Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Wide field of view chiral imaging with a liquid crystal planar lens enabled by digitalized nanogratings

Open Access Open Access

Abstract

To compensate for the inability for polarization imaging by conventional methods, metasurface optics with compactness and multi-function emerge as an approach to provide images with different linear and circular polarizations. Here, we propose a liquid crystal (LC) geometric phase-based chiral imaging lens (CIL) that simultaneously forms images of objects with opposite helicity. The CIL (Diameter 2.3 cm) was optimized by a spatial multiplexing algorithm and realized using the digital holography technique, where the LC domains were regulated by pixelated nanogratings with varied orientation. We investigated the potential of the patterning technique toward high order LC alignment by balancing the periodicity and depth of the nanogratings. The CIL exhibited a wide field of view of ±20°, which is attributed to the self- assembling effects of LC molecules. The compactness, lightness, and ability to produce chiral images of the LC CIL even at large angles have significant potential for practical polarization imaging.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Polarization is the inherent property of light which expresses the vibration of electric vector. Unlike the intensity and color information, human eyes are blind to light polarization [1,2], however, creations such as bees and squilla have evolved the capability to discriminate the light polarization for navigation and hunting. Motivated by such creations, polarization imaging emerges as the technique to decode polarization properties of scattered light, which could provide valuable information about imaged objects including texture, chirality, shape and even its material constituents, opening applications ranging from remote sensing to industrial inspection and biology [3]. Conventional polarization imaging operates with discrete optical elements such as polarizers, rotators, aspherical lens, apertures, etc. al., in the requirements of delicate mechanical alignment and calibration, resulting in bulky and complex optical systems. The development of polarization imaging systems towards miniaturization and on-chip integration was inevitable. Benefiting from the precise control of the wavefronts using sub-wavelength resonant elements [4], geometric metasurface offers a flexible platform for the independent manipulation of polarization information, i.e., the flat lens could simultaneously provide images in different linear and circular polarizations without the requirement of additional optical elements [5], outperforming traditional bulky devices. To date, the capabilities of the single-layered metasurface in polarization imaging have been demonstrated, e. g., chiral imaging in the visible [5] and terahertz band [6], which was further extended to both linear polarization imaging and chiral imaging in the visible [7] and infrared band [8]. The ultra-thin metasurface element was further integrated with the imaging lens and the CMOS array to enable a compact full-Stokes polarization camera [9]. However, the fabrication of these subwavelength resonant elements to induce the abrupt phase change requires complex steps such as electron beam lithology, selective etching or deposition. As a result, the size and cost of the metasurface element for polarization imaging was highly restricted [10] (below 1 mm), exhibiting as an obstacle from scientific demonstration to practical application. In addition, the small sized metasurface element would allow very limited light to be imaged, affecting imaging resolution and field of view. These shortcomings would be even more severe at large viewing angles and the field of view performance of the metasurface polarization imaging was barely investigated and optimized.

LC optics based on the geometrical phase have recently attracted numerous attention and was regarded as the fourth generation optics. By controlling the optical axis orientation in the anisotropic material, where the thickness corresponds to the half wavelength retardation, one could manipulate the phase change of transmitted light with 100% efficiency [11]. Such phase modulation is not dependent on the optical path and can be physically continuous according to the desired phase wavefront. Due to the nature of soft materials, LC optics were realized via the self-assembly of the anisotropic molecules on the patterned surface after injecting the LC or coating the LC polymer instead of complex etching or deposition processes [12]. As a result, the LC geometrical phase optics not only retains the advantages of planarity, miniaturization and ease for integration as the metasurface optics, but also could scale up to large aperture for practical purposes with proper alignment techniques. In addition, traditional LC materials could respond to external stimulus such as heat, electric field and light, opening possibilities for realizing tunable and active planar optics. Apart from using the traditional LC materials, LC polymers are recently recognized as fantastic materials for optics, which exhibit high optical transparency, large birefringence [13] and high resistance [14,15] to moisture and UV light [16]. The LC polymer could further be processed by simple coating and UV curing steps, providing a route to ultra-thin and large aperture optics. To date, photonic components such as polarization grating [17], broadband imaging lens [18,19], vortex plate [20,21] and holography film [22] have been realized using the LC geometrical phase, which further opened novel applications including beam steering [23], augmented reality [24], compact imaging [25], quantum information [21], etc. al. However, the exploration into the potential of LC planar photonics was still underestimated. The demonstrations of novel optical elements or photonic applications using LC geometrical phase would not only provide insights into the mechanisms and dynamics of soft photonics, but also pave a way for practical applications which may not be reached by common refractive optics or metasurface optics.

In this work, we propose and demonstrate a CIL based on the LC geometrical phase. The lens provides simultaneous imaging of the left-handedness circular polarization (L-CP) and right-handedness circular polarization (R-CP). The LC lens was segmented and pattered using the pixelated nanogratings. The grooves of the nanogratings enables sufficient anchoring strength for LC alignment, where the orientation of the grooves controls the LC half-wave plate directions and thus the geometrical phase. Compared with common photoalignment techniques, the resulted LC elements exhibit resistance to UV light and long-time degradation. Further, the replication of pixelated nanogratings using nanoimprinting techniques would offer the possibility for the volume fabrication of LC planar optics. The CIL provides a wide-field view of ±20°, which may be attributed to the compensation property of the LC molecules.

