciting technology that aims to enhance the reality by overlaying virtual content and achieving a high-quality see-through performance. Numerous research studies and techniques are being developed to create the necessary optical elements, sensors, and sensing systems for head-mounted devices (HMDs) or near-eye devices (NEDs) of AR [1–5]. The AR wearable device's primary structure consists of light engines, projection lens modules, and light guides. However, several challenges still need to be addressed, with optics being the primary bottleneck. Current AR wearable device users commonly experience a visual phenomenon called vergence-accommodation conflict (VAC), which is a mismatch in cues between the vergence and accommodation of the eye, causing the brain to receive conflicting information. Additionally, human eye refractive errors necessitate the use of prescription lenses to view computer-generated images (virtual images) and real-world objects (or real images) in the surroundings, further complicating matters. To tailor AR wearable devices to individual needs, it is necessary to develop active adaptive optical components that can compensate for potential issues. Potential elements to consider in such a development may include focus-tunable liquid crystal(LC) lenses, variable diffusers, and light modulators [6–10]. By harnessing the spatial LC director orientations under external electric fields, LC lenses are capable of electrically tuning their focal lengths, which allows for the modulation of incoming wavefronts. LC lenses offer several advantages, such as high durability, low power consumption, and small form factor with a thin LC layer (<100 microns). Since 1979, many types of LC lenses have been proposed and developed, resulting in versatile applications such as tunable photonic systems for ophthalmic lenses, endoscopes, and optical zoom devices [11–29]. The refractive index of LCs can be modified by applied electric field, resulting in a change in the phase profile of LC lenses. But, there are still many drawbacks of LC lenses that need to be addressed, such as low optical efficiency limited by a polarizer and a slow optical response time due to thick LC layer for more optical phase. These factors lead to limitation of gradient-index LC lenses for mobile or wearable devices. However, some research has successfully managed to overcome these limitations either through specific geometric configurations or by employing two cross oriented LC layers, demonstrating the feasibility of such devices [11,13,26,30–33]. Recently, focus has shifted towards the development of optically isotropic LCs (OILCS), characterized by their optically isotropic phase. Moreover, using an LC-polymer composite system can enable the creation of OILCs without the need for a polarizer. Recently, researchers are developing optically isotropic LCs (OILCs), whose phase is optically isotropic. In prior arts, optically isotropic LCs can be achieved by means of LC-polymer composite materials [34–37].

The LC-polymer composite is comparable to polymer-dispersed LC (PDLC), where LC droplets are dispersed in a polymeric matrix. Although LCs are embedded in polymeric pores, the diameter of these pores is in a range of subwavelength of visible light. This size reduction is necessary to avoid light scattering and achieve polarization-independent optical phase modulation, particularly in applications like tunable LC lenses. [38] To attain the optical isotropy in the nano-PDLC, the typical LC concentration of the composite mixture should be less than 50%. However, having a large amount of polymer in the system leads to a low Kerr constant of the nano-PDLC (K ∼ 0.75 nm/V²) [34], which causes the small optical phase. In addition, when the concentration of LCs is low, fewer LC molecules are available to response to the applied voltage. As a result, higher driving voltage might be required to achieve noticeable changes in the LC alignment, facilitating the desired optical effects in the nano-PDLC system. In the previous study [39], our investigation focused on the origins of the Kerr and orientation phases of a nanometer size encapsulation LC (NSE-LC), to achieve a high concentration of LCs in the polymeric matrix with embedded LCs. However, further investigation is still needed on the electro-optical (EO) performance of NSE-LC samples of varying thicknesses, something that is important for LC photonic devices. In this work, we studied the EO performance of NSE-LC samples with varying thickness. We analyzed the data from measurements of the transmittance versus voltage and optical response time. Our experimental results show that the optical phase of NSE-LC is effectively increased without compromising the electro-optical performance. The main reason for this phenomenon is attributed to the high concentration of LCs in NSE-LC, and the thickness can be readily increased through various coating methods. As a result, we achieved a LC-polymer composite film of NSE-LC with large phase modulation and reliably switching between isotropic and anisotropic phase under an external electric field. Such a NSE-LC device exhibits not only scattering-free but also polarization-independency, particularly in applications like tunable LC lenses. Moreover, the operating voltage of the NSE-LC device is low (< 25V_rms), the corresponding response time is fast (< 10 msec) in LC-polymer composite system. The proposed NSE-LC EO device would make itself a valuable component in upcoming tunable photonic systems with high optical efficiency and we attribute it to the high Kerr constant of NSE-LC.

