crystals

Article Monochromatic Depolarizer Based on

Paweł Mar´c* , Noureddine Bennis, Anna Spadło , Aleksandra Kalbarczyk , Rafał W˛egłowski, Katarzyna Garbat and Leszek R. Jaroszewicz Faculty of New Technologies and Chemistry, Military University of Technology, 2 gen. S. Kaliskiego St., 00-908 Warsaw, Poland * Correspondence: [email protected]; Tel.: +48-261-839-424

 Received: 24 May 2019; Accepted: 22 July 2019; Published: 28 July 2019 

Abstract: is a very useful parameter of a light beam in many optical measurements. Improvement of holographic systems requires optical elements which need a diffused and depolarized light beam. This paper describes a simple monochromatic depolarizer based on a pure vertically aligned liquid crystal without pretilt. In this work we present an extended description of depolarizer by analyzing its electro-optic properties measured in spatial and time domains with the use of crossed and polarimetric configurations. Crossed polarizers set-up provides information on spatial and temporal changes of microscopic textures while polarimetric measurement allows to measure voltage and time dependence of degree of polarization. Three different thicknesses, i.e., 5 µm, 10 µm and 15 µm have been manufactured in order to analyze another degree of freedom for this type of depolarizer device based on a liquid crystals’ material. Consideration of the light scattering capability of the cell is reported.

Keywords: depolarization; liquid crystals; Mueller matrices

1. Introduction Depolarized light is very useful in optical measurements continuously finding application as for example spatial diffused phase element in holography [1]. Commercially used light sources are polarized or at least partially polarized. However, in many spectroscopic devices it is desirable to work with unpolarized light. Therefore, special devices should be developed to depolarize it. In general, light can be depolarized by reflection from diffused media or transmission through specially designed birefringent or scattering optical elements. Light backscattered from materials with a high roughness is a good depolarizer [2–4] and carries valuable information on optical properties of illuminated surfaces [5,6]. However, it is difficult to use such light as a source due to random direction of reflected light. This makes necessity to use the lenses’ system in a detection unit because of a photodetector’s limited active area. The most popular and currently used depolarizers are designed in two ways as spatially distributed linear retarders or a composition of at least two birefringent plates having optical thickness greater than coherence length of the broad band light source. Spatial distribution has brought common forms known as Cornu or wedge types of depolarizers [7], and spectral birefringence distribution as Lyot depolarizer [8]. They are used in both, bulk optic systems [1] and optical fiber systems, as well [9]. Narrow band and laser line sources are difficult to be depolarized and both mentioned above types of optical elements are insufficient to depolarize such light sources. Therefore, an effective depolarization of such light is performed by illumination of a transparent diffused material or an optical element having spatially distributed birefringence. In the first case the transmitted light is depolarized but optical losses increase sufficiently due to the scattering effect. In the latter every particular point of an output light beam is polarized but the mean Stokes vector integrated in the cross-section of the beam shows it as depolarized light. For this reason the process is named pseudo-depolarization.

Crystals 2019, 9, 387; doi:10.3390/cryst9080387 www.mdpi.com/journal/crystals Crystals 2019, 9, 387 2 of 12

Passive depolarizers and active depolarizers based on liquid crystals (LCs) were early identified as effective devices for light depolarization. Devices available commercially and described in the literature give possibility to depolarize both narrow and broad band light sources. It is made by using scattering properties or a spatially distributed birefringence of the used LC based materials. Scattering properties of silica nanoparticles in LCs matrix [10] and cholesteric LCs in a wedge configuration [11] were presented as effective depolarizers. Spatial distribution of birefringence in LCs’ polymers and different processes of LCs’ polymer alignment layers were shown, as well. A commercially available depolarizer of linearly polarized light consists of stripped patterns of microretarder arrays with variable orientations of fast axes. This array is manufactured with an LC polymer [12]. Other types of spatial distributed birefringence are based on modifications of alignment layers of standard LCs’ cells by using mechanical microrubbing [13], photoalignment [14], and homeotropic alignment by using surfactants [15] for selected nematic LCs. The last configuration of the LCs was identified as an optical element with the best developing potential in designing an LC based depolarizer. Regarding the control of Vertically Aligned Nematic (VAN) cells by means of a substrate surface treatment, there are different methods for achieving better control of such device [15]. Any one of these methods has its advantages and disadvantages and what is useful for some applications may not be useful for another one. If the surface alignment layer is modified to have a given pretilt angle [16], then the LC directors will always have a predetermined reorientation upon switching by external electric field in order to find application in spatial light modulators. However, in the case of Pure VAN (PVAN) cell with zero pretilt, the local orientation of LC director will be undefined upon switching. In this case, the cell usually generates disordered birefringent medium related to undefined switching direction of molecules which produce random polarization of the transmitted light by LCs’ cell without scattering. Therefore, depolarization effect may be performed and the cell cannot be used for the phase control. However, it can be used as a depolarizer which is effective for either monochromatic light or light with any spectral range. Most of depolarizers based on LCs described above are passive optical elements. Only devices with pure homeotropic LC director configuration allow to use LC electro-optic properties in order to tune degree of polarization (DOP) level by electric field [17]. In this paper we present an extended analysis of depolarization properties of PVAN cells. The key issue to use the above concept is to have a proper spatial distribution of birefringence upon switching. To reach this goal, a biopolymer alignment layer like deoxyribonucleic acid (DNA) derivatives crosslinked with surfactant complex such as hexadecyltrimethylammonium chloride (CTMA) needs to be used [15]. When the LC material is introduced close to the surface, LC molecules align parallel to hydrophobic tails of the surfactant surrounding the DNA, thereby aligning homeotropically with the surface. In the first stage of the study depolarization effectiveness of the PVAN cells, DOP measurements were used. This parameter strongly depends on spatial distribution of birefringence [1,17] and spectral characteristics of light sources used in the experiments [18], as well. For this type of optical element the measured DOP depends on size of the incident beam and its input state of polarization (SOP). Therefore, a narrow band red line of the stabilized He-Ne laser has been used as a light source. All manufactured PVAN cells were characterized in frame of their electro-optic properties and were analyzed in spatial domain, as well as time domain by using crossed polarizers and polarimetric set-up. Additional measurement of Mueller matrices allows to characterize dichroic and birefringence properties of the manufactured PVAN cell. Real time control of micrographic images of PAVN cell gives information about long term stability of depolarization effect of the proposed device. This type of optical element was applied to validate depolarization sensitive interferometric system [19]. Crystals 2019, 9, 387 3 of 12 Crystals 2018, 8, x FOR PEER REVIEW 3 of 13