2. Principle of the LC planar lens for chiral imaging

In refractive optics, the phase profile of the element is represented by the dynamic phase, which is assigned to the optical path in different media and achieved by machining the geometric profile of the lens. In contrast, the LC geometrical originates from the phase acquired when the polarization undergoes a cyclic evolution and depends on the specific evolution route. The polarized light (${E_{ix}}$, $\textrm{}{E_{iy}})$T gains additional phase after propagating through the LC layer, and the exit light is (${E_{tx}}$, $\textrm{}{E_{ty}}$)T =t (${E_{ix}}$, $\textrm{}{E_{iy}})$T. where t is the Jones matrix of LC. When the angle between the LC molecular director and the x-axis is $\emptyset $, the outgoing light can be expressed as [26,27]:

$$\left[ \begin{array}{l} {E_{\textrm{tx}}}\\ {E_{\textrm{ty}}} \end{array} \right] = \left[ {\begin{array}{cc} {\cos \phi }&{\sin \phi }\\ {\sin \phi }&{\cos \phi } \end{array}} \right]\left[ {\begin{array}{cc} 1&0\\ 0&{{\textrm{e}^{i\partial }}} \end{array}} \right]\left[ {\begin{array}{cc} {\cos \phi }&{\sin \phi }\\ { - \sin \phi }&{\cos \phi } \end{array}} \right]\left[ \begin{array}{l} {E_{\textrm{ix}}}\\ {E_{\textrm{iy}}} \end{array} \right]$$
Where $\partial = ({2\pi /\lambda } )({{n_e} - {n_0}} )\textrm{d}$ represents the phase delay between the fast and slow axis; d is the thickness of the LC layer and $\lambda $ is the incident light wavelength. When $\partial = \mathrm{\pi }$, and the incident light is circularly polarized light ${J_ \pm } = {[1, \pm i]^T}$, the outgoing light will become $J_ \pm ^\mathrm{^{\prime}} = {[1, \mp i]^T}{e^{ {\pm} 2i\emptyset }}$. It is clear that the phase of the transmitted circular light $\mathrm{\varphi }$ can be controlled by the azimuthal angle of the half-wave plate axis $\emptyset $ and the corresponding phase change is $2\emptyset $. Furthermore, the handedness of the transmitted circular light exhibits reversion to the handedness of the incident circular light. The foundations of the geometrical phase and the opposite phase dependence of the L-CP and R-CP would be utilized to design the LC lens with chiral imaging properties in the following.

The working principle and design diagram of the LC CIL are shown in Fig. 1. The LC planar lens was segmented to direct the independent imaging of the L-CP and R-CP information. The left-handedness LC segments would concentrate and diverge lights of L-CP and R-CP with opposite foci, respectively. As a result, the collimated L-CP lights would be focused into an off-axis spot by the left-handedness LC segments (Fig. 1(a)), while R-CP lights incident on these regions would be divergent into space. Similarly, the collimated R-CP and L-CP lights incident on the right-handedness LC segments would be concentrated into the other off-axis spot (Fig. 1(b)) and divergent into space, respectively. Therefore, different chiral information of the object would be separately imaged by a delicate control of the magnification ratio and the off axis distance (Fig. 1(c)). We further provided a calculation route to optimize the distribution of right-handedness and left-handedness segments. As a start, a 90-µm-diameter lens with a focal length f of 100 µm (the phase surface expression is:$2\mathrm{\varphi } = 2\mathrm{\pi }\left( {f - \sqrt {{x^2} + {y^2} + {f^2}} } \right)/\mathrm{\lambda }$) is designed to focus the incident beam at the wavelength $\lambda $ of 633 nm. The Fresnel approximation calculation (Eq. (2)) shows a diffraction limited focal spot with a full width at half maximum (FWHM) of 0.80 µm [28] (Fig. 1(dI)).

$$U(x,y) = \exp (jkd)/j\lambda d\int {\int\limits_{ - \infty }^{ + \infty } {{U_0}({x_{0,}}{y_0})} } \exp \{ jk[{(x - {x_0})^2} + {(y - {y_0})^2}]/2d\} d{x_0}{y_0}$$

 figure: Fig. 1.

Fig. 1. Working principle and schematic design diagram of the LC CIL. (a) Incident L-CP light was focused into the left sided off-axis position. (b) Incident R-CP light was focused into the right sided off-axis position. (c) Unpolarized light is focused by CIL. (d) Calculated phase profiles and diffraction patterns for single and spatially multiplexed LC CIL.

Download Full Size | PDF

The simplest method for segmenting the LC regions for L-CP and R-CP is to divide the lens into two equal parts, with symmetric images on the left and right sides, corresponding to L-CP and R-CP information of the observed object. The phase distribution of left and right-hand polarization imaging is represented by ${\varphi _1}$ and ${\varphi _2}$, respectively, where $\textrm{}{\varphi _1} = \mathrm{\pi }\left( {f - \sqrt {x_1^2 + y_1^2 + {f^2}} } \right)/\mathrm{\lambda }$, ${\varphi _2} ={-} \mathrm{\pi }\left( {f - \sqrt {x_2^2 + y_2^2 + {f^2}} } \right)/\mathrm{\lambda }$, λ is the wavelength of the incident light and f is the focal length. We have assigned equal off-axis distance of the two focusing points. It was shown that the calculated two foci were stretched horizontally (Fig. 1(dII)) due to the reduced aperture of each individual sub-lens in the horizontal direction [29]. In order to reduce the imaging aberrations and allow equal regions for L-CP and R-CP light collection, we presented the optimized hybridization of the radial segments for L-CP and R-CP imaging (Fig. 1(dIII)). According to simulation, collimated L-CP and R-CP lights would be focused into left and right spots with nearly diffraction-limited diameter, indicating the potential superior imaging performance of the spatially multiplexed CIL.

