Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Switchable Plasmonic Holograms Utilizing the Electro-Optic Effect of a Liquid-Crystal Circular Polarizer Bernhard Atorf, Hoda Rasouli, Holger Mühlenbernd, Bernhard J. Reineke, Thomas Zentgraf, and Heinz Kitzerow* Center for Optoelectronics and Photonics Paderborn (CeOPP), University of Paderborn, Warburger Str. 100, 33098 Paderborn, Germany ABSTRACT: A concept for switchable holograms with high diffraction efficiency based on geometrical metasurfaces is proposed. The phase hologram studied is composed of plasmonic nanoantennae with varying orientations. Its diffraction pattern is known to depend on the state of polarization of the incident radiation. Maximum brightness of the reproduced holographic images is obtained by circularly polarized radiation, while the position of the respective image depends on the handedness of this circularly polarized radiation. For the purpose of switching, the hologram is illuminated through an electrically addressable liquid-crystal filter, which transforms linear polarization to either right circular or left circular polarization, depending on the applied voltage. First experimental results indicate reasonable switching when a twisted nematic active layer and a uniform nematic passive layer are combined in a compact polarization converter. phase19). Thus, phase objects (including holograms) can be manufactured by carefully designing the local distribution of the nanoantenna alignment. If the gold nanoantennas, a separating dielectric layer, and a uniform gold layer form local Fabry− Perot cavities (Figure 1b), reflective holograms with very high diffraction efficiencies can be obtained.17,18 Figure 1c−e shows the dependence of the phase delay on the nanoantenna orientation, an electron micrograph of the gold nanoantennas composing a hologram, and a photograph of its reconstructed holographic image, respectively. In a previous paper,18 the development of geometric metasurface holograms has been described that may provide a reconstructed holographic image in a particular position under illumination with circularly polarized light of a certain handedness. However, when the same hologram is illuminated with circularly polarized light of the opposite handedness, the reconstructed image appears at a different position or even a different image appears. Two holographic images with a lower intensity appear under illumination with unpolarized or linearly polarized light. The present paper describes first attempts to combine such holograms with a switchable polarizing filter based on electrically addressed liquid crystals (LCs).20 The filter is expected to provide right circularly polarized (RCP) light in one switching state and left circularly polarized (LCP) light in the opposite state to enable most effective switching between two holographic images. In the following section, we discuss different options, which type of LC and which electro-optic
1. INTRODUCTION The development of optical metamaterials1,2effective media that are composed of different materials and very specifically structured on a subwavelength length scalehas changed some fundamental assumptions about the achievable range of optical properties. For example, a large variability of the magnetic permeability at optical frequencies, extreme values of the refractive index (including negative values), and tailoring of the spatial distribution of the refractive index have been demonstrated.3,4 Possible applications include, for example, the fabrication of super- and hyperlenses with subwavelength resolution, integrated waveguiding by micro- and nanostructured media, and even optical cloaking.5−7 Tunable or switchable optical metamaterials pave the way toward practically applicable and active optical devices.8−11 Two-dimensional structures with subwavelength featuresmetasurfaces12are readily accessible by lithographic techniques and enable optical filters or phase plates with unusual properties. Despite their easier fabrication on planar surfaces, metasurfaces have shown great potential in altering the wavefront of light in nearly arbitrarily ways, for example, to form lenses or other phase masks.13,14 Recently, holograms based on plasmonic nanoantenna metasurfaces have found particular attention.15−18 They may be composed of simple linear gold antennas with varying azimuthal angles (Figure 1a,d), which form a geometric metasurface. If the metasurface, as shown in Figure 1, is illuminated with an elliptically polarized beam, nanoantennas with different alignment angles are excited at slightly different times, which cause a phase shift between the respective scattered beams (geometric phase or Pancharatnam−Berry © XXXX American Chemical Society
Received: December 22, 2017 Revised: February 6, 2018 Published: February 6, 2018 A
DOI: 10.1021/acs.jpcc.7b12609 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 1. Reflective holograms with high diffraction efficiency based on geometric metasurfaces composed of metallic nanoantennae. (a) Schematic representation of a gold nanorod and its azimuthal orientation angle ϕ. (b) Side view of the layered nanostructure. (c) Relation between the azimuthal angle ϕ and the phase delay appearing for illumination with circularly polarized light. (d) Electron micrograph of a hologram. (e) Holographic image reproduced from the hologram. Reprinted from ref 18 with kind permission by the Nature Publishing Group.
