Diffractive waveplate technology presents an opportunity for designing arrays of all types of optical components. We present here different architectures of arrays of waveplate lenses and vector vortex waveplates. Due to the continuous nature of diffractive waveplate coatings and the high spatial resolution of the technology, the sizes of array elements can span from micrometers to tens of millimeters. Both fixed and electrically switchable arrays are discussed. Arrays of diffractive waveplates present new challenges and opportunities for digital light polarization holography for applications in polarizer-free displays, smart windows, optical communications, beam shaping, and other photonics technologies.
© 2017 Optical Society of America
Arrays are important in optics and photonics. Arrays of lenses are used, for example, for concentrating solar energy, increasing the optical efficiency of focal plane arrays, including CMOS imagers, collimating beams of laser diodes, imaging and wavefront measurement systems, beam shaping, homogenizing, illumination, projection displays, etc. Microprism arrays have found important uses, particularly, in LCDs. The size of elements in arrays may scale from micrometers to millimeters and even to meters if the James Webb Space Telescope’s primary mirror segments are considered as parts of an array.
Recent advances in the development of the new generation of optics, diffractive waveplates (DWs), suggest new opportunities for optical arrays. DWs function as lenses, prisms, spiral phase retarders, etc., depending on the orientation pattern of the optical axis in the waveplate [1–6]. These components make use of geometrical phase modulation produced, particularly, by orientation modulation in liquid crystals (LCs) and liquid crystal polymers (LCPs). LC materials are highly birefringent, even for commercial LCs, and for research materials . Thus, the half-wave retardation condition required for near 100% efficiency of DW components [8,9] is achieved in micrometer thin highly transparent layers. Fabrication processes of LCP DW optics are fast and straightforward as coatings that can be deposited on desired substrates—glass, polymer, crystalline. Thus, DW components have no structural discontinuities as opposed to Fresnel lenses or conventional spiral phase plates. Because the optical functionality is induced by the molecular orientation pattern, intricate array geometries can be designed and fabricated beyond the capabilities of conventional optics. Being thin allows DWs and their arrays to be combined in series for increasing optical power of components—producing faster lenses, steeper prisms, and higher topological charge of phase vortices.
In this paper, we discuss some results of development of DW arrays of various architectures. Waveplate lens arrays (WLAs) and vortex arrays both, in LCP, nematic LC (NLC) as well as cholesteric LC (CLC) are demonstrated in transmission and reflection. LC DW arrays are electrically switchable between diffractive (lensing, in particular) and nondiffractive states.
The major purpose of the present paper is thus to draw attention to the wide variety of opportunities for polarization holography, particularly, enabling nature of digital holography for this new generation optics.
2. MATERIALS AND SETUPS
The fabrication processes for DW arrays are essentially the same as for all variety of DWs [1–6]. First, a substrate coated with a photoanisotropic material, or a cell made of substrates coated with photoanisotropic materials, is exposed to a light beam. The polarization modulation pattern determines the size and optical function of the individual elements of the array, for example, the size and the focal lengths of the lenses in a lens array. Next, the substrate is coated with LCP or the cell is filled with an LC. The thickness of the LCP layer, or the cell gap of the LC cell, along with the optical anisotropy of the LCP or the LC, determine the diffraction efficiency spectrum of the array element. The polarization modulation pattern is produced by polarization holography , digital light polarization modulation , or mechanically, by translating the substrate across the beam exposing different areas at different times . Polarization holography is most suitable for recording patterns that can simply be produced in an interferometric setup. Digital polarization modulation is a lot more versatile; however, it is typically limited to small pattern sizes and requires tiling for large area recording. Mechanically moving the photoalignment substrate in the beam with high spatial, including angular, resolution thus allows recording complex patterns over large area.
