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Tunable Nematic Liquid Crystal PS–NPS Lens
Optics Communications 450 (2019) 222–227
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Tunable Nematic Liquid Crystal PS–NPS Lens Mehrzad Javadzadeh ∗, Farzaneh Panahi, Habib Khoshsima Research Institute for Applied Physics and Astronomy, University of Tabriz, 5166614776, Tabriz, Iran
ARTICLE Keywords: Liquid crystal Diffraction efficiency Photon sieve Negative photon sieve
INFO
ABSTRACT This work introduces a tunable nematic liquid crystal Photon Sieve-Negative Photon Sieve lens based on UVcurable polymer. The LC molecules that aligned in the different zones of the NPS–PS lens makes a refractive index difference. The fabricated lens can deform from PS to NPS mode and reverse in two various linear polarisations. The maximum focus efficiency that reached (∼38.5%) for the PS lens mode and (∼22%) for NPS lens mode that measured by applying a suitable AC voltage which was close to the maximum theoretical diffraction efficiency (∼40.5%). Electrically tunable diffraction efficiency, focal points variations and, a dual lens like mode were the features of our designed optical device.
1. Introduction Most optical devices inspired from eyes of species that have the general functions of light collection, judgement of distance, imaging for finding mates and confronting the predators [1,2]. The lenses that contract in mammalian eyes can deform to change the focal length [3,4]. For simulating such lenses in industry, artificial lenses with tunable focal length feature which called tunable lenses, have developed [5–7]. Tunability trait of these lenses, gained from an anisotropic optical medium, such as nematic liquid crystal (LC) that can change the light path length propagation [8]. Nematic LCs are materials with the properties of optical and dielectric anisotropy. Directions of LC molecules can be changed under the external electric field due to the electric torque that exerted onto the induced dipole momentums of these materials [9]. The moving speed of incident light, according to its entry angle and polarisation, can be shift [10–13]. Various LC lenses have developed that Berreman et al., Kipp et al. and Sato were the pioneers of this science [14–17], wherein the Diffractive Optical Elements (DOEs) are the most promising [17–19]. The old kind of DOE was Fresnel Zone Plate (FZP) which constituted by series of concentric absorbing and transmitting angular zones [18–21] that can be used for focusing the light [22,23]. The resolution of FZP limited by the smallest zone width which occurs at the peripheral zone [24]. In 2001, Kipp et al. developed a novel DOE which consisted of many pinholes distributed appropriately over the zones of FZP, called Photon Sieve (PS) [25]. He analysed the light amplitude using Fresnel–Kirchhoff diffraction integral [26]. PS uses a significant number of pinholes of different sizes to replace the clear zones which are superior to the counterpart FZP in that higher resolution capability can achieve [27]. The locations of the pinholes ∗
in the PSs satisfies the criterion for constructive interference, which requires that the light path length from the source via the centre of the holes to the focal point is an integral multiple of 𝜆 [28–30]. Several theoretical and experimental studies on PS have reported targeting a more diffractive lens [31,32]. Also, there is a contrary kind of PS which named Negative PS (NPS). In this kind of PS, the place of dark and bright zones has changed. Cao et al. proved that low diffraction efficiency and some peculiar optical inadequacy for large pinholes situated in NPS made this kind of lenses less valuable than the basic one [33]. Due to PS’s extraordinary properties, these lenses have widely used in space telescopes [34,35], nanoimaging of X-ray, extreme ultraviolet (EUV) [31,36], improved signal-to-noise ratios in LIDAR systems [37], spectral imaging [38], focusing elements in mask-less photolithography [24], nanometre lithography [31], free space laser communication systems, differential interference contrast imaging [39,40], increasing the focusing ability of axicons [41] and fibre-to-silicon photonics waveguide coupling [42]. In this work, we demonstrated an NPS–PS lens based on the polymers UV-alignment feature. It should be noted that the diffraction efficiency and focal length changing of this lens were tunable. The LC sample fabricated using a homogeneously coated substrate [43–46] and a non-aligned glass. 2. Experiment 2.1. Calculating an appropriate mask For an infinite conjugate system, the focal length of binary PS (f) at wavelength 𝜆, is the radial distance to the centre of the bright zone
Corresponding author. E-mail addresses: [email protected] (M. Javadzadeh), [email protected] (F. Panahi), [email protected] (H. Khoshsima).
https://doi.org/10.1016/j.optcom.2019.05.055 Received 26 January 2019; Received in revised form 1 April 2019; Accepted 26 May 2019 Available online 31 May 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
M. Javadzadeh, F. Panahi and H. Khoshsima
Optics Communications 450 (2019) 222–227
Fig. 3.
Fig. 1.
Fig. 2.
The designed mask profile.