3. Experimental details

High resolution LC alignment technique is the key enabler for the realization of geometrical phase LC optics [30], which regulates the director of each LC domain for the precise construction of the designed phase front for chiral imaging. Photoalignment technology is the well-adopted approach for geometrical phase LC optics, which utilized patterned polarized light to exposure photosensitive materials and produced patterned anisotropic surface forces to induce the orientation of LC domains. Photoalignment was superior in flexibility and resolution, however, issues such as the longtime photothermal stability and mass production capability still need to be addressed [31]. In this work, we proposed the patterned alignment of LCs using the pixelated nanogratings. The grooves in pixelated nanogratings implement the boundary anchoring effect and induce the LC alignment along the groove orientation with high degree of order. The nanograting morphology could be transferred to robust materials such as the UV adhesives using the nanoimprinting technology. Thus, this approach has the potential of mass production of LC planar optics with high photothermal stability. According to Berreman’s theory [32,33], the anchoring strength of relief gratings is in inverse proportion with the periodicity. In order to obtain high ordered LC alignment, the fabrication of subwavelength gratings with nanogrooves is a prerequisite. However, the manufacturing of pixelated nanogratings with tunable periods and orientations required electron beam lithography, which limited the practical potential of the technique. In order to overcome this limitation, a homemade multifunctional digital holography system was developed (see Appendix A for the setup diagram). The laser beam was separated into ±1 orders at the diffraction optical element (DOE) and the two beams were redirected to overlap for the generation of the interference field by the objective lens. The on-axis position and the off-axis rotation of the DOE were used to control the periodicity and orientation of the interference field, respectively. The digitalized interference field was utilized to expose the photoresist, providing relief nanogratings after development. The recording of each nanograting was completed in one laser pulse and the system could distribute nanogratings with controlled periodicity and orientation at 1000 pixels/second, overcoming the fabrication efficiency limitation of electron beam lithography. The designed phase front in Fig. 1(dIII) was discretized and converted into the LC domain orientation distribution according to the geometrical phase rule, which was further decoded in the digitalized nanogratings. The system was capable of providing a patterned area up to 65 “, compatible with large-aperture LC planar optics.

The detailed preparation steps of LC CIL are shown in Fig. 2, which can be summarized as follows:

  • (1) The glass substrate was cleaned and processed using the UVO cleaner to remove residue organic pollutants.
  • (2) The photoresist PZM4620 (500 rpm/s for 10 s and 2500 rpm/s for 30 s) was spin-coated onto the substrate and baked at 90°C for 2 min (to harden the film).The thickness of the resulted photoresist was 1 µm.
  • (3) The photoresist was exposed using the digitalized holography system. Pixelated relief nanogratings were obtained after development in sodium hydroxide solution.
  • (4) The replication of the nanogratings was implemented by the following steps. The PDMS precursor was onto the patterned photoresist and cured by placing the sample in an oven at 70°C for 4 hours. The cured PDMS mold with nanogratings was stripped from the patterned resist (Fig. 2(a)–2(c)). The PDMS mold was pressed against the UV resin on the glass substrate, which leaves the nanoimprinted polymer film after UV curing and removal of the PDMS mold (Fig. 2(d)–2(e)).
  • (5) The reactive LC monomers (OCM-A0, Raito Materials Technology Co., Ltd. Suzhou, China) were spin-coated onto the nanoimprinted polymer film (800 rpm/min for 10 s and 2700 rpm/s for 30 s) and UV cured (365 nm, 89.6 mw/cm2, 1 min), resulting in a LC polymer planar lens for chiral imaging (Fig. 2(f)). The thickness of the LC polymer film was optimized to achieve high optical efficiency at the wavelength of 633 nm. The photoresist and the PDMS molds with were reusable to replicate the nanogratings in the polymer film, opening the possibility for volume manufacturing of LC planar optics.

 figure: Fig. 2.

Fig. 2. Fabrication process of the LC CIL using replicated nanogratings. (a) The PDMS precursor was poured onto the photoresist nanogratings, (b) The relief nanogratings were transferred to the PDMS, (c) the PDMS mold with nanogratings was stripped from the photoresist, (d) the PDMS mold was pressed against the UV resin on the glass substrate, (e) after UV curing, the nanograings were replicated from the PDMS mold, (f) reactive LC monomers were spin-coated onto the imprinted nanogratings to obtain LC CIL after UV curing.

Download Full Size | PDF

4. Results and discussions

The anchoring performance of nematic LCs on sinusoidal wavy surfaces has been theoretically investigated by Berreman model [34] that the local molecular orientation would be parallel to nanogratings. The morphology of the nanogratings fabricated by the digital lithography technique was characterized by scanning electron microscopy (SEM). The orientation of each nanograting to direct the alignment of the LC domain was adjusted by rotating the DOE in the digital holography system during each light exposure (Fig. 3(a)–3(d)), generating spatially varied nanogratings for CIL with high efficiency. The cross-sectional image of the nanograting exhibited uniform tooth-like topography (Fig. 3(e)). According to the Berreman’s theory, the anchoring force of nanogatings on nematic LC molecules is proportional to the nanogratings depth and inversely proportional to the periodicity. In interference lithography, the aspect ratio of the resulted grating was often less than 1 due to the light penetration and chemical development in the photoresist. Thus, the two important parameters of depth and periodicity in LC alignment are correlated in digital holography. In order to gain more insight into the anchoring foundations of the proposed technique, we investigated the dependence of LC ordering on the periodicity of the nanograting (Fig. 3(f)). The grating depth increases from 60 nm to 300 nm as the periodicity adjusted from 400 nm to 800 nm. Correspondingly, the order degree of LC varied between 0.70 and 0.79 due to the compensation effect of the groove depth at a high periodicity. It was also revealed that the order degree peaks at the periodicity of 550-600 nm, where the two parameters reached an optimization for LC ordering. It was also worth to mention that the diffraction effects of these subwavelength nanogratings would not disturb the photonic properties of the resulted LC planar elements, as the height of the nanograting and the refractive index contrast between LC and the UV adhesive was low. The patterned LC areas exhibit uniform bright and dark states under the polarization optical microscopy (POM) inspection (Appendix B). The digitalized nanogratings exhibited comparable LC alignment performance with the photoalignment technique, indicating the feasibility of the technique in LC patterning (Appendix B). The LC order parameter decreases slightly when the film thickness increases, as the nanograting surface provides one-sided anchoring for the LC polymer.