effect might be used to achieve the targeted optical effect. The subsequent sections describe an experimental investigation for one of these options. The results seem to indicate that integrated switchable holograms based on geometric metasurfaces can be manufactured, where the hologram and the electrically addressed polarization converter are combined in a compact single device. Our first attempt is not perfect and not fully integrated, but a feasible way to overcome the remaining deficiency is proposed in the last section. The way toward full integration of the polarization converter and the hologram is straightforward.
(2) A passive circular polarizer (e.g., based on CLC, BP, TGB, or FLC) combined with an optical retarder, which can be switched from zero retardation to a retardation of π (changing the handedness of the circularly polarized radiation in the latter case). The Frederiks effect in a uniformly aligned nematic LC (NLC)25 or the Kerr effect of BP26−28 could be used for an active component in this case. The latter would have the advantage that no alignment layer is necessary and could possibly provide faster switching than NLC but would presumably require higher voltages. (3) A passive linear polarizer followed by a switchable optical retarder, where the difference of optical path lengths between the ordinary and the extraordinary beam Δn·d can be switched either from −λ/4 to +λ/4 or from λ/4 to 3λ/4. A dual-frequency addressable BP29 or an NLC25 could be used, respectively. For either material, an appropriate voltage would have to be applied in both switching states. The choice of compounds and the adjustment of these voltages would be very challenging. (4) A passive linear polarizer followed by a switchable optical retarder, where the path length difference of λ/4 is fixed and the azimuthal angle φc of the optical axis of the retarder can be changed by π/2 (from φc = +π/4 to φc = −π/4 with respect to the plane of polarization of the incident light). For this purpose, a surface-stabilized FLC30 would be appropriate and could provide fast switching. However, finding an FLC with a sufficiently large and temperature-independent switching angle of π/ 2 is difficult. (5) A passive linear polarizer followed by a switchable optical rotator and a passive retarder with a path length difference of λ/4. The active layer (optical rotator) could consist of a switchable retarder, a λ/2 plate with
2. METHODS The development of an integrated switchable hologram based on the type of geometric metasurfaces described above requires a polarization converter that enables switching between RCP and LCP light. Various solid-state optical modulatorssuch as Pockels cells or photoelastic modulatorsmay be considered for this purpose. However, in this study, we have focused our attention on LCs because a combination of only two thin LC layers (d ≤ 100 μm) in close proximity should be sufficient. The large variety of LCs and their versatile optical properties enable different approaches toward the goal of switching between RCP and LCP light at a specific wavelength λ, depending on the applied voltage: (1) One can use an LC that reflects or transmits circularly polarized light owing to its helical phase structure, for example, a cholesteric LC(CLC), blue phase (BP), twist grain boundary phase (TGB), or ferroelectric LC (FLC).21 Field-induced helical unwinding22−24 could provide switching from circularly polarized to unpolarized light. However, we prefer switching from RCP to LCP and vice versa. B
DOI: 10.1021/acs.jpcc.7b12609 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 2. (a,b) LC cell transforming linearly polarized light to (a) RCP light if no voltage is applied or (b) LCP light if a voltage of a few volts is applied. (c,d) Experimental setups used in this study. P: polarizer; TN: twisted nematic cell; λ/4: quarter-wave plate; H: hologram; and D: detector. (e) Fully integrated switchable hologram, which combines the layers P, TN, λ/4, and H in a single device.