Norland Products, 𝑛𝑝 = 1.56 at 25 ◦ C). Acetone and prepolymer NOA81 with a weight ratio of 1:1 mixed and spin-coated onto the substrate to form the surface-relief PS pattern. The process of the fabrication of the LC PS briefly described below: In the first step, a 2% Polyvinyl Alcohol (PVA) (E. MFLEX UK Ltd.) and 98% deionised water solution prepared and spin coated for the 30 s at a speed of 1500 rpm on a 3.5×1.3 cm glass substrate with indium tin oxide (ITO) pre-coated layer. The substrate with the PVA coating was pre-baked at 60 ◦ C for 1 min, and then over-baked at 100 ◦ C for about 1.5 h. Then, the alignment layer rubbed with velvet under fixed pressure in direction R. Afterward, the solution of the prepolymer (NOA81) in acetone spin-coated onto the prepared substrate. In the next step, unpolarised UV light with an intensity of ∼1 W/cm2 irradiated onto the ITO+PVA+Polymer coated layer through the lithographic PS mask for 10 min. Finally, the irradiated substrate immersed in 20:80 of acetone: ethanol mixture to remove the unpolymerised NOA81 prepolymer. The second ITO coated glass separated from the PS layer with 10 μm thick ball spacers. Drops of liquid crystal then injected into the empty cell by capillary force [48–54]. Fig. 3 illustrates the prepared NPS–PS cell. After inserting the LC molecules into the cell, they aligned along the alignment direction R. Fig. 4 illustrates the scheme of the orientation process of LC molecules with only one alignment layer. Because of the elastic continuum theory, LC molecular placement was like the homogeneously aligned LC cell [55]. By applying an external electric field (∼1 kHz), molecules situated to a perpendicular direction.
Negative PS and its specifications.
given by 𝑟𝑛 [18,47]: √ 𝑛2 𝜆2 𝑟𝑛 = 𝑛𝜆𝑓 + 4
(1)
The width (w) of each region is such that the section is a constant 𝜋𝜆𝑓 , so [31]: 𝑤𝑛 =
𝜆𝑓 2𝑟𝑛
Fabricated NPS-PS nematic Liquid Crystal cell.
3. Results and discussions
(2)
To analyse the lithographed mask’s quality, we checked it out under an optical microscope. Fig. 5 shows the middle, centre, and edge of the PS mask, respectively. Notable that, to print Photon Sieve pattern on the UV-curable surface, we used a negative stencil-like PS mask. In order to study focal points variation of the prepared NPS–PS cell, a 1 mW, nonpolarised He-Ne laser beam that passed through a linear polariser, was probed the sample in no-voltage condition. The exposure beam expanded using the linearising lens method, which included two objectives. The above mentioned setup shown in Fig. 6. As for the higher-order Fourier components, a diffraction lens has multiple foci at f, f/3, f/5,. . . , f/(n+1). However, most of the incident light diffracts into the primary focus [41]. Experiments showed that, according to incident beam polarisation, NPS–PS lens could switch between NPS and PS lens modes. For the measurement process, due to the initial aligning direction, first, a parallel polarised beam exposure to the cell. Accordingly, the light encountered with a refractive index difference with 𝑛𝑝 in the polymer region and 𝑛𝑒 in the LC regions (𝑛𝑝 <𝑛𝑒 ). It observed that NPS lens mode appears because of polarisation
A basic PS has holes of diameter w, the corresponding bright zones, though they can make more significant as detailed by Kipp et al. [25, 29]. We designed a PS mask for 𝜆 = 632.8 nm wavelength by using the lithography technique with 𝑓 = 114.17 cm, 𝑛 = 30 rings and 𝑤30 = 3 nm specifications. Also, 𝑟30 was calculated to 4.7 mm. Fig. 1 is showing the properties of the designed mask. Looking at the differences between the two lenses, as shown in Fig. 2 it is understandable that Negative Photon Sieve is reverse kind of regular Photon Sieve. The focal length that measured for NPS calculated (∼129.06 cm). 2.2. Manufacturing the cell The Liquid Crystal that we used was a nematic 1294-1b LC (E. AWAT-PPT Poland, 𝑛𝑜 = 1.501 and 𝑛𝑒 = 1.813 at 25 ◦ C). The surfacerelief PS formed using a UV-curable prepolymer adhesive, NOA81 (E. 223
M. Javadzadeh, F. Panahi and H. Khoshsima
Optics Communications 450 (2019) 222–227
Fig. 7. Refractive index ellipsoid of LC in confronting with two different linear polarisations.
Fig. 4.
Cross-section of the NPS–PS sample with UV-cured surface-relief.
hence the experimental focal length of 116.5 cm (∼2% error) measured. direction dependence of refractive index. Hence the experimental focal length of 131.7 cm (∼2% error) measured. Second, a vertical polarisation beam irradiated to the sample. Therefore, light encountered with a refractive index difference 𝑛𝑝 and 𝑛𝑜 that in the same regions (𝑛𝑝 >𝑛𝑜 ). According to observations, because of confrontation polarisation direction and refractive index difference, PS lens mode appeared. Fig. 7 is showing refractive index ellipsoid of LC.