2. Operating principle and sample preparation

Figures 1(a) and 1(b) provide a clear illustration of operating principles of NSE-LC, as well as schematic diagrams to aid in understanding the device. The structure consists of a layer of NSE-LC and a glass substrate coated with transparent conductive comb electrodes for in-plane switching. The width and the electrode space between ITO comb electrodes are 3 microns and 7 microns, respectively. The thickness of NSE-LC ranges from 2 microns to 7 microns. The alignment of the LC molecules along the LC droplet interface is caused by the anchoring energy between polymer and LC. NSE-LC is optically isotropic under absence of the electric field. The total optical phase shift (Δф_theory) of the NSE-LC samples at V >> Vth according to

 

Fig. 1. Schematic diagrams of NSE-LC. (a) NSE-LC droplets randomly orient themselves when voltage is turned off. (b) The orientations of optic axes are along the electric field when voltage is turned on. Red dotted lines represent the electric fields. The orange rectangular parts are glass substrates.

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In LC-polymer composites with nematic LCs, the external electric fields lead to birefringence in optically isotropic LCs. This effect, known as the Kerr effect, can be described as follows [41]:

The applied electric field (E) determine the direction of the optic axis of the refractive index tensor modulation under external field. The birefringence ($\mathrm{\Delta }$n) of the host nematic LC is always greater than the $\mathrm{\Delta }{n_{ind}}$ (i.e. Δn >>$\mathrm{\Delta }{n_{ind}}$). This is because the refractive index change resulting from local reorientation of the molecules is larger than the one resulting from the field-induced Kerr effect. It is reasonably assumed that the average-refractive index is constant under various electric fields, n_avg = (n_e (E) + 2n_o (E)) / 3 ≡ n_iso(E), where n_e(E) and n_o(E) are the field-dependent extraordinary refractive index (n_e) and ordinary refractive index (n_o) [42].

According to extend the Kerr effect, Eq. (3) could be expressed as [43]:

When the applied electric field is strong, the field-induced birefringence of Kerr effect is described in Eq. (4). This equation involves the change in the saturation refractive index (δn_sat) and the saturation electric field (E_sat), which are key parameters when the refractive index change approaches to the saturation point ($\textrm{i}.\textrm{e}.\,\mathrm{\Delta }{n_{ind}}(E )\sim \delta {n_{sat}}$).

In case of OILCs, the Kerr constant is governed by several factors, including the dielectric anisotropy Δε, birefringence Δn, the elastic constant K_LC, and the pores size R replaces the chiral pitch. As a result, the Kerr constant (K) is governed as follows [44],

While Eq. (5) provides useful information on the electrically responsive optical properties of optically isotropic LC-in-polymer composites, the filling ratio of LCs is a crucial factor that is not taken into account. To fully comprehend the relationship between filling ratio and the Kerr constant, it may be useful to explore alternative approaches to the polymerization-induced phase separation method. In particular, the refractive index change is modified as Δn ($\Delta {n_{composite}}$) in Eq. (5) in order to account for the effect of the LC to polymer matrix volume filling ratio [39].

3. Sample preparation

In the experiments, we utilized a nematic LC (n_e = 1.75, n_o = 1.51, Δn = 0.24, and Δε = 18) as host LC, paring it with polyvinyl alcohol (PVA) as stabilizer and wall-forming material, Glutaraldehyde (Sigma Aldrich) as a cross-linking agent, and Surfynol 420 (BASF) as a surfactant chosen specifically to minimize the surface tension of LC-polymer interface. To encapsulate the LCs, we employed micro-channel emulsification methods [45]. Figure 2(a) illustrates a schematic depiction of the NSE-LC process. Initially, we combined the aqueous PVA solution (PVA in DI water with a concentration of 1.5wt%), surfactant and host LC material together at 75°C and at the magnetic stirring speed of 500 rpm for 2 hours. The process of LC encapsulation involves the utilization of micro channel emulsification. After introducing the crosslinker, we maintained the stir speed 500 rpm to reduce the potential aggregation of nano-sized capsules during crosslinking reaction. We let the crosslinking reaction going on for 5 hours. Upon completion of the crosslinking process, we used an evaporator to achieve a viscosity level in the mixture compatible with our coating requirement.

 

Fig. 2. (a) Schematic of NSE-LCs process. (b) A diameter distribution of NSE-LCs (273.3 ± 26.2 nm) after analyzing a particle size analyzer based on the dynamic light scattering experiment.