PAAD-72 (BEAM Co.) photoanisotropic material was used for photoalignment in this study. The peak absorption of PAAD-72 occurs at 424 nm wavelength. PAAD series materials absorb in the visible spectrum, and blue or green laser beams can be used for recording. This is particularly important because a large variety of high power and relatively inexpensive laser sources are available for those wavelengths. For deposition, PAAD-72 is dissolved in dimethylformamide (DMF) at a concentration of 0.5–1.5 wt. %. The solution is spin-coated on glass substrates at typically 3000 rpm speed for 30 s. The thickness of the PAAD layer obtained in this regime is , and it is transparent. Following the photoalignment, for fabrication of LCP DWs, a LC monomer solution is coated over the photoaligned layer. The spin coating time, typically 1 min, combined with different acceleration and speed regimes, makes it possible to produce layers of different thickness, hence, of different diffraction spectra. LCP layers with peak diffraction efficiency at 442, 488, or 532 nm are of particular interest. The LC monomer is cured with unpolarized UV light of 365 nm wavelength and intensity with 5 min exposure time.
High diffraction efficiency can be obtained over the visible spectrum using either conventional techniques developed for broadband waveplates , by combining diffractive waveplates layers , as well as by using chiral LCP layers of opposite handedness [14,15]. In this study, the first layer was obtained by spin-coating LC monomer solution RLCS-7/RH-VIS (BEAM Co.) at 1100 rpm, while the second layer was obtained from a solution of LC monomer RLCS-7/LH-VIS (BEAM Co.) under the same deposition conditions.
NLC cells were made using substrates coated with ITO or graphene-oxide-based electroconductive layers. The assembled cells were photoaligned and filled with nematic LC R-237 (BEAM Co.) characterized by low birefringence, . For reflective components, CLC mixtures were used with 532 nm wavelength at the center of its bandgap in cells with 4 μm gap.
To work with the best beam quality and high enough power, we used gas lasers, an argon-ion laser operated at 488 nm wavelength or a He–Cd laser operated at 442 nm wavelength, in optical recording setups. A system of lenses expands the beam to typically 1 in. in diameter, and a diaphragm selects a central area of the beam with spatially homogeneous power distribution.
3. LIQUID CRYSTAL POLYMER WAVEPLATE LENS ARRAY (WLA)
A. Architecture with Continuous Structure
A broadband waveplate lens (BB-WL), 20 mm in diameter and 410 mm focal length at 488 nm wavelength, was used to convert linear polarization of the input beam into the modulation pattern corresponding to the molecular orientation in the WL being recorded. It is, essentially, Fermat’s spiral, , where is the radial coordinate and is the angle of molecular orientation in the waveplate. This technique of printing DW components  requires that the spatial frequency of molecular orientation in the template waveplate be two times smaller than the spatial frequency of the component being recorded.
Lenslets of different sizes are obtained by focusing the polarization modulation pattern at the output of the BB-WL onto the substrate with the photoalignment layer. The size and the focal length of the lenslets can be varied by changing the position of the substrate in the focal region and the projection conditions. The paraxial focal length is related to grating spacing at a distance from the center of the lenslet as for wavelength . The individual lenslets were recorded with 1 min exposure time at beam power density measured at the input of BB-WL. A programmable 2D mechanical stage allowed controlling the position of the substrate and the recording pattern. The advantage of this system is versatility in the number of array elements and feasible array architectures.
Figure 1 shows the molecular alignment pattern in a square grid of round LCP WLs, and an array of lenslets, each lenslet 2 mm in diameter. Note that the arrays of DW optical structures can be designed to maintain continuity of the optical axis orientation across the boundaries between elements of the array, as illustrated in Fig. 1(a). The array can further be used as a template for printing derivative WLAs. Photos of the template array are shown in Figs. 1(b) and 1(c), and the diffraction spectra of both the template and the derivative arrays are shown in Fig. 1(d). The derivative LCP WLA was optimized for peak diffraction efficiency (half-wave retardation) at 532 nm wavelength.