Fig. 5.
Fig. 8, shows the polarisation tunability feature of the prepared cell. The images that obtained under a parallel and perpendicular linearly polarised optical microscope (POM). Also, Figs. 5 and 8 comparison reveals that the resolution of the preformed UV-cured surface-relief patterns was incredibly high. Fig. 9 shows the focal point variations (∼16 cm) with changing exposure beam polarisation.
Images of (a) middle, (b) centre and (c) edge parts of designed PS mask.
Fig. 6. The NPS–PS lens’s focal point variation analysing setup.
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Optics Communications 450 (2019) 222–227
Fig. 10. Focusing profiles: (a) PS lens and (b) NPS lens.
Fig. 8. PS and NPS pattern under the polarised microscope: (a) shows the NPS pattern under 0◦ (parallel) polarisation and (b) illustrates PS pattern under 90◦ (perpendicular) polarisation.
Fig. 11. The intensity profiles of PS and NPS at the focal points.
light in vacuum and the film thickness, respectively. The value of 𝜋 in 𝛿𝑃 𝑎𝑟𝑎𝑙𝑙𝑒𝑙 or 𝛿𝑃 𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 determined by the intrinsic path difference between the adjacent zones in an ordinary DOE. Substituting 𝑛𝑜 = 1.501, 𝑛𝑒 = 1.813, 𝑛𝑝 = 1.56, 𝜆0 = 632.8 nm and d = 10 μm into 𝛿𝑃 𝑎𝑟𝑎𝑙𝑙𝑒𝑙 or 𝛿𝑃 𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 , yields the values of 𝛿𝑃 𝑎𝑟𝑎𝑙𝑙𝑒𝑙 and 𝛿𝑃 𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 as 9.86𝜋 and 2.86𝜋, respectively, which correspond to intermediate and entirely constructive interference. Therefore, the lens has better focusing ability for perpendicular polarised light. To measure the diffraction efficiency of the manufactured cell, we used focal points variation’s measuring setup. Eventually, the probed beam collected by a power metre (E. Thorlabs) (see Fig. 12). By applying the external electric field (∼1 kHz), due to nematic 1294-1b’s positive anisotropy of the constant dielectric feature, the LC molecules reoriented in the direction of the external applied electric field and settled perpendicularly according to the cell’s surface. The beam that passed through the cell merely encountered with ordinary refractive index and polymer’s fixed refractive index which contributed to PS like mode. The experimental diffraction efficiency defined as:
Fig. 9. The measured focal point variation of fabricated NPS–PS lens with variation of the incident light beam polarisation.
Furthermore, as shown in Fig. 10 for observing the focal point’s intensities that contribute to NPS and PS lens modes, we used a CCD (E. Samsung). Fig. 11 displays the beam intensity profiles at the focal plane at V = 0 V, and demonstrates the focusing properties of the NPS–PS LC lens. The curves represent the beam profiles of parallel and perpendicular polarised lights focused through the lens. The focusing power of the LC lens for vertically polarised light exceeds for the parallel polarised light. According to Fig. 11, the polarisation-dependent focusing effect can be reasonably explained as follows: through the NPS–PS LC lens, the phase differences of parallel and perpendicular polarised lights between the adjacent zones are 𝛿𝑃 𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = 2𝜋𝑑 (𝑛𝑒 − 𝑛𝑝 ) + 𝜋 and 𝛿Perpendicular = 𝜆 2𝜋𝑑 (𝑛𝑝 𝜆0
𝜂=
𝑃 − 𝑃0 × 100 𝑃𝑡
(3)
where P is the optical intensity at the focal point, 𝑃𝑡 is the intensity that passed through the NPS–PS LC lens when no driving voltage applied, and 𝑃𝑜 the residual optical intensity due to noise [21]. With increasing applied voltage, the diffraction efficiency increased from 22% (which contributed to NPS mode in V = 0 V) to 38.5% (that related to PS mode in V = 180 V). Fig. 13 illustrates the changes in the first-order diffraction efficiency with the applied voltage, for parallel and perpendicularly polarised lights. The first-order focusing diffraction efficiency defined as the ratio of the first-order diffraction intensity and the total transmitted intensity
0
− 𝑛𝑜 ) + 𝜋 where 𝜆0 and d are the wavelength of the incident 225
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Optics Communications 450 (2019) 222–227
Fig. 12. The NPS–PS LC lens’s diffraction analysing setup.