Thorlabs, λ = 980 nm, λ−1 = 10.204 cm−1, P = 10 mW) through a switchable electro-optic polarizing filter, which consists of a linear polarizer, a TN cell (without analyzer), and a passive λ/4 plate aligned with its optical axis at an azimuthal angle of 45° with respect to the initial plane of polarization of the incident light (Figure 2). For preliminary studies, we filled commercial test cells made of glass (from EHC, Japan, cell gap 10 or 50 μm), which are equipped with transparent indium tin oxide (ITO) electrodes and appropriate polyimide alignment layers, with the LC mixture E7 (Merck). While these TN cells are quite insensitive to variations of the wavenumber and the ambient temperature, the λ/4 plate needed more careful adjustment. The latter was manufactured by in situ photopolymerization of a uniformly aligned photoreactive NLC,32 which yields a birefringent, highly cross-linked polymer NLC (PNLC). The photoreactive compounds used for this purpose are displayed in Figure 3. To control the sample thickness
varying retardations [as discussed in paragraph (2)], or with varying azimuthal angles [as discussed in paragraph (4)]. Alternatively, a twisted nematic (TN) cell,31 the LC analogue of Reusch’s pile of mica plates, could be applied for this purpose. From these few of many alternatives listed above, we have chosen the last option for our study. The TN cell is known to be a very robust electro-optic element.20,31 It utilizes a twisted NLC layer between two glass substrates equipped with transparent electrodes, where alignment layers provide planar anchoring with azimuthal alignment directions differing by π/2 at the two substrates. Illuminated with linearly polarized light, the twisted director field of the initial state (without voltage) causes a rotation of the plane of polarization by π/2. Application of a sufficiently high voltage yields a nontwisted perpendicular orientation of the director, which leaves the plane of polarization of the transmitted light unchanged. We decided to use this effect, which has been very well-studied and applied for many years in most flat-panel displays, because it is known to rotate the plane of polarization reliably by π/2, independent on the sample thickness d (provided that d ≫ λ) and almost independent on wavelength and on temperature. The polarization converter targeted in this study is shown in Figure 2. It consists of a TN cell, which rotates the plane of polarization at V = 0 V from an azimuthal angle of φp = π/2 of the incident light to φp = π for the transmitted light and a passive λ/4 plate with its optical axis adjusted at φc = π/4. Therefore, the device finally delivers RCP light. If a voltage of a few volts is applied, the light transmitted through the TN cell is unaltered (i.e., linearly polarized with φp = π/2) and the light finally transmitted through the λ/4 plate is LCP.
Figure 3. Photoreactive monomer compounds used in this study.
accurately, we again used commercial test cells (from EHC, Japan) with cell gaps of d = 3 μm and d = 4 μm, which were filled with the cross-linkable NLC methylbenzene-1,4-diyl bis{4-[3-(acryloyloxy)propoxy]benzoate} (RM257, Merck) (d = 3 μm) or with a mixture containing 85 wt % RM257 and 15 wt % n-dodecyl acrylate (C12A, Sigma-Aldrich) (d = 4 μm), respectively. The photoreactive NLC was doped with a small amount of radical photoinitiator (Irgacure 561, Ciba Geigy),
3. EXPERIMENTAL SECTION The metasurface hologram used in this study was designed and fabricated by e-beam lithography, as described earlier. It was exposed to radiation from a laser diode (type L980P010, C
DOI: 10.1021/acs.jpcc.7b12609 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 4. Performance of λ/4 retardation plates made of the uniformly aligned NLC RM257. (a) IR transmission spectra of the following setup: a linear polarizer (azimuthal angle φp = 0°)/NLC (d = 3 μm, optical axis at φc = 45°)/analyzer at four different angles φa. (b) Normalized Stokes vector components34 vs wavenumber. (c,d) Wavenumber corresponding to a retardation of λ/4 vs temperature: (c) Unpolymerized NLC (d = 3 μm) on (solid red diamond) heating and (solid blue triangle) cooling and (solid maroon rectangle) polymerized NLC. Inset: (solid red diamond) Birefringence Δn(T) of the unpolymerized sample during the first heating and () orientational order parameter S(T). (d) Polymerized NLC (d = 4 μm) at (solid blue rectangle) V = 0 V and (solid red triangle) V = 50 V.