Figures 2(a) and 2(b) illustrate the optical axis pattern of a single lenslet of the DW lenslet array shown in Fig. 1(b). The fringe spacing at 0.9 mm from the center of one of the lenslets in this array was 14.4 μm in the template WLA, Fig. 2(c), and 7.2 μm in the derivative WLA, Fig. 2(d). This corresponded to 26.6 mm focal length of the lenslets at 488 nm for the template WLA and 12.2 mm focal length at 532 nm wavelength for the derivative WLA. Note the doubling of the fringe spatial frequency in the derivative WLA also is revealed in twice-reduced focal length of the lenslets. Because the template WLA is essentially a half-wave retarder with a complex pattern of optical axis orientation, the local spatial derivative of the optical axis orientation angle in the derivative WLA is twice that of the template WLA.
The pattern of the optical anisotropy axis alignment in the plane of the lenslets, as measured with a Mueller matrix spectropolarimeter (Axoscan), is shown in Figs. 2(e) and 2(f). The color change from blue to red corresponds to 180° rotation of the anisotropy axis.
The basic effects of the WLA on a light beam are shown in Fig. 3. The beam is split into beamlets focused or defocused with focal length , with the sign of the focal length depending on the handedness of circular polarization of the beam. Both focused and defocused beams are present for unpolarized or linearly polarized beams. Leakage of light into the undiffracted order is also evident around the edges of the lenslets where the LCP orientation pattern is lost due to limited recording resolution as well as due to defects in the orientation patterns between the lenslets. Far from the focus, the beam is expanded and homogenized independent of polarization.
B. Architectures with Overlapping Structures
The optical properties of WLAs depend both on the ability of the LC material to orient according to the pattern created by photoalignment at the surfaces of substrates, as well as on packaging of the lenslets. WLAs provide unprecedented versatility of array architectures. Two examples, a brick-wall pattern and a fish-scale array pattern, are shown in Figs. 4 and 5.
The brick-wall LCP WLA, Fig. 4, comprises square lenslets of sizes, each having 25 mm focal length at 442 nm and minimum fringe spacing of 6 μm. The lenslets were recorded individually by translating the substrate in and directions by motorized stages. The He–Cd laser beam provided power density allowing only 1 min exposure for individual lenslets. LCP coating regimes were adjusted for half-wave retardation at 442 nm wavelength, Fig. 4(d).
The fish-scale array elements of Fig. 5 were recorded in 1 min intervals through a 4.5 mm diameter mask with 3.6 mm shifts in and directions between exposures. The LCP WLA further used as a template for recording new arrays is demonstrated in Figs. 5(a) and 5(b). It is characterized by broadband diffraction in the visible spectrum, 400–700 nm, Fig. 5(d). The focal length of the template lenslets is 50 mm at 442 nm wavelength with 12.2 μm fringe spacing at the edge.
The lenslet structures in overlapping areas viewed with a polarizing microscope are shown in Fig. 6. The transition areas between the lenslets are around 10 μm wide.
4. ELECTRICALLY SWITCHABLE NEMATIC LIQUID CRYSTAL WAVEPLATE LENS ARRAYS
LC WLAs can be effective beam-shaping elements for light beams changing their optical state from diffractive/diffusive to transparent with application of an electric field . Optical beam shaping and diffusing with static components is a well-known technology . Test LC WLA cells were made using substrates coated with PAAD-72 (0.5 wt. %) in a solution of DMF. The empty cell was exposed for 10 min to an expanded and collimated argon-ion laser beam of power density through the template LCP WLA. The cell with 4 μm gap was then filled with LC. The obtained orientation pattern in the LC cell is as smooth as for samples made of LCP, as is evident by comparison of Figs. 2(b) and 2(d) with Figs. 7(a) and 7(b).
The clear nondiffractive state of LC WLA is achieved due to switching of the alignment of LC molecules from a patterned to homeotropic state at application of an electric field. Attenuation of a light beam propagated through the WLA can be characterized as the ratio of light intensity in diffractive (no voltage) and nondiffractive (voltage on) states. Argon-ion laser beams of different wavelengths used for such characterization were expanded and collimated to fill the aperture of a power meter at a distance 1 m from the LC WLA. Attenuation as a function of applied voltage is shown in Fig. 7(f) for 514 nm wavelength.