4. Conclusion In conclusion, this work demonstrates a highly efficient, electrically and polarisation dependent tunable NPS–PS lens based on the UV-cured polymer besides the nematic liquid crystal. The LC alignments were orthogonally homogeneous. The polarisation dependence of the NPS– PS lenses experimentally analysed under two various linearly polarised probing states of the incident beam. The maximum focusing efficiency at PS mode was (∼38.5%) under an applied AC voltage of 180 V that was close to the theoretical maximum value (∼40.5%). The discrepancy possibly caused by the scattering, which occurs at the boundary between the LC and polymer regions in the present LC lens. Also, the maximum diffraction efficiency achieved in NPS mode (∼22%). References [1] B.A. Palmer, A. Hirsch, V. Brumfeld, E.D. Aflalo, I. Pinkas, A. Sagi, S. Rosenne, D. Oron, L. Leiserowitz, L. Kronik, S. Weiner, L. Addadi, Optically functional isoxanthopterin crystals in the mirrored eyes of decapod crustaceans, Proc. Natl. Acad. Sci. (2018) http://dx.doi.org/10.1073/pnas.1722531115. [2] J. Chappell, Book review: Bio-inspired artificial intelligence: Theories, methods, and technologies, Am. J. Hum. Biol. (2009) http://dx.doi.org/10.1002/ajhb. 20948. [3] J. Cartaud, E. Kordeli, A. Cartaud, Postsynaptic membranes at the neuromuscular junction: Molecular organization, in: Encycl. Life Sci., 2006, http://dx.doi.org/ 10.1038/npg.els.0000252. [4] M.F. Land, The optical structures of animal eyes, Curr. Biol. (2005) http://dx. doi.org/10.1016/j.cub.2005.04.041. [5] H.C. Lin, M.S. Chen, Y.H. Lin, A review of electrically tunable focusing liquid crystal lenses, Trans. Electr. Electron. Mater. (2011) http://dx.doi.org/10.4313/ TEEM.2011.12.6.234. [6] H. Ren, S.T. Wu, Introduction to Adaptive Lenses, 2012, http://dx.doi.org/10. 1002/9781118270080. [7] F. Yaraş, H. Kang, L. Onural, State of the art in holographic displays: A survey, IEEE/OSA J. Disp. Technol. (2010) http://dx.doi.org/10.1109/JDT.2010. 2045734. [8] V.G. Chigrinov, Liquid Crystal Applications in Photonics, 2016, pp. 927–930. [9] I.C. Khoo, Nonlinear optics of liquid crystalline materials, Phys. Rep. 471 (2009) 221–267, http://dx.doi.org/10.1016/j.physrep.2009.01.001. [10] I. Dierking, Handbook of liquid crystals, Liq. Cryst. Today (2017) http://dx.doi. org/10.1080/1358314x.2017.1279443. [11] A.D. Kiselev, V.G. Chigrinov, Optics of short-pitch deformed-helix ferroelectric liquid crystals: Symmetries, exceptional points, and polarisation-resolved angular patterns, Phys. Rev. E (2014) http://dx.doi.org/10.1103/PhysRevE.90.042504. [12] F. Schmidt, Photonics, in: Handb. Optoelectron. Device Model. Simul. Lasers, Modul. Photodetectors, Sol. Cells, Numer. Methods, 2017, http://dx.doi.org/10. 4324/9781315152318. [13] D. Andrienko, Introduction to liquid crystals, J. Mol. Liq. (2018) http://dx.doi. org/10.1016/j.molliq.2018.01.175. [14] V.G. Chigrinov, Liquid crystals for photonics, Photonics Lett. Pol. (2011) http: //dx.doi.org/10.4302/plp.2011.1.01.
Fig. 13. The measured diffraction efficiency of fabricated NPS–PS lens as a function of applied AC (∼1 kHz) voltage.
via the NPS–PS lens. The theoretical limit of the first-order diffraction efficiency is ∼40.5% that relevant to Equation (4) [32]: 𝑚𝜋 𝑚𝜋 2 𝜂1 = [sin( )∕( )] (4) 2 2 where m denotes the diffraction order. Accordingly, the first-order point is at the focus of the NPS–PS lens, and the plus (minus) mth orders are the reversely conversing real points (regular diverging imaginary points) [50]. The 0th order is the real standard point that sized equal to the irradiated beam diameter [54]. As the applied voltage increases from 0 V to 180 V, the LC director tends to reorient normal to the sample substrates, and the incident parallel polarised light undergoes a decline in the phase difference between the adjacent odd and even regions through the lens from 9.86𝜋 to 2.86𝜋. This change corresponds to a decrease in a difference of [𝑛𝑒𝑓 𝑓 (𝜃)-n𝑝 ], between the extraordinary index of LC and the polymer index, where 𝜃 is the angle between the LC director and the 𝑧-axis. However, the incident perpendicularly polarised light gains a constant phase difference of 𝛿𝑃 𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 = 2.86𝜋 as the applied voltage increases because of the corresponding constant difference between the ordinary index of LC and the polymer index, which is (𝑛𝑝 - n𝑜 ). It is notable that, according to theory, the maximum diffraction efficiency occurs when the phase difference is equal to an odd multiple of 𝜋 [53]. 226
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Tunable Nematic Liquid Crystal PS–NPS Lens Mehrzad Javadzadeh ∗, Farzaneh Panahi, Habib Khoshsima Research Institute for Applied Physics and Astronomy, University of Tabriz, 5166614776, Tabriz, Iran
ARTICLE Keywords: Liquid crystal Diffraction efficiency Photon sieve Negative photon sieve
INFO
ABSTRACT This work introduces a tunable nematic liquid crystal Photon Sieve-Negative Photon Sieve lens based on UVcurable polymer. The LC molecules that aligned in the different zones of the NPS–PS lens makes a refractive index difference. The fabricated lens can deform from PS to NPS mode and reverse in two various linear polarisations. The maximum focus efficiency that reached (∼38.5%) for the PS lens mode and (∼22%) for NPS lens mode that measured by applying a suitable AC voltage which was close to the maximum theoretical diffraction efficiency (∼40.5%). Electrically tunable diffraction efficiency, focal points variations and, a dual lens like mode were the features of our designed optical device.