 figure: Fig. 3.

Fig. 3. The morphology and structure of the nanogratings and the characterization of the order degree of the LC molecules. (a)-(d) SEM images of the nanogratings in different orientations. (e) Characterization of the period and depth of the prepared nanogratings. (f) Dependence of LC order degree on the period and depth of the nanogratings.

Download Full Size | PDF

In the following part, we would analyze the LC molecular configuration and imaging performance of the prepared CIL in detail. The CIL depicts alternating dark and bright rings (Fig. 4(a)) under POM investigation. Unlike the binary optics using relief microstructures where the optical efficiency was strictly limited by the number of phase steps, the efficiency of the LC PB optics would be significantly higher than 90% with a polarization step number of four. This was attributed to the self-assembling nature of the LC molecules, as they are in contact with each other and the molecules should experience a continuous director change at the interface which brings a smooth phase profile and improved optical performance. The LC regions with perpendicular molecular orientations have same brightness under POM, and the ring appearance inversed when the sample was rotated by 45° (Fig. 4(b)). The magnified directional arrangement of LC molecules in rings of the CIL is further shown in Figs. 4(c)–4(d). The orientation distribution of different ring regions with regard to left-handedness and right-handedness imaging lens is opposite, which enables the complementary phase distribution to focus the L-CP and R-CP light respectively.

 figure: Fig. 4.

Fig. 4. Characterization of the LC CIL enabled by digitalized nanogratings. POM image of the CIL with the orientation of 0° (a) and 45° (b), with the corresponding LC molecular arrangement of (c) and (d). Optical path diagram used to measure the focusing performance of CIL (e). Intensity distribution of the left and right off-axis spots with L-CP light (f) and R-CP light (g) incidence.

Download Full Size | PDF

To verify the imaging capabilities of the LC CIL, the lens was subjected to focusing tests on collimated light with different chirality. In the optical path (Fig. 4(e)), the collimated and expanded laser beam (633 nm) passes through the polarizer, the quarter-wave plate and the CIL in sequence, where the polarization state of incident light is changed by rotating the quarter-wave plate. The focused spot was received by a CCD camera. When the incident light is L-CP, it focuses in the left-handed region of the lens and diverges in the right-handed region of the lens (Fig. 4(f)) and the vice versa (Fig. 4 g). Under both chiral polarizations illumination, light was mainly focused into the corresponding off-axis spots with Gaussian distribution, indicating high imaging performance. Some light leaked into the other off-axis focus, which may be attributed to the crosstalk of spatially interlaced left-handedness and right-handedness LC lens rings. The diameter of the focused spot for L-CP and R-CP light was estimated to be around 342 µm and 330 µm, respectively, by fitting the intensity distribution curves. The size of the focused off-axis spots was larger than the theoretical value by the Airy equation (L = 1.22 $\lambda /NA$). This may be due to the preparation conditions such as the groove inhomogeneity in pixelated nanogratings and the stitching error at the adjacent pixels, resulting in nonuniform anchoring force and abrupt phase change. The focusing performance was further verified by irradiating the CIL with a collimated linearly polarized laser beam. The focused light at different cutting planes was detected (see Appendix C), which showed the evolution of the left and right off-axis focusing along the propagation direction.

The circular dichroism performance of the CIL at different field angles was characterized by measuring the focused spot energy at different incident polarizations and angles. When the CIL was irradiated with linearly polarized light at 0° (Fig. 5(a)) and 90° (Fig. 5(b)), the intensity of the right off-axis spot was almost equal to that of the left off-axis spot, which agrees well with the fact that the linear polarization was composed of opposite circular polarizations with identical intensity. Thus, the corresponding circular dichroism defined as the intensity ratio of the left and right spots was around the ideal value of 1. We further measured the circular dichroism ratio of the CIL under L-CP and R-CP incidence (Fig. 5(c)–5(d)), and the circular dichroism was around 9.1 and 7.4 with a focusing efficiency up to 85%. The higher the dichroism ratio, the higher accuracy of the CIL in retrieving the information of different chiral polarizations. It was also revealed from the measurements that the intensity of the focused off-axis spots and the circular dichroism barely changes when the incident angle was within -20° and +20°, indicating the LC CIL would preserve chiral imaging performance in the field of view range. The wide field of view performance of the LC CIL would be attributed to the large aperture of the lens and the self-compensating properties of LC molecules, where incident light from different angles would experience corrected phase change in the long-range ordered rod-like molecules.

 figure: Fig. 5.

Fig. 5. Circular dichroism characterization of the LC CIL at different incident angles. The intensity of right off-axis spot, the intensity of left off-axis spot and the intensity ratio with (a) 0° linearly polarized light, (b) 90° linearly polarized light, (c) L-CP light and (d) R-CP light.