The attenuation can be increased throughout the visible spectrum by combining two or more LC WLAs. Figure 8 shows the effect of a system of two LC WLAs on radiation of three wavelengths of an argon-ion laser beam.
The attenuation was increased from about 10 (single LC WLA) to 106 (two LC WLAs) for 514 nm wavelength and was equal to 108 for 488 nm and 45 for 457 nm wavelength.
Two NLC WLAs were combined for switching contrast enhancement by reducing light leakage. Empty cells were exposed to a He–Cd laser beam using template fish-scale LCP WLA. The pattern was recorded at power density during 25 min. The cells were filled with NLC R-237 (BEAM Co.). The effect of the system of LC WLAs on a laser beam and on visibility of an eyechart at 2 m distance from WLAs is demonstrated in Fig. 9.
The attenuation of the system depends on the arrangement of the two arrays. If each of the arrays focuses a laser beam of the same circular polarization, the system of two arrays in series collimates the beam because the first array reverses the circular polarization handedness. If one of the WLAs in the system focuses while the second one defocuses light of one circular polarization handedness, the system focuses (or defocuses) light with effective focal length half that of a single array. The transmission of a single LC WLA was 84% at 10 V. The average attenuation coefficient at 1 m distance was 70 for a single LC WLA and 420 for the combined system of two WLAs.
A fish-scale LCP WLA of lenslets of 15 mm focal length, 5.4 μm minimum edge fringe spacing, 2.5 mm diameter, and 1.8 mm shift between lenslets in and directions is shown in Fig. 10. With the LCP layer adjusted for half-wave retardation at 442 nm wavelength, it was used to record a derivative NLC WLA. The lenslets in derivative NLC WLAs are characterized by 6.3 mm focal length for 532 nm wavelength and 2.7 μm fringe spacing at their edge.
Figure 11 demonstrates the attenuation obtained with two NLC WLAs. The average attenuation coefficient at 1 m distance was 35 for a single NLC WLA and 550 with two such arrays. Thus, WLAs are highly suitable for beam control and shaping applications with advantages in resolution, optical strength, fabrication cost, and efficiency.
5. REFLECTIVE CHOLESTERIC LIQUID CRYSTAL WAVEPLATE LENS ARRAYS
Figure 12(a) shows the effect of a CLC WLA on a green laser beam printed from the template LCP array illustrated in Fig. 1. As expected, the beam is reflected for one of circular polarization handedness (left-hand circular polarization [LHCP] in the particular case) and transmitted for the orthogonal one (right-hand circular polarization [RHCP] in this particular case) for the specific CLC mixture.
The beam transmitted through the CLC WLA does not show wavefront changes. However, it clearly reveals lensing effects, focusing and defocusing, in the reflected bandgap mode, Figs. 12(d) and 12(e). Just as for LCP WLs, the lenslets are concave for the beam reflected from one side of the CLC WLA, and they are convex for reflection from the opposite side. The lenslets are concave for the side of the CLC cell that faced the recording beam when using LCP WLA that focused LHCP beam. The WLA elements have 12.2 mm focal length, half the focal length of each lenslet of the template LCP array. The focusing/defocusing features of a CLC WL are demonstrated in Figs. 13 and 14.
Wavefront modulation induced by the CLC WL element was directly measured with the aid of a Shack–Hartmann wavefront sensor, Fig. 15. To keep the modulation at a minimum, the CLC cell was made with no spacers for this purpose, which typically results in 1–2 μm layer thickness. The bell-shaped (parabolic) modulation was evident at the reflected beam and was equal to three waves at 543 nm. The transmitted beam though had a practically flat phase profile over most of the beam area with maximum change in phase less than one wave.
6. VECTOR VORTEX WAVEPLATE ARRAYS
Digital polarization holography  is the best tool for recording DWAs, particularly, complex structures with continuous orientation patterns. The continuous pattern of lens arrays discussed above is only one example. Other interesting examples include arrays of vector vortex waveplates (VVWs) of different topological charges. Figure 16 illustrates such an array for topological charge .