1. Introduction Most optical devices inspired from eyes of species that have the general functions of light collection, judgement of distance, imaging for finding mates and confronting the predators [1,2]. The lenses that contract in mammalian eyes can deform to change the focal length [3,4]. For simulating such lenses in industry, artificial lenses with tunable focal length feature which called tunable lenses, have developed [5–7]. Tunability trait of these lenses, gained from an anisotropic optical medium, such as nematic liquid crystal (LC) that can change the light path length propagation [8]. Nematic LCs are materials with the properties of optical and dielectric anisotropy. Directions of LC molecules can be changed under the external electric field due to the electric torque that exerted onto the induced dipole momentums of these materials [9]. The moving speed of incident light, according to its entry angle and polarisation, can be shift [10–13]. Various LC lenses have developed that Berreman et al., Kipp et al. and Sato were the pioneers of this science [14–17], wherein the Diffractive Optical Elements (DOEs) are the most promising [17–19]. The old kind of DOE was Fresnel Zone Plate (FZP) which constituted by series of concentric absorbing and transmitting angular zones [18–21] that can be used for focusing the light [22,23]. The resolution of FZP limited by the smallest zone width which occurs at the peripheral zone [24]. In 2001, Kipp et al. developed a novel DOE which consisted of many pinholes distributed appropriately over the zones of FZP, called Photon Sieve (PS) [25]. He analysed the light amplitude using Fresnel–Kirchhoff diffraction integral [26]. PS uses a significant number of pinholes of different sizes to replace the clear zones which are superior to the counterpart FZP in that higher resolution capability can achieve [27]. The locations of the pinholes ∗
in the PSs satisfies the criterion for constructive interference, which requires that the light path length from the source via the centre of the holes to the focal point is an integral multiple of 𝜆 [28–30]. Several theoretical and experimental studies on PS have reported targeting a more diffractive lens [31,32]. Also, there is a contrary kind of PS which named Negative PS (NPS). In this kind of PS, the place of dark and bright zones has changed. Cao et al. proved that low diffraction efficiency and some peculiar optical inadequacy for large pinholes situated in NPS made this kind of lenses less valuable than the basic one [33]. Due to PS’s extraordinary properties, these lenses have widely used in space telescopes [34,35], nanoimaging of X-ray, extreme ultraviolet (EUV) [31,36], improved signal-to-noise ratios in LIDAR systems [37], spectral imaging [38], focusing elements in mask-less photolithography [24], nanometre lithography [31], free space laser communication systems, differential interference contrast imaging [39,40], increasing the focusing ability of axicons [41] and fibre-to-silicon photonics waveguide coupling [42]. In this work, we demonstrated an NPS–PS lens based on the polymers UV-alignment feature. It should be noted that the diffraction efficiency and focal length changing of this lens were tunable. The LC sample fabricated using a homogeneously coated substrate [43–46] and a non-aligned glass. 2. Experiment 2.1. Calculating an appropriate mask For an infinite conjugate system, the focal length of binary PS (f) at wavelength 𝜆, is the radial distance to the centre of the bright zone
Corresponding author. E-mail addresses: [email protected] (M. Javadzadeh), [email protected] (F. Panahi), [email protected] (H. Khoshsima).
https://doi.org/10.1016/j.optcom.2019.05.055 Received 26 January 2019; Received in revised form 1 April 2019; Accepted 26 May 2019 Available online 31 May 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
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Optics Communications 450 (2019) 222–227
Fig. 3.
Fig. 1.
Fig. 2.
The designed mask profile.