4. RESULTS
and the photoreaction was performed by irradiation with an ultraviolet (UV)-emitting diode (type CUN*6A1A, Seoul Optodevice, λ = 365 nm) for 75 min. Prior to UV exposure, the transmission spectra of the respective birefringent cell placed between two polarizers were recorded as a function of temperature. Then, the temperature was adjusted to an appropriate value and controlled during the UV-initiated polymerization reaction to achieve an optical retardation of π/2 at the targeted wavenumber λ−1 = 10.204 cm−1. The results will be described in more detail in the next section. After accumulating sufficient experience with the fabrication of birefringent NLC polymer films acting as a λ/4 plate, the polymerized films were separated from the substrates and integrated with the TN cell to form a switchable circularly polarizing filter. After polymerization, the cell containing the λ/ 4 retardation film was soaked with sodium hydroxide solution, which enabled its separation from the glass substrates. The isolated retarder was then transferred to a new glass substrate covered with ITO electrodes. Subsequently, an aqueous solution of poly(vinyl cinnamate) was deposited by spincoating on the open side of the retarder film and exposed to linearly polarized UV radiation to yield an LC alignment layer through the formation of a linearly polymerized photopolymer (LPP).33 A second glass substrate, equipped with an ITO counter electrode and a planar alignment layer made of rubbed poly(vinyl alcohol), separated by 100 μm Mylar spacers, was affixed. Finally, the cell gap between the two twisted alignment layers was filled with the LC mixture E7, thereby yielding the polarization switch shown in Figure 2.
Fabrication of the holograms has been described previously,18 and the principles of TN cells are very well-known. However, the application of photoreactive mesogens for fabricating an optical retarder required a rather specific manufacturing process to achieve a retardation of λ/4 at the desired wavelength of λ = 980 nm (λ−1 = 10.204 cm−1). For preliminary optical characterization of the photocurable NLC, we placed a uniformly aligned celladjusted with its optical axis perpendicular to the light propagation at an azimuthal angle of φc = 45°between a linear polarizer with a horizontal plane of polarization (φp = 0°) and a linear analyzer with varying azimuthal angles φa. Using this setup, the transmission spectrum was measured for four different angles, φa = −45°, 0°, 45°, and 90° (Figure 4a). For ideally polarized light, the four components I, M, C, and S of the Stokes vector34 can be calculated from the intensities I−45°, I0°, I+45°, and I90° measured in this setup I = I0 ° + I90 ° M = I0 ° − I90 ° C = I45 ° − I −45 ° S = √ (I 2 − M 2 − C 2 )
(1)
If the sample represents a homogeneous linear retarder adjusted with its optical axis at an azimuthal angle φc = 45°, the following intensities are expected D
DOI: 10.1021/acs.jpcc.7b12609 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C 1 I(1 + cos δ) = I cos2(δ /2) 2 1 I+45 ° = I −45 ° = I 2 1 I90 ° = I(1 − cos δ) = I sin 2(δ /2) 2
diffraction spots to the right and to the left of the grating were measured by means of an Si sensor power meter (Thorlabs, sensitive from 400 to 1.100 nm). The state of polarization of the incident radiation was controlled by transmitting the beam through a linear polarizer, a TN cell, and a λ/4 plate made of PNLCs. Two types of TN cells were prepared by filling the NLC mixture E7 in a commercial test cell with cell gaps of d = 10 μm and d = 50 μm, respectively. The results are shown in Figure 5. As expected, the polarizing filter setup delivers RCP
I0 ° =
(2)