An electrically switchable NLC array of VVWs of is shown in Fig. 17. At voltage-off state, Fig. 17(a), the array produces a ring pattern due to redistribution of light energy from the center to the periphery of the array [23,24]. At voltage values of the order of 10 V (at 1 kHz), the NLC molecules get aligned perpendicular to the cell substrates, eliminating the array function, and the light beam propagates through the cell with no changes, Fig. 17(b). When illuminated by white light, and at application of voltage, the spectrum of the transmitted light varies according to phase retardation condition. Light of wavelengths near full-wave retardation condition is transmitted without diffraction, while other wavelengths, particularly those closer to the half-wave retardation condition, are deflected into a ring, Fig. 17(c). In a NLC cell with small variations of the cell gap, different VVW pixels output light of different color as seen in Fig. 17(c). An individual VVW pixel color is controlled with very small variations of voltage, Fig. 17(d).
DW array technology has been under maturation for many years now. LC orientation patterns in those arrays, due to high spatial resolution, present novel types of diffraction gratings. In the case of VVWs, these are gratings of topological singularities.
LCP DW arrays can be made on polymer films, and switchable LC DW arrays can be made using thin, flexible, polymer substrates. All polymer realization of DW arrays considerably expands their applications. Figure 18(a) shows an array of lenses produced as a coating on a polycarbonate substrate, whereas Figs. 18(b) and 18(c) show an array of VVWs on a curved polycarbonate lens. An electrically switchable array of lenses made of polycarbonate substrates is shown in Figs. 18(d) and 18(e) in both off and on states.
The clear/transmittive state of an LC-based WLA or VVW array is typically obtained with application of voltage. However, the arrays can be combined to compensate for the focusing action to produce a clear state at the absence of voltage. Figure 19 demonstrates the concept for two identical WL elements that are arranged with opposite signs with respect to each other. A half-wave retarder, a planar-aligned NLC cell meeting the half-wave retardation condition, switches the handedness of polarization components at the output of the first lens, allowing the second lens to restore the collimation of the incident beam. Switching off the half-wave action by application of voltage leads the second lens to double the effective focal length of the system, thus generating a divergent beam in the far field independent on polarization of the incident beam.
The WLAs provide a unique opportunity for such a compensating function because they can be brought very close to each other due to their thinness. Figure 19 demonstrates the divergent and compensating states of a brick-wall array. Thus, switchable lenslet arrays may act as pixels of projection displays producing high contrast with no polarizers.
Among other important applications, let us mention the so-called smart windows that are switched between clear and diffuse states for privacy or to act as projection screens. Some of such functionality is currently obtained by polymer-dispersed LCs (PDLCs). Their major drawback is high switching voltages, . Not only are LC WLAs switched at low voltages; they also can be used for active light distribution and serve an esthetic purpose as well.
A better-known application of lens arrays is in beam shaping devices. The diffractive waveplate technology allows obtaining lensing patterns at very high spatial frequencies, thus enabling fabrication of high-efficiency, high-quality, low-loss beam shaping components, including switchable.
A sample of beam shaping due to orientation patterning of a LCP using digital light polarization holography is shown in Fig. 20. The orientation pattern presents an extreme case of an “array” that looks practically random in both distribution and functionality of array elements.
The components made of LC polymers are highly durable and radiation resistant, adequate for most applications. The broadband waveplate lens, for example, that we used as a template for recording lenslet arrays, was fabricated still in 2013, and its performance did not deteriorate during its extensive use. LC and LCP diffractive waveplates can be optimized for visible, near infrared, and even in certain regions of mid- and far-infrared spectral bands [25–27].
Summarizing, arrays of diffractive waveplates present a wonderful challenge and an opportunity for applications of digital polarization holography with applications ranging from smart windows to displays and optical communication.
Natick Soldier Research, Development and Engineering Center (NSRDEC).
We thank U. Hrozhyk, Z. Liao, A. Tabirian, L. de Sio, L. Wickboldt, and H. Xianyu for discussions and assistance at different stages of the development.
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