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To identify the size of NSE-LCs, we analyzed NSE-LCS using a particle size analyzer (PSA), utilizing a dynamic light scattering method. Due to the high capsule density in the NSE-LC solutions, it is difficult to measure particle size precisely using the conventional measurement equipment. Thus, we diluted our NSE-LC solution 1.0 wt% with DI water for the purpose of making a sample with a suitable capsule density. Generally, for the analysis of nanometer sized particles, dynamic light scattering technique is widely adopted as a particle size analyzer such as Zetasizer (Malvern) and ELSZ-2000 (Otsuka). Typically, we outsource the measurement of the capsule size to an external institute equipped with the necessary measuring apparatus. Figure 2(b) shows sampling data taken with ELSZ-2000 for our NSE-LC samples. The measured results present a size distribution centered around a diameter 273.3 ± 26.2 nm.

To analyze the electro-optical (EO) performances of NSE-LCs, we prepared in-plane switching cell which consists of patterned comb type transparent conductive electrode (electrode width = 3 µm and electrode space = 7 µm), and the NSE-LCs were coated on the substrate with the patterned electrode [46]. Thereafter, the cell was cured at 70°C for 30 min to polymerize as well as solidify the polymeric matrix. During our experiments, we fabricated three NSE-LC samples with different thicknesses: 2.55 µm, 3.25 µm and 6.55 µm, respectively.

4. Experimental results and discussion

4.1 NSE-LC optical properties

To confirm the size of the LC pores in NSE-LC, we utilized scanning electron microscopic(SEM) to observe SEM images of the samples after removal of LCs. Figures 3(a) to 3(d) are the side views of the sample. We observed that some areas featured larger LC pores (3∼5 µm) potentially caused by environmental particles or clumped NSE-LC droplets. Therefore, we focused our observations on areas with uniformly dispersed pores (Figs. 3(b) and 3(d)) to avoid areas with particle or lump defects. The diameters of the droplets were measured using the software Image J (National Institutes of Health). After analyzing the observed distribution of pores diameter except defect droplets, the diameter is around 284 ± 55 nm, 273 ± 93 nm, and 282 ± 42 for the sample thickness of 2.55um, 3.25um and 6.55um, respectively. This result is consistent with the results from particle size analysis (275.3 ± 26.2 nm). From Figs. 3(b) and (d), the calculated the areal filling ratio around 55%∼60%. Apparently, the NSE-LC has a higher areal filling ratio (>55%) than conventional optically isotropic LC (nano-sized PDLC) whose filling ratio is under 40% [39].

 

Fig. 3. (a) The side view of scanning electron microscope(SEM) image of the coated NSE-LC composite film. Thickness of the coated NSE-LC composite film: 2.55 µm. (b) is the magnified SEM image in the red square area of (a). (c) is the side view of SEM image of the sample with the thickness of 6.55 µm . (d) is the magnified SEM image in the red square area of (c).

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Following this, we proceeded to analyze the electro-optic properties of the NSE-LC with different layer thicknesses. We first observed the images under a polarizing optical microscope(POM) of samples. We staged the samples under the crossed polarizers and then recorded the images by rotating the samples under applied voltages (20V_rms). We continued to rotate the samples until maximum transmission was observed. Thus, the optic axis of the uniaxial medium was aligned 45degres with respect to one of the polarizers. Thereafter, we fixed the position of the samples in POM and recorded the images at different voltage, displayed in Fig. 4. The white arrows in Fig. 4 represent the transmission axis of two polarizers and the red arrows represent the direction of the applied electric field. The yellow rods stand for the corresponding field-induced refractive-index-ellipsoid triggered by applied electric fields. We observed the variation of the transmissions in Figs. 4(a), 4(b) and 4(c) at different applied voltages. At V = 0 (the left column of Fig. 4), three figures exhibit the dark state of NSE-LC which indicates the samples are optically isotropic. This implies that the pores size of the encapsulated LC is subwavelength of visible light, resulting in no scattering in the dark state. However, we still observed some bright spots or light leakage at V = 0 (the left column) because some LC droplets sizes are large which leads to samples with not perfectly-optically isotropic caused by environment particle and a lump of NSE-LC droplets. The increased thickness facilitated an increase in both particle presence and NSE-LC lump accumulation, both contributing to enhanced light leakage. As a result, the thicker sample, the stronger light leakage. When we applied voltages to the samples, the transmission increases with voltage. This is because the voltage dependent phase retardation attributed to two effect: one is field induced birefringence from Kerr effect and the other is the orientation of LC molecules in the LC droplets. Operating the NSE-LC through an in-plane-switching architecture allows the NSE-LC to function as an electrically tunable uniaxial phase retarder. Consequently, the transmittance (T) of the NSE-LC samples placed between the crossed polarizers can be represented by [47,48]:

 

Fig. 4. Polarizing optical microscope (POM) images of the NSE-LC samples at different voltages for the layer thickness of (a) 2.55µm and (b) 3.25 µm (c) 6.55µm. The white arrows and the red arrows represent the transmission axis of two polarizers and the direction of applied electric field, respectively. The yellow rods stand for the corresponding field-induced refractive-index-ellipsoid triggered by applied electric fields.

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Fig. 5. The refractive index change δn as a function of E². In (a), (b), and (c), red lines and blue lines represent the measured refractive index change and the extended Kerr effect with Eq. (4) for three samples with LC layer thickness of 2.55µm, 3.25µm and 6.55µm. In (d), (e), and (f), red lines are measured refractive index change, and the green lines are the modified extended Kerr effect with Eq. (8) for three samples with LC layer thickness of 2.55µm, 3.25µm and 6.55µm.

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Figure 5 shows the changes in refractive index (δn) as a function of electric field squared (E²). The change in refractive index (δn) linearly increases with small E² . Then δn reaches its maximum value and goes to a state of saturation when the electric field exceeds the saturation electric field (E_sat), as described by Eq. (4). The blue lines in Figs. 5(a), 5(b) and 5(c) represent the quadratic field response of the induced birefringence, calculated from Eq. (4). However, the experimental results (represented by red lines) did not align with the results derived from Eq. (4) (represented by blue lines). In previous studies, it was reported that polymer-dispersed liquid crystals with small droplets (<333 nm) exhibit a two-step electro-optical response, which corresponds to the Kerr phase (phase shift induced by Kerr effect) and orientational phase (phase change due to molecular orientation effect) [42]. The Kerr phase observed in the experiment is thought to be resulting from the alignment of liquid crystal (LC) molecules at the center of LC droplets, while the orientational phase is a result of the alignment of LC molecules near the interfaces between LCs and polymer. Thus, NSE-LC demonstrates not only field-induced birefringence but also orientational birefringence, which Eq. (4) fails to fully take into account. Field-induced birefringence results from the alignment of liquid crystal (LC) molecules at the center of the droplet, which in turn causes a linear optical phase shift directly proportional to the electric field strength. The orientational birefringence is significantly affected by the orientation of LC molecules at the interface between the LC and polymer. Consequently, to accurately determine the saturation electric fields, we need to modify the extended Kerr effect by acknowledging these factors. This would result in a reasonable modification of Eq. (4) as follows:

Based on Eq. (8), we recalculated the changes in induced birefringence using the modified extended Kerr effect formula that corresponded with the measurements. We calculated correlation coefficients of 0.993 (for 2.55 µm), 0.981 (for 3.25 µm), and 0.987 (for 6.25 µm) using Eq. (4). Similarly, correlation coefficients of 0.995 (for 2.55 µm), 0.993 (for 3.25 µm), and 0.997 (for 6.25 µm) were obtained using Eq. (8). A comparison of the results from Eq. (4) and (8) in Fig. 5 shows a better-fit quality with Eq. (8). Although Eq. (8) does employ more fitting-parameters, its use is justified by the significantly higher accuracy it achieves. The fitted parameters in Eq. (8) are listed in Table 1. The adjusted curves obtained from the modified extended Kerr effect (illustrated as green lines in Fig. 5(d) to 5(f) matched the measured results well (represented by the red lines in Fig. 5(d) to 5(f). The fitting results are δn_sat ∼0.048 with 70% of field induced birefringence contribution (A = 0.7) under E_sat1 = 0.8 V/µm and 30% of orientational birefringence contribution (B = 0.3) under E_sat2 = 3.5 V/µm in the 2.55 µm thickness of NSE-LC. For 3.25 µm thickness of NSE-LC, δn_sat ∼0.048 with 80% of field induced birefringence contribution under E_sat1 = 0.8 V/µm and of 20% orientational birefringence contribution under E_sat2 = 3.5 V/µm. Similarly, for 6.55µm thickness of NSE-LC, δn_sat ∼0.048 with 90% of field induced birefringence contribution under E_sat1 = 0.8 V/µm and of 10% orientational birefringence contribution under E_sat2 = 3.5 V/µm. The results suggest that a thicker sample results in a greater contribution to field-induced birefringence, and conversely, a lesser contribution to orientational birefringence. Both E_sat1 and E_sat2 exhibit a slight decrease alongside an increase in sample thickness. Because the increased thickness led to an increase in lumped NSE-LC accumulation, result in more light leakage and effect to orientational phase and maximum Kerr phase.