Download Full Size | PDF

5. Polarization imaging analysis

The capabilities of the LC CIL in wide view polarization imaging were further characterized and demonstrated in practical measurements. The laser beam with modulated polarization was used to illuminate the resolution plate and the image plane was received through a CCD (Fig. 6(a)). This polarization imaging capability is shown in Fig. 6(b). Under linearly polarized light illumination, images with identical resolution and intensity were found in the left-handed and right-handed regions of the lens. It was an indication that the light-field contains same amount of L-CP and R-CP information, which agrees with the fact that the linear polarization is a superposition of L-CP and R-CP with same intensity. The two chiral images were well separated in the imaging plane, which is suitable for real-time chiral imaging. Under L-CP or R-CP illumination, the resolution plate is imaged solely in the left and right off-axis region, respectively, further verifying the precision of the CIL in retrieving chiral information. The minimum resolvable linewidth of the resolution plate was 3.18 lp /mm, 2.83 lp /mm and 1.78 lp/mm for the view Angle of 0°, ± 10° and ±25°, respectively. The LC CIL provides sufficiently high quality chiral images within a viewing field of ±20°. This large FOV imaging feature is of great significance for the practical application of miniaturized optical systems [35,36]. Beyond that, the chiral images show comparatively large distortion and low resolution. The imaging quality of the LC CIL can be further improved by preparing more uniform nanogratings, optimizing the grating seaming error, or reducing the edge line width.

 figure: Fig. 6.

Fig. 6. Field of view dependent polarization imaging performance of the LC CIL. (a) Schematic diagram of the optical path for polarization imaging, which composed of the laser (633 nm), the collimating beam expander, the resolution plate, the quarter wave plate, the CIL and CCD. (b) Images of the resolution plate at different viewing angles under the illumination of 0° linear polarization, 90° linear polarization, L-CP and R-CP.

Download Full Size | PDF

We have further implemented practical chiral imaging demonstrations using the planar LC CIL, where the chiral masked letters and 3D glasses are observed. The upper and lower halves of these two images correspond to L-CP and R-CP information of the objects and were simultaneously imaged through spatially multiplexed regions in CIL (Figs. 7(a)–7(b)). To clearly present the chiral objects with different rotations, their Stoke vector S3 images (S3 represents the intensity difference between L-CP and R-CP light) can be extracted (Figs. 7(c)–7(d)), demonstrating the simultaneous chiral imaging of the LC CIL in the same focal plane.

 figure: Fig. 7.

Fig. 7. Polarization imaging of chiral targets. (a) Polarization image of letters ‘H''D’ with illumination of chiral light. (b) Polarization image of 3D glasses. (c) Stokes vector S3 extracted from letters image and (d) 3D glasses image.

Download Full Size | PDF

6. Conclusion

In conclusion, we have designed and realized a planar CIL with LC geometrical phase, which simultaneously forms two images with opposite helicity within a large field-of-view of ±20°. The introduction of digital holography technique and the directing of LC domain orientation using the nanogratings provides a feasible approach toward large aperture and high stability LC planar optics. Chiral information of different objects can be probed using the CIL and a CCD camera without addition of polarizers or imaging optics, paving a way for miniaturized and compact polarization systems. The circular dichroism and wide field of view imaging performance was also investigated, which indicated superior chiral imaging characteristics. These results provoke the potential of planar LC optics in realizing a multifunctional and compact device with unprecedented polarization imaging capabilities.

Appendix A

A schematic diagram of the nanograting lithography system is shown in Fig. 8. The collimated and amplified laser beam illuminates a grating modulation system consisting of two Fourier transform lenses and a diffractive optical element (DOE) interposed between them. The many diffracted beams of the DOE then form an interference pattern at the back focal plane of the second Fourier transform lens. Finally, the light field of the coherent image is reduced by the objective lens and projected onto the photoresist. The pattern structure of the reflector reduces the multi-beam interference pattern of the DOE. Furthermore, the DOE axial displacement and axial rotation between the two Fourier transform lenses changed the orientation and periodic scale factor of the patterned 2D nanogratings, respectively.

 figure: Fig. 8.

Fig. 8. Schematic illustration of the digitalized holography system for pixelated nanogratings.

Download Full Size | PDF

Appendix B

Fig. 9 investigated the anchoring force of the nanograting on the LC molecules through the order degree. Figure 9(a) shows the optical path diagram of the order degree test. The collimated laser beam laser at 633 nm passes through the polarizer, the test sample (LC polymers anchored by fixed azimuthal nanogratings) and the analyzer in sequence. The intensity of the emitted beam is received by the optical power meter. The incident light beam after the polarizer was expressed as ${E_i} = {[1,0]^T}$. After passing the sample with a phase delay of δ, the outgoing light beam can be expressed as:

$${E_\textrm{t}} = \left[ {\begin{array}{cc} {{{\cos }^2}\theta }&{\frac{1}{2}\sin 2\theta }\\ {\frac{1}{2}\sin 2\theta }&{{{\sin }^2}\theta } \end{array}} \right]\cos (\frac{\delta }{2})\left[ {\begin{array}{cc} 1&{ - i\tan (\frac{\delta }{2})}\\ { - i\tan (\frac{\delta }{2})}&1 \end{array}} \right]\left[ {\begin{array}{c} 1\\ 0 \end{array}} \right]$$
Where $\mathrm{\delta }$ represents the phase delay of the sample, θ represents the angle between the optical axis of the LC polymer and that of the analyzer. In this experiment, keeping the angle of the polarizer and the optical axis of the test sample constant at 45°, rotating the analyzer. The final outgoing beam intensity is $\textrm{I} = ({\textrm{cos}2\mathrm{\theta } + \mathrm{cos\delta }} ))/2$.
$$\frac{{{I_{\min }}}}{{{I_{\max }}}} = \frac{{|{\cos 2{\theta_1}\textrm{ + }\cos \delta } |}}{{|{\cos 2{\theta_2} + \cos \delta } |}}$$

 figure: Fig. 9.