where I is the total intensity of the incident light and δ = 2πΔnd/λ is the optical retardation. In agreement with this expectation, the intensities I+45° and I−45° measured at φa = −45° and φa = 45°, respectively, are equal (Figure 4a). Otherwise, the transmission spectra differ from each other, except for one specific wavenumber λ−1δ=π/2, where the initially linearly polarized light is transformed to circularly polarized light (Figure 4a). From the spectra (Figure 4a), the components of the normalized Stokes vector SN can be calculated (Figure 4b), with SN = (1, 0, 0, 1)T at the wavenumber λ−1δ=π/2. When the temperature of the NLC retarder cell increases, the wavenumber λ−1δ=π/2 is shifted toward larger values (Figure 4c). The respective birefringence Δn can be calculated from the corresponding condition δ = 2πΔndλ−1 = π/2. On first heating of the nonpolymerized sample, the increase of the wavenumber λ−1δ=π/2 with temperature is relatively large (red diamonds in Figure 4c). The size of the decrease of the corresponding birefringence Δn(T) can be explained by the scalar order parameter S(T) calculated from the Maier−Saupe theory20 for the compound RM257 (clearing temperature TNI = 128 °C) (inset in Figure 4c). However, on subsequent cooling and heating cycles, the wavenumber λ−1δ=π/2 shows a much lower temperature dependence (≈1−6 cm−1/K). We conclude that the first heating above 100 °C initiates thermal polymerization, which is sufficient to fix the order parameter. The assumption of thermal prepolymerization was confirmed by the observation that a different sample, which was heated above the clearing temperature TNI = 128 °C, remained isotropic after cooling to room temperature even without any UV exposure. The birefringent sample corresponding to the data shown in Figure 4c was photocured by UV exposure at a temperature of Tpolym = 70 °C. Subsequently, it remained birefringent even on heating up to 200 °C. The residual dependence of the birefringence Δn and thus the wavenumber λ−1δ=π/2 on temperature can be explained by thermal expansion. The data shown in Figure 4b indicate a dispersion of the birefringence of ∂(Δn)/∂(λ−1) ≈ 2 × 10−5 cm. This yields a temperature coefficient as small as ∂(Δn)/∂(T) = ∂(Δn)/∂(λ−1) × ∂(λ−1)/∂(T) ≈ 2−12 × 10−5 K−1. In summary, the photopolymerization of the reactive nematic compound yields a stable, slightly temperaturesensitive optical retarder. The wavenumber λ−1δ=π/2, where this retarder operates as a quarter-wave plate, can be fine-tuned by the thermal pretreatment of the nonpolymerized sample. For the operation of the modulator shown in Figure 2, it is essential that the retarder is fully polymerized and thus passive, that is, not sensitive to an applied voltage. This property was tested by applying a very high voltage of 50 V to the retarder (Figure 4d). The test confirms that there is no difference of the optical performances at 0 and 50 V, once the cell is photocured (Figure 4d). For a first test of the individual optical components, a simple diffraction grating made of a geometric metasurface was exposed to the collimated beam of a laser diode operating at λ = 980 nm (Figure 2c). The intensities of the first-order
Figure 5. Relative power of the diffraction spots (red rectangle, green circle, blue diamond) to the left and (solid red rectangle, solid green circle, solid blue diamond) to the right of a geometric metasurface grating illuminated through (red rectangle, solid red rectangle) a TN cell with d = 10 μm and a λ/4 plate, (green circle, solid green circle) a TN cell with d = 50 μm and a λ/4 plate, and (blue diamond, solid blue diamond) an integrated RCP/LCP electro-optic switch incorporating both a TN cell (d = 100 μm) and a λ/4 plate.