Table 1. The parameters of two samples of NSE-LC. F is the areal filling ratio, D is diameter of the cavities, A is the coefficient of field induced birefringence, B is coefficient of orientational birefringence, δn_sat is saturated refractive index change, and E_sat1 and E_sat2 are saturated electric field strengths. 2.55µm, 3.25µm and 6.55µm are the thicknesses of three samples^a

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The total optical phase shift (Δф_theory) of the NSE-LC is determined by two parameters: the NSE-LC layer thickness (d) and the voltage-dependent induced birefringence ($\mathrm{\Delta }{n_{ind}}$), which are related to the transmittance in Eq. (7). Figure 6(a) depicts the measured optical intensity as a function of the electric field for NSE-LC samples, which varied in thickness at 2.55um, 3.25um, and 6.55um. The three NSE-LC samples demonstrated optical intensities of 15.0%, 31.0%, and 100% for thicknesses of 2.55um, 3.25um, and 6.55um respectively at driving electric fields of 3.7 V/um. In Fig. 6(a), the sample is thicker, the optical intensity is higher. This is because of larger phase retardation at the thicker sample. Another information provided in Fig. 6(a) is a highly filled LC-polymer composite system can effectively reduce the operating voltage, whereas the threshold field E_th in an in-plane-switching architecture can be expressed as [23].

 

Fig. 6. (a) The measured optical intensity for samples of NSE-LC with the thickness of 2.55µm, 3.25µm, and 6.55µm. (b) is the normalized measured optical intensity of (a).

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Additionally, in Fig. 5 (red lines), we can observe the fluctuation of the induced birefringence at high E². The frequency of AC voltage we applied was 100 Hz corresponding to 10 msec. The fluctuation in Fig. 5 should be because of the fast response time of the NSE-LC. To clarify this point, we also conducted an analysis of the response time based on the measurements of time-dependent transmittance. The response time was determined using τ_on and τ_off, which respectively represent the time duration for the transmittance change from 10% to 90% when we turn on the voltage, and transmittance change from 90% to 10% when we turn off the voltage. The measurements yielded response times of τ_on (τ_off) = 1.8 (5.8) ms for 2.55µm thickness, τ_on (τ_off) = 1.3 (6.55) ms for 3.25µm thickness, and τ_on (τ_off) = 1.1 (4.4) ms for 6.55µm thickness when a voltage of 4.0 V/um was applied. The three samples, despite differing in thickness, showed comparable response times in terms of order of magnitude. This is reasonable because of the similar droplet size for the samples. The measured response times of NSE-LCs are faster than 10 msec. Therefore, the sample transmittance oscillated with the applied alternating current voltage at a frequency of 100 Hz, leading to fluctuations in the induced birefringence.

5. Conclusion

Utilizing the encapsulation method, we successfully fabricated a high filling ratio of LCs within the polymeric matrix. With this approach, we attain NSE-LC with high filling ratio of 58% LC to the total LC-polymeric matrix system, which is significantly higher than the less than 40% filling ratio typically achieved with other polymer dispersed isotropic LCs. We propose a modification to the extended Kerr effect (Eq. (8)) to account for two-step saturation points caused by field-induced birefringence at low electric fields with threshold characteristics, and the orientational birefringence that is linked with the anchoring energy of LC molecules at the LC-polymer interface. The measured values and the fitting curves using modified extended Kerr effect have a good agreement. We conducted measurements on NSE-LC samples with three different thicknesses. The results demonstrated that E_th does not increase with increased NSE-LC layer thickness. Increasing the NSE-LC layer thickness enhances phase modulation without increasing driving voltage. The response time of NSE-LC is similar with that of other isotropic LCs. We can confirm that increasing the NSE-LC layer thickness through multiple layered coatings effectively enhances phase modulation in NSE-LC. Our experimental demonstration using the proposed LC-in-polymer encapsulation method achieved excellent electro-optic performance. LC phase modulation is not only polarization-independent but also allows for flexible devices. This study makes a significant contribution by providing a solution for versatile applications in various up-and-coming tunable photonic systems. This is especially relevant given the high optical efficiency allowed by the high Kerr constant of NSE-LC.