Fig. 9. Molecular order degree characterization of LC polymers. (a) Optical path diagram of order degree measurement. (b) Dependence of the LC order degree on the thickness of LCP for nanograting regulation and photoalignment. Polarization optical microscopy images at a viewing angle of 0° (c) and 45° (d).

Download Full Size | PDF

The thickness of the detected sample is similar to the half-wave condition($\mathrm{cos\delta } < 0$, phase difference $\mathrm{\delta } = 2\mathrm{\pi }\varDelta \textrm{nd}/\mathrm{\lambda }$) When the angle between the analyzer and the polarizer is 0$^\circ $, the light intensity in the short-axis direction of the outgoing elliptically polarized light is detected, and the light intensity is the smallest; when the angle is 90$^\circ $, detect the light intensity in the long axis direction of elliptically polarized light, and the light intensity is the largest, the LC order degree could be calculated by monitoring the maximum and minimum intensity when rotating the analyzer. Figure 9(b) presents the dependence of the LC order degree on the thickness of LCP for nanograting regulation and photoalignment. The two approaches have comparable performance in terms of LC alignment and the order parameter was between 0.7 and 0.83 (Fig. 9(b)). Figures 9(c)–9(d) depict the POM of the test sample after spin-coating the LC polymer, The period of the test sample is 595 nm, the groove depth is 186 nm, and the orientation angles of the nanogratings are 0$^\circ $ and 90$^\circ $, respectively (the boundaries of different regions can be clearly seen in the figure), and the contrast between bright and dark is obvious, indicating that the nanograting has a strong anchoring force to the LC molecules.

Appendix C

The evolution of the LC CIL focusing at different cutting planes are presented in Fig. 10. A linearly polarized laser beam at 633 nm was used for illumination. The focusing performance of the CIL was recorded by placing the CCD camera at different distances from the CIL sample. Its focal plane is determined by measuring the size of the focused laser spot and is further shown in the inset.

 figure: Fig. 10.

Fig. 10. The evolution of LC CIL focusing at different cutting planes.

Download Full Size | PDF

Appendix D

Figure 11 shows the polarization imaging test of LC CIL, changing the direction of the long axis of the quarter-wave plate in the imaging optical path of the mask to make it 45 with the optical axis of the perpendicular polarizer attached to the mask (Fig. 11(b)). The outgoing light of the circularly polarized light with the opposite hand is imaged through the different chirality regions of the CIL, and finally recorded by the CCD. Figure 11(c) is an actual picture of the CIL, in the LC polymer region with nanograting anchors, which is more transparent compared to other regions. Meanwhile, the fabrication of large-scale LC CILs is possible due to the use of photolithographic processes to fabricate nanogratings.

 figure: Fig. 11.

Fig. 11. Polarization imaging test. (a) Schematic diagram of the test path, (b) The quarter-wave plate coverts the S polarization and P polarization into L-CP and R-CP, (c) Image of the LC CIL with a diameter of 2.3 cm.

Download Full Size | PDF

Funding

National Natural Science Foundation of China (62175170, 62275180); Priority Academic Program Development of Jiangsu Higher Education Institutions.

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data that support the findings of this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. Q. Fan, Y. Wang, M. Liu, and T. Xu, “High-efficiency, linear-polarization-multiplexing metalens for long-wavelength infrared light,” Opt. Lett. 43(24), 6005–6008 (2018). [CrossRef]  

2. M. Miyata, M. Nakajima, and T. Hashimoto, “Compound-eye metasurface optics enabling a high-sensitivity, ultra-thin polarization camera,” Opt. Express 28(7), 9996–10014 (2020). [CrossRef]  

3. L.-L. Ma, S.-B. Wu, W. Hu, C. Liu, P. Chen, H. Qian, Y. Wang, L. Chi, and Y.-Q. Lu, “Self-assembled asymmetric microlenses for four-dimensional visual imaging,” ACS Nano 13(12), 13709–13715 (2019). [CrossRef]  

4. W. A. Britton, Y. Chen, F. Sgrignuoli, and L. D. Negro, “Compact dual-band multi-focal diffractive lenses,” Laser Photonics Rev. 15(2), 2000207 (2021). [CrossRef]  

5. M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral Chiral Imaging with a Metalens,” Nano Lett. 16(7), 4595–4600 (2016). [CrossRef]  

6. B. Yao, X. Zang, Y. Zhu, D. Yu, J. Xie, L. Chen, S. Han, Y. Zhu, and S. Zhuang, “Spin-decoupled metalens with intensity-tunable multiple focal points,” Photonics Res. 9(6), 1019–1032 (2021). [CrossRef]  

7. E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-stokes imaging polarimetry using dielectric metasurfaces,” ACS Photonics 5(8), 3132–3140 (2018). [CrossRef]  

8. C. Yan, X. Li, M. Pu, X. Ma, F. Zhang, P. Gao, K. Liu, and X. Luo, “Midinfrared real-time polarization imaging with all-dielectric metasurfaces,” Appl. Phys. Lett. 114(16), 161904 (2019). [CrossRef]  