light, when no voltage is applied to the TN cell. Consequently, the diffraction spot to the right of the hologram (filled squares and circles in Figure 5) exhibits a much larger intensity than the diffraction spot to the left (open squares and circles). However, the intensity ratios are reversed, when a voltage of about 4 V (sufficiently larger than the threshold voltage of about 2 V) is applied to the TN cell. This indicates that the light incident on the geometric metasurface grating is LCP for V ≥ 4 V, as intended. Comparing the two TN cells with d = 10 μm (squares) and d = 50 μm (circles) shows that the dependence of the diffraction intensities on the applied voltage is essentially independent on the sample thickness d. This corresponds to the well-known behavior of TN cells, where the influences of the cell gap d on the electric field strength and on the twist energy of the director field compensate each other.20 Once the separate optical components were shown to operate properly, the next challenge was separating the λ/4 retardation film from its confining substrates to integrate it with the TN cell into a compact device (Figure 2d). The λ/4 plate used for the experiment described above contained a mixture of 85 wt % RM257 and 15 wt % C12A. Because this mixture exhibits a lower birefringence than pure RM257, a film thickness of 4 μm (instead of 3 μm for samples with pure RM257) was used. The addition of the monofunctional compound C12A was motivated by our expectation that the resulting polymer shows a lower cross-linking density and can be more easily separated from the glass substrate than the highly cross-linked films obtained from the bifunctional reactive monomer RM257. However, this expectation turned out to be wrong. The films obtained from RM257/C12A mixtures adhere still vigorously to the substrate. Thus, we tried an alternative E
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The Journal of Physical Chemistry C method to separate the retarder films from the substrates. After completing photopolymerization, the cells containing the retarder film are soaked in sodium hydroxide solution until the polymer film is released from the substrates. This latter method also works very well with the retarder films manufactured from pure RM257. The respective retarder film was isolated accordingly and transferred to a new ITO-coated substrate to manufacture a TN cell with an integrated λ/4 retardation film (as described in the last paragraph of the Experiment section). To cover the retarder film with an LC alignment layer without rubbing, the LPP effect33 was used. Because its anchoring energy is known to be weaker than the anchoring energy of rubbed polymer layers,35,36 a cell gap as large as 100 μm was used to keep the elastic energy of the TN director field small. Qualitatively, the integrated switchable circular polarizer (diamonds in Figure 5) shows the same effect on the diffraction intensities as the separate optical components (squares and circles in Figure 5), that is, switching of the major diffraction intensity from the left to the right side of the hologram, indicating a change of the handedness of the elliptically polarized incident light at moderate voltages of a few volts. However, the asymmetry of the diffraction pattern is less pronounced in the field-off state. This remaining deficiency is discussed in the next section of this article. Illuminating a holographic image through this setup reveals that the reproduced image appears in different positions for the two switching states, as expected. If an imaging charge-coupled device detector is placed in one of these two positions, the image reproduced by diffraction appears and nearly disappears in the field-on and field-off states, respectively (Figure 6).
Fanchoring =
1 Wϕ(ϕ − ϕ0)2 2
(3)
and the free energy of the twist deformation per volume ftwist =
⎛1 ⎞2 1 1 K 22(∂ϕ/∂z)2 = K 22⎜ π /d⎟ ⎝2 ⎠ 2 2
(4)
that is, Fanchoring = f twist·d, yields ϕ − ϕ0 =
1 π[K 22/(Wϕd)]1/2 2
(5)
where ϕ is the azimuthal angle of the director at the alignment layer, ϕ0 is its value at the minimum surface energy (easy axis20), K22 is the twist elastic constant, and Wϕ is the anchoring energy coefficient. Inserting typical values,20,33 K22 ≈ 5 × 10−12 N, Wϕ ≈ 5 × 10−6 J/m2, and the thickness d = 100 μm of the TN cell, indicates that the deviation of the director alignment from the ideal case can be expected to be ϕ − ϕ0 ≈ 0.05π, which corresponds to 9°. This deviation can be reduced by adding a chiral mesogenic dopant to the TN layer, which causes an intrinsic twist, thereby compensating the deformation energy f twist. We suspect that the passive PNLC layer influences the surface anchoring of the director of the neighboring active NLC too. For the targeted optical performance, it is necessary to align the director of the PNLC layer at an azimuthal angle of 45° with respect to the easy axis of the LPP alignment layer. Owing to its anisotropy, the surface of the PNLC layer is likely to have an aligning effect, which competes with the aligning effect of the LPP layer. A very thin isotropic layer separating the LPP layer from the PNLC layer could solve this problem.