Norland Products, 𝑛𝑝 = 1.56 at 25 ◦ C). Acetone and prepolymer NOA81 with a weight ratio of 1:1 mixed and spin-coated onto the substrate to form the surface-relief PS pattern. The process of the fabrication of the LC PS briefly described below: In the first step, a 2% Polyvinyl Alcohol (PVA) (E. MFLEX UK Ltd.) and 98% deionised water solution prepared and spin coated for the 30 s at a speed of 1500 rpm on a 3.5×1.3 cm glass substrate with indium tin oxide (ITO) pre-coated layer. The substrate with the PVA coating was pre-baked at 60 ◦ C for 1 min, and then over-baked at 100 ◦ C for about 1.5 h. Then, the alignment layer rubbed with velvet under fixed pressure in direction R. Afterward, the solution of the prepolymer (NOA81) in acetone spin-coated onto the prepared substrate. In the next step, unpolarised UV light with an intensity of ∼1 W/cm2 irradiated onto the ITO+PVA+Polymer coated layer through the lithographic PS mask for 10 min. Finally, the irradiated substrate immersed in 20:80 of acetone: ethanol mixture to remove the unpolymerised NOA81 prepolymer. The second ITO coated glass separated from the PS layer with 10 μm thick ball spacers. Drops of liquid crystal then injected into the empty cell by capillary force [48–54]. Fig. 3 illustrates the prepared NPS–PS cell. After inserting the LC molecules into the cell, they aligned along the alignment direction R. Fig. 4 illustrates the scheme of the orientation process of LC molecules with only one alignment layer. Because of the elastic continuum theory, LC molecular placement was like the homogeneously aligned LC cell [55]. By applying an external electric field (∼1 kHz), molecules situated to a perpendicular direction.
Negative PS and its specifications.
given by 𝑟𝑛 [18,47]: √ 𝑛2 𝜆2 𝑟𝑛 = 𝑛𝜆𝑓 + 4
(1)
The width (w) of each region is such that the section is a constant 𝜋𝜆𝑓 , so [31]: 𝑤𝑛 =
𝜆𝑓 2𝑟𝑛
Fabricated NPS-PS nematic Liquid Crystal cell.
3. Results and discussions
(2)
To analyse the lithographed mask’s quality, we checked it out under an optical microscope. Fig. 5 shows the middle, centre, and edge of the PS mask, respectively. Notable that, to print Photon Sieve pattern on the UV-curable surface, we used a negative stencil-like PS mask. In order to study focal points variation of the prepared NPS–PS cell, a 1 mW, nonpolarised He-Ne laser beam that passed through a linear polariser, was probed the sample in no-voltage condition. The exposure beam expanded using the linearising lens method, which included two objectives. The above mentioned setup shown in Fig. 6. As for the higher-order Fourier components, a diffraction lens has multiple foci at f, f/3, f/5,. . . , f/(n+1). However, most of the incident light diffracts into the primary focus [41]. Experiments showed that, according to incident beam polarisation, NPS–PS lens could switch between NPS and PS lens modes. For the measurement process, due to the initial aligning direction, first, a parallel polarised beam exposure to the cell. Accordingly, the light encountered with a refractive index difference with 𝑛𝑝 in the polymer region and 𝑛𝑒 in the LC regions (𝑛𝑝 <𝑛𝑒 ). It observed that NPS lens mode appears because of polarisation
A basic PS has holes of diameter w, the corresponding bright zones, though they can make more significant as detailed by Kipp et al. [25, 29]. We designed a PS mask for 𝜆 = 632.8 nm wavelength by using the lithography technique with 𝑓 = 114.17 cm, 𝑛 = 30 rings and 𝑤30 = 3 nm specifications. Also, 𝑟30 was calculated to 4.7 mm. Fig. 1 is showing the properties of the designed mask. Looking at the differences between the two lenses, as shown in Fig. 2 it is understandable that Negative Photon Sieve is reverse kind of regular Photon Sieve. The focal length that measured for NPS calculated (∼129.06 cm). 2.2. Manufacturing the cell The Liquid Crystal that we used was a nematic 1294-1b LC (E. AWAT-PPT Poland, 𝑛𝑜 = 1.501 and 𝑛𝑒 = 1.813 at 25 ◦ C). The surfacerelief PS formed using a UV-curable prepolymer adhesive, NOA81 (E. 223
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Optics Communications 450 (2019) 222–227
Fig. 7. Refractive index ellipsoid of LC in confronting with two different linear polarisations.
Fig. 4.
Cross-section of the NPS–PS sample with UV-cured surface-relief.
hence the experimental focal length of 116.5 cm (∼2% error) measured. direction dependence of refractive index. Hence the experimental focal length of 131.7 cm (∼2% error) measured. Second, a vertical polarisation beam irradiated to the sample. Therefore, light encountered with a refractive index difference 𝑛𝑝 and 𝑛𝑜 that in the same regions (𝑛𝑝 >𝑛𝑜 ). According to observations, because of confrontation polarisation direction and refractive index difference, PS lens mode appeared. Fig. 7 is showing refractive index ellipsoid of LC.