9. N. A. Rubin, G. D’Aversa, P. Chevalier, Z. Shi, W. T. Chen, and F. Capasso, “Matrix fourier optics enables a compact full stokes polarization camera,” Science 365(6448), eaax1839 (2019). [CrossRef]  

10. F. Ding, S. Tang, and S. I. Bozhevolnyi, “Recent advances in polarization-encoded optical metasurfaces,” Adv. Photonics Res. 2(6), 2000173 (2021). [CrossRef]  

11. N. V. Tabiryan, S. V. Serak, S. R. Nersisyan, D. E. Roberts, B. Y. Zeldovich, D. M. Steeves, and B. R. Kimball, “Broadband waveplate lenses,” Opt. Express 24(7), 7091–7102 (2016). [CrossRef]  

12. Z. He, Y.-H. Lee, R. Chen, D. Chanda, and S.-T. Wu, “Switchable Pancharatnam–Berry microlens array with nano-imprinted liquid crystal alignment,” Opt. Lett. 43(20), 5062–5065 (2018). [CrossRef]  

13. S. Nocentini, D. Martella, C. Parmeggiani, and D. S. Wiersma, “3D Printed photoresponsive materials for photonics,” Adv. Opt. Mater. 7(16), 1900156 (2019). [CrossRef]  

14. M. D. Pozo, J. A. H. P. Sol, A. P. H. J. Schenning, and M. G. Debije, “4D Printing of liquid crystals: What’s right for me?” Adv. Mater. 34(3), 2104390 (2022). [CrossRef]  

15. M. D. Pozo, C. Delaney, M. P. D. Cunha, M. G. Debije, L. Florea, and A. P. H. J. Schenning, “Temperature-responsive 4D liquid crystal microactuators fabricated by direct laser writing by two-photon polymerization,” Small Struct. 3(2), 2100158 (2022). [CrossRef]  

16. K. Sueda, K. Tsubakimoto, N. Miyanaga, and M. Nakatsuka, “Control of spatial polarization by use of a liquid crystal with an optically treated alignment layer and its application to beam apodization,” Appl. Opt. 44(18), 3752–3758 (2005). [CrossRef]  

17. S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Characterization of optically imprinted polarization gratings,” Appl. Opt. 48(21), 4062–4067 (2009). [CrossRef]  

18. Q. Xu, T. Sun, and C. Wang, “Coded liquid crystal metasurface for achromatic imaging in the broadband wavelength range,” ACS Appl. Nano Mater. 4(5), 5068–5075 (2021). [CrossRef]  

19. Y. Li, T. Zhan, Z. Yang, C. Xu, P. L. Likamwa, K. Li, and S.-T. Wu, “Broadband cholesteric liquid crystal lens for chromatic aberration correction in catadioptric virtual reality optics,” Opt. Express 29(4), 6011–6020 (2021). [CrossRef]  

20. P. Chen, L.-L. Ma, W. Duan, J. Chen, S.-J. Ge, Z.-H. Zhu, M.-J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y.-Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018). [CrossRef]  

21. W. Duan, P. Chen, S.-J. Ge, B.-Y. Wei, W. Hu, and Y.-Q. Lu, “Helicity-dependent forked vortex lens based on photo-patterned liquid crystals,” Opt. Express 25(13), 14059–14064 (2017). [CrossRef]  

22. J. Xiong, Q. Yang, Y. Li, and S.-T. Wu, “Holo-imprinting polarization optics with a reflective liquid crystal hologram template,” Light: Sci. Appl. 11(1), 54 (2022). [CrossRef]  

23. S. Nocentini, D. Martella, C. Parmeggiani, S. Zanotto, and D. S. Wiersma, “Structured optical materials controlled by light,” Adv. Opt. Mater. 6(15), 1800167 (2018). [CrossRef]  

24. T. Zhan, Y.-H. Lee, and S.-T. Wu, “High-resolution additive light field near-eye display by switchable pancharatnam-berry phase lenses,” Opt. Express 26(4), 4863–4872 (2018). [CrossRef]  

25. K. Yin, Z. He, and S.-T. Wu, “Reflective polarization volume lens with small f-number and large diffraction angle,” Adv. Opt. Mater. 8(11), 2000170 (2020). [CrossRef]  

26. J. Bai, W. Hu, N. Guo, W. Lei, Y. Lv, X. Zhang, J. Si, X. Chen, and W. Lu, “Performance optimization of insb infrared focal-plane arrays with diffractive microlenses,” J. Electron. Mater. 43(8), 2795–2801 (2014). [CrossRef]  

27. M. Honma and T. Nose, “Liquid-crystal fresnel zone plate fabricated by microrubbing,” Jpn. J. Appl. Phys. 44(1A), 287–290 (2005). [CrossRef]  

28. E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized pancharatnam–berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003). [CrossRef]  

29. D. Lin, A. L. Holsteen, E. Maguid, P. Fan, P. G. Kik, E. Hasman, and M. L. Brongersma, “Polarization-independent metasurface lens employing the pancharatnam-berry phase,” Opt. Express 26(19), 24835–24842 (2018). [CrossRef]  

30. H.-G. Park, J.-J. Lee, K.-Y. Dong, B.-Y. Oh, Y.-H. Kim, H.-Y. Jeong, B.-K. Ju, and D.-S. Seo, “Homeotropic alignment of liquid crystals on a nano-patterned polyimide surface using nanoimprint lithography,” Soft Matter 7(12), 5610–5614 (2011). [CrossRef]  