6. CONCLUSIONS In summary, the results presented here demonstrate that switchable holograms can be manufactured, which consist of a geometrical metasurface and a polarizing filter transforming linearly polarized into either right-handed or left-handed circularly polarized light, depending on the applied voltage. So far, this switchable polarizing filter works well, when its two components, an active TN layer and a passive PNLC retarder, are separated. However, our prototype of an integrated switchable polarizer combining the active and the passive layer still needs to be improved. In future attempts, adding a chiral dopant to the twisted NLC and separating the NLC alignment layer and the PNLC surface by a thin isotropic separating layer are likely to overcome this deficiency. Once this remaining problem is solved, it is straightforward to assemble the entire layer sequence on the substrate that carries the metasurface, thereby unifying the switchable linear → circular polarization converter and the hologram in a single switchable holographic device (Figure 2e).
Figure 6. Reconstruction of the hologram from the geometric metasurface described in ref 18 (Figure 1) by means of the integrated RCP/LCP electro-optic switch delineated in Figure 2 at (a) 0 V (RCP light) and (b) 10 V (LCP light), respectively.
5. DISCUSSION A closer look on the diffraction intensities presented in Figure 5 reveals that the combination of the active TN layer and the passive retardation layer works well as long as these two layers are separated (Figure 2c). However, the sample combining the two layers in one integrated cell (Figure 2d) does not yield optimum diffraction efficiencies in the twisted field-off state (diamonds in Figure 5). Obviously, this twisted state yields elliptically polarized light but not the targeted circularly polarized light. This deviation is expected to appear, when the director field is twisted by less than 90°. In part, this can be explained by the competition between the limited anchoring of the director at the LPP alignment layer33 and the deformation energy of the twisted director field.20 Balancing the anchoring energy per surface area20
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[email protected]. Phone: (+49) 5251 602 156. Fax: (+49) 5251 604 208. ORCID
Thomas Zentgraf: 0000-0002-8662-1101 Heinz Kitzerow: 0000-0003-3808-7888 Author Contributions
The manuscript was written through contributions from all authors. All authors have given approval to the final version of the manuscript. F
DOI: 10.1021/acs.jpcc.7b12609 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Funding of this research by the Deutsche Forschungsgemeinschaft (DFG) through the graduate program “Micro- and Nanostructures in Optoelectronics and Photonics” (GRK 1464) and the Bundesministerium für Bildung und Forschung (BMBF grant no. IB-KOR-2014-008) is gratefully acknowledged.
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ABBREVIATIONS BP, blue phase; C12A, n-dodecyl acrylate; CCD, chargecoupled device; CLC, cholesteric liquid crystal; FLC, ferroelectric liquid crystal; IR, infrared; ITO, indium tin oxide; LC, liquid crystal; LCP, left circularly polarized light; NLC, nematic liquid crystal; PI, polyimide; PNLC, polymer nematic liquid crystal; RCP, right circularly polarized light; RM257, methylbenzene-1,4-diyl bis{4-[3-(acryloyloxy)propoxy]benzoate}; SSFLC, surface-stabilized ferroelectric liquid crystal; TGB, twist grain boundary phase; TN, twisted nematic; UV, ultraviolet
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DOI: 10.1021/acs.jpcc.7b12609 J. Phys. Chem. C XXXX, XXX, XXX−XXX