Fig. 5.
Fig. 8, shows the polarisation tunability feature of the prepared cell. The images that obtained under a parallel and perpendicular linearly polarised optical microscope (POM). Also, Figs. 5 and 8 comparison reveals that the resolution of the preformed UV-cured surface-relief patterns was incredibly high. Fig. 9 shows the focal point variations (∼16 cm) with changing exposure beam polarisation.
Images of (a) middle, (b) centre and (c) edge parts of designed PS mask.
Fig. 6. The NPS–PS lens’s focal point variation analysing setup.
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Optics Communications 450 (2019) 222–227
Fig. 10. Focusing profiles: (a) PS lens and (b) NPS lens.
Fig. 8. PS and NPS pattern under the polarised microscope: (a) shows the NPS pattern under 0◦ (parallel) polarisation and (b) illustrates PS pattern under 90◦ (perpendicular) polarisation.
Fig. 11. The intensity profiles of PS and NPS at the focal points.
light in vacuum and the film thickness, respectively. The value of 𝜋 in 𝛿𝑃 𝑎𝑟𝑎𝑙𝑙𝑒𝑙 or 𝛿𝑃 𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 determined by the intrinsic path difference between the adjacent zones in an ordinary DOE. Substituting 𝑛𝑜 = 1.501, 𝑛𝑒 = 1.813, 𝑛𝑝 = 1.56, 𝜆0 = 632.8 nm and d = 10 μm into 𝛿𝑃 𝑎𝑟𝑎𝑙𝑙𝑒𝑙 or 𝛿𝑃 𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 , yields the values of 𝛿𝑃 𝑎𝑟𝑎𝑙𝑙𝑒𝑙 and 𝛿𝑃 𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 as 9.86𝜋 and 2.86𝜋, respectively, which correspond to intermediate and entirely constructive interference. Therefore, the lens has better focusing ability for perpendicular polarised light. To measure the diffraction efficiency of the manufactured cell, we used focal points variation’s measuring setup. Eventually, the probed beam collected by a power metre (E. Thorlabs) (see Fig. 12). By applying the external electric field (∼1 kHz), due to nematic 1294-1b’s positive anisotropy of the constant dielectric feature, the LC molecules reoriented in the direction of the external applied electric field and settled perpendicularly according to the cell’s surface. The beam that passed through the cell merely encountered with ordinary refractive index and polymer’s fixed refractive index which contributed to PS like mode. The experimental diffraction efficiency defined as:
Fig. 9. The measured focal point variation of fabricated NPS–PS lens with variation of the incident light beam polarisation.
Furthermore, as shown in Fig. 10 for observing the focal point’s intensities that contribute to NPS and PS lens modes, we used a CCD (E. Samsung). Fig. 11 displays the beam intensity profiles at the focal plane at V = 0 V, and demonstrates the focusing properties of the NPS–PS LC lens. The curves represent the beam profiles of parallel and perpendicular polarised lights focused through the lens. The focusing power of the LC lens for vertically polarised light exceeds for the parallel polarised light. According to Fig. 11, the polarisation-dependent focusing effect can be reasonably explained as follows: through the NPS–PS LC lens, the phase differences of parallel and perpendicular polarised lights between the adjacent zones are 𝛿𝑃 𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = 2𝜋𝑑 (𝑛𝑒 − 𝑛𝑝 ) + 𝜋 and 𝛿Perpendicular = 𝜆 2𝜋𝑑 (𝑛𝑝 𝜆0
𝜂=
𝑃 − 𝑃0 × 100 𝑃𝑡
(3)
where P is the optical intensity at the focal point, 𝑃𝑡 is the intensity that passed through the NPS–PS LC lens when no driving voltage applied, and 𝑃𝑜 the residual optical intensity due to noise [21]. With increasing applied voltage, the diffraction efficiency increased from 22% (which contributed to NPS mode in V = 0 V) to 38.5% (that related to PS mode in V = 180 V). Fig. 13 illustrates the changes in the first-order diffraction efficiency with the applied voltage, for parallel and perpendicularly polarised lights. The first-order focusing diffraction efficiency defined as the ratio of the first-order diffraction intensity and the total transmitted intensity
0
− 𝑛𝑜 ) + 𝜋 where 𝜆0 and d are the wavelength of the incident 225
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Optics Communications 450 (2019) 222–227
Fig. 12. The NPS–PS LC lens’s diffraction analysing setup.