31. H.-S. Kwok, V. G. Chigrinov, H. Takada, and H. Takatsu, “New developments in liquid crystal photo-aligning by azo-dyes,” J. Disp. Technol. 1(1), 41–50 (2005). [CrossRef]  

32. E. S. Lee, P. Vetter, T. Miyashita, T. Uchida, M. Kano, M. Abe, and K. Sugawara, “Control of liquid crystal alignment using stamped-morphology method,” Jpn. J. Appl. Phys. 32(Part 2, No. 10A), L1436–L1438 (1993). [CrossRef]  

33. B. T. Hallam and J. R. Sambles, “Groove depth dependence of the anchoring strength of a zeros order grating-aligned liquid crystal,” Liq. Cryst. 27(9), 1207–1211 (2000). [CrossRef]  

34. J.-I. Fukuda, M. Yoneya, and H. Yokoyama, “Surface-groove-induced azimuthal anchoring of a nematic liquid crystal:Berreman's model reexamined,” Phys. Rev. Lett. 98(18), 187803 (2007). [CrossRef]  

35. L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013). [CrossRef]  

36. F. Zhang, M. Pu, X. Li, X. Ma, Y. Guo, P. G. H. Yu, M. Gu, and X. Luo, “Extreme-angle silicon infrared optics enabled by streamlined surfaces,” Adv. Mater. (Weinheim, Ger.) 33(11), 2008157 (2021). [CrossRef]  

Data Availability

Data that support the findings of this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1.
Fig. 1. Working principle and schematic design diagram of the LC CIL. (a) Incident L-CP light was focused into the left sided off-axis position. (b) Incident R-CP light was focused into the right sided off-axis position. (c) Unpolarized light is focused by CIL. (d) Calculated phase profiles and diffraction patterns for single and spatially multiplexed LC CIL.
Fig. 2.
Fig. 2. Fabrication process of the LC CIL using replicated nanogratings. (a) The PDMS precursor was poured onto the photoresist nanogratings, (b) The relief nanogratings were transferred to the PDMS, (c) the PDMS mold with nanogratings was stripped from the photoresist, (d) the PDMS mold was pressed against the UV resin on the glass substrate, (e) after UV curing, the nanograings were replicated from the PDMS mold, (f) reactive LC monomers were spin-coated onto the imprinted nanogratings to obtain LC CIL after UV curing.
Fig. 3.
Fig. 3. The morphology and structure of the nanogratings and the characterization of the order degree of the LC molecules. (a)-(d) SEM images of the nanogratings in different orientations. (e) Characterization of the period and depth of the prepared nanogratings. (f) Dependence of LC order degree on the period and depth of the nanogratings.
Fig. 4.
Fig. 4. Characterization of the LC CIL enabled by digitalized nanogratings. POM image of the CIL with the orientation of 0° (a) and 45° (b), with the corresponding LC molecular arrangement of (c) and (d). Optical path diagram used to measure the focusing performance of CIL (e). Intensity distribution of the left and right off-axis spots with L-CP light (f) and R-CP light (g) incidence.
Fig. 5.
Fig. 5. Circular dichroism characterization of the LC CIL at different incident angles. The intensity of right off-axis spot, the intensity of left off-axis spot and the intensity ratio with (a) 0° linearly polarized light, (b) 90° linearly polarized light, (c) L-CP light and (d) R-CP light.
Fig. 6.
Fig. 6. Field of view dependent polarization imaging performance of the LC CIL. (a) Schematic diagram of the optical path for polarization imaging, which composed of the laser (633 nm), the collimating beam expander, the resolution plate, the quarter wave plate, the CIL and CCD. (b) Images of the resolution plate at different viewing angles under the illumination of 0° linear polarization, 90° linear polarization, L-CP and R-CP.
Fig. 7.
Fig. 7. Polarization imaging of chiral targets. (a) Polarization image of letters ‘H''D’ with illumination of chiral light. (b) Polarization image of 3D glasses. (c) Stokes vector S3 extracted from letters image and (d) 3D glasses image.
Fig. 8.
Fig. 8. Schematic illustration of the digitalized holography system for pixelated nanogratings.
Fig. 9.
Fig. 9. Molecular order degree characterization of LC polymers. (a) Optical path diagram of order degree measurement. (b) Dependence of the LC order degree on the thickness of LCP for nanograting regulation and photoalignment. Polarization optical microscopy images at a viewing angle of 0° (c) and 45° (d).
Fig. 10.
Fig. 10. The evolution of LC CIL focusing at different cutting planes.
Fig. 11.
Fig. 11. Polarization imaging test. (a) Schematic diagram of the test path, (b) The quarter-wave plate coverts the S polarization and P polarization into L-CP and R-CP, (c) Image of the LC CIL with a diameter of 2.3 cm.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

[ E tx E ty ] = [ cos ϕ sin ϕ sin ϕ cos ϕ ] [ 1 0 0 e i ] [ cos ϕ sin ϕ sin ϕ cos ϕ ] [ E ix E iy ]
U ( x , y ) = exp ( j k d ) / j λ d + U 0 ( x 0 , y 0 ) exp { j k [ ( x x 0 ) 2 + ( y y 0 ) 2 ] / 2 d } d x 0 y 0
E t = [ cos 2 θ 1 2 sin 2 θ 1 2 sin 2 θ sin 2 θ ] cos ( δ 2 ) [ 1 i tan ( δ 2 ) i tan ( δ 2 ) 1 ] [ 1 0 ]
I min I max = | cos 2 θ 1  +  cos δ | | cos 2 θ 2 + cos δ |
Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.