4. Conclusion In conclusion, this work demonstrates a highly efficient, electrically and polarisation dependent tunable NPS–PS lens based on the UV-cured polymer besides the nematic liquid crystal. The LC alignments were orthogonally homogeneous. The polarisation dependence of the NPS– PS lenses experimentally analysed under two various linearly polarised probing states of the incident beam. The maximum focusing efficiency at PS mode was (∼38.5%) under an applied AC voltage of 180 V that was close to the theoretical maximum value (∼40.5%). The discrepancy possibly caused by the scattering, which occurs at the boundary between the LC and polymer regions in the present LC lens. Also, the maximum diffraction efficiency achieved in NPS mode (∼22%). References [1] B.A. Palmer, A. Hirsch, V. Brumfeld, E.D. Aflalo, I. Pinkas, A. Sagi, S. Rosenne, D. Oron, L. Leiserowitz, L. Kronik, S. Weiner, L. Addadi, Optically functional isoxanthopterin crystals in the mirrored eyes of decapod crustaceans, Proc. Natl. Acad. Sci. (2018) http://dx.doi.org/10.1073/pnas.1722531115. [2] J. Chappell, Book review: Bio-inspired artificial intelligence: Theories, methods, and technologies, Am. J. Hum. Biol. (2009) http://dx.doi.org/10.1002/ajhb. 20948. [3] J. Cartaud, E. Kordeli, A. Cartaud, Postsynaptic membranes at the neuromuscular junction: Molecular organization, in: Encycl. Life Sci., 2006, http://dx.doi.org/ 10.1038/npg.els.0000252. [4] M.F. Land, The optical structures of animal eyes, Curr. Biol. (2005) http://dx. doi.org/10.1016/j.cub.2005.04.041. [5] H.C. Lin, M.S. Chen, Y.H. Lin, A review of electrically tunable focusing liquid crystal lenses, Trans. Electr. Electron. Mater. (2011) http://dx.doi.org/10.4313/ TEEM.2011.12.6.234. [6] H. Ren, S.T. Wu, Introduction to Adaptive Lenses, 2012, http://dx.doi.org/10. 1002/9781118270080. [7] F. Yaraş, H. Kang, L. Onural, State of the art in holographic displays: A survey, IEEE/OSA J. Disp. Technol. (2010) http://dx.doi.org/10.1109/JDT.2010. 2045734. [8] V.G. Chigrinov, Liquid Crystal Applications in Photonics, 2016, pp. 927–930. [9] I.C. Khoo, Nonlinear optics of liquid crystalline materials, Phys. Rep. 471 (2009) 221–267, http://dx.doi.org/10.1016/j.physrep.2009.01.001. [10] I. Dierking, Handbook of liquid crystals, Liq. Cryst. Today (2017) http://dx.doi. org/10.1080/1358314x.2017.1279443. [11] A.D. Kiselev, V.G. Chigrinov, Optics of short-pitch deformed-helix ferroelectric liquid crystals: Symmetries, exceptional points, and polarisation-resolved angular patterns, Phys. Rev. E (2014) http://dx.doi.org/10.1103/PhysRevE.90.042504. [12] F. Schmidt, Photonics, in: Handb. Optoelectron. Device Model. Simul. Lasers, Modul. Photodetectors, Sol. Cells, Numer. Methods, 2017, http://dx.doi.org/10. 4324/9781315152318. [13] D. Andrienko, Introduction to liquid crystals, J. Mol. Liq. (2018) http://dx.doi. org/10.1016/j.molliq.2018.01.175. [14] V.G. Chigrinov, Liquid crystals for photonics, Photonics Lett. Pol. (2011) http: //dx.doi.org/10.4302/plp.2011.1.01.
Fig. 13. The measured diffraction efficiency of fabricated NPS–PS lens as a function of applied AC (∼1 kHz) voltage.
via the NPS–PS lens. The theoretical limit of the first-order diffraction efficiency is ∼40.5% that relevant to Equation (4) [32]: 𝑚𝜋 𝑚𝜋 2 𝜂1 = [sin( )∕( )] (4) 2 2 where m denotes the diffraction order. Accordingly, the first-order point is at the focus of the NPS–PS lens, and the plus (minus) mth orders are the reversely conversing real points (regular diverging imaginary points) [50]. The 0th order is the real standard point that sized equal to the irradiated beam diameter [54]. As the applied voltage increases from 0 V to 180 V, the LC director tends to reorient normal to the sample substrates, and the incident parallel polarised light undergoes a decline in the phase difference between the adjacent odd and even regions through the lens from 9.86𝜋 to 2.86𝜋. This change corresponds to a decrease in a difference of [𝑛𝑒𝑓 𝑓 (𝜃)-n𝑝 ], between the extraordinary index of LC and the polymer index, where 𝜃 is the angle between the LC director and the 𝑧-axis. However, the incident perpendicularly polarised light gains a constant phase difference of 𝛿𝑃 𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 = 2.86𝜋 as the applied voltage increases because of the corresponding constant difference between the ordinary index of LC and the polymer index, which is (𝑛𝑝 - n𝑜 ). It is notable that, according to theory, the maximum diffraction efficiency occurs when the phase difference is equal to an odd multiple of 𝜋 [53]. 226
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