2. Technology of the PVAN CellCell

2.1. Preparation of Biopolymer Alignment Layer DNA-based biopolymer was used in this research with set of experiments in order to stabilize its aligning properties. The The pure pure DNA, DNA, as as a a linear and unbranched biopolymer, is soluble only in aqueous solutionssolutions whichwhich isis notnot compatiblecompatible with with typically typically devices devices fabrication fabrication processes. processes. Definitely, Definitely, it isit convenientis convenient to depositto deposit thin thin alignment alignment layers layers of DNA of DNA complexed complexed with with a suitable a suitable cationic cationic surfactant. surfactant. Such modificationSuch modification makes surfactantmakes surfactant complexes complexe of DNA solubles of DNA only insoluble organic only solvents. in organic Additionally, solvents. this alignmentAdditionally, surface this appearsalignment to surface be a stable appears at high to processingbe a stable temperaturesat high processing with notemperatures visible degradation with no ofvisible the film. degradation The required of the modification film. The required of DNA modification with some cationic of DNA surfactant with some complex cationic (see surfactant Figure1), suchcomplex as hexadecyltrimethylammonium (see Figure 1), such as chloride hexadecy (CTMA)ltrimethylammonium or dimethyldioctadecylammonium chloride (CTMA) chloride or (DODMAC)dimethyldioctadecylammonium was done based mainly chloride on the (DODMAC) procedure mentioned was done in based references mainly [20, 21on]. Inthe the procedure aqueous solutionmentioned DNA in references with a cationic [20,21] surfactant. In the aqueous combine solution through DNA ion exchangewith a cationic mechanism surfactant in which combine the + sodiumthroughions ion Naexchangepresent mechanism in DNA salt in which back bone the sodium are replaced ions byNa surfactant+ present in groups DNA [salt15] asback is presented bone are inreplaced Figure 1by. surfactant groups [15] as is presented in Figure 1.

Figure 1.1. DNADNA structure structure with with a surfactant a surfactant DODMAC, DODMAC, where: where: A, T, GA, and T, C—fourG and nitrogen-containingC—four nitrogen- nucleobasescontaining nucleobases and hydrogen and bonds hydrogen bind the bonds nitrogenous bind the bases nitrogenous of the two separatebases of polynucleotides. the two separate polynucleotides. CTMA was chosen because it is a standard surfactant with a single aliphatic tail for technological applications of DNA complexes. The choice of DODMAC surfactant was motivated by its two long CTMA was chosen because it is a standard surfactant with a single aliphatic tail for technological aliphatic tails supposed to more tightly fill the space around the DNA helix as compared to CTMA. applications of DNA complexes. The choice of DODMAC surfactant was motivated by its two long Long alkyl chains of the cationic surfactant molecules are oriented perpendicular to the film plane and aliphatic tails supposed to more tightly fill the space around the DNA helix as compared to CTMA. chiral DNA helices are oriented in the direction parallel to the film plane (perpendicular to the long Long alkyl chains of the cationic surfactant molecules are oriented perpendicular to the film plane alkyl chain) because of electrostatic attraction and thermodynamic stability [22]. and chiral DNA helices are oriented in the direction parallel to the film plane (perpendicular to the The DNA conversion was performed according to the procedure in which the aqueous solution long alkyl chain) because of electrostatic attraction and thermodynamic stability [22]. of the DNA polymer was added to an equal amount of the DODMAC aqueous solution and the The DNA conversion was performed according to the procedure in which the aqueous solution precipitate was collected by filtration under vacuum and purified by rinsing with de-ionized water. of the DNA polymer was added to an equal amount of the DODMAC aqueous solution and the DNA-DODMAC was dissolved in butanol and the solution was mixed in a glass bottle at 60 C. Once precipitate was collected by filtration under vacuum and purified by rinsing with de-ionized◦ water. completely dissolved, the solution was filtered through a 0.4 µm pore size syringe filter. DNA-DODMAC was dissolved in butanol and the solution was mixed in a glass bottle at 60 °C. Once 2.2.completely Manufacturing dissolved, Process the ofsolution the Cells was filtered through a 0.4 µm pore size syringe filter.

2.2. ManufacturingTest cells for DOP Process measurements of the Cells were prepared using glass plates coated with conductive layer of Indium Thin Oxide (ITO) having resistivity of 20 Ohms/square. Monopixel of a 1 cm2 area was Test cells for DOP measurements were prepared using glass plates coated with conductive layer patterned in the ITO by photolithography process. DNA-DODMAC complex was dissolved in butanol of Indium Thin Oxide (ITO) having resistivity of 20 Ohms/square. Monopixel of a 1 cm2 area was at a concentration of 3 wt. %. The solution was spin coated onto the substrates. Then, the film was patterned in the ITO by photolithography process. DNA-DODMAC complex was dissolved in baked at 80 ◦C for 1 hour to remove residual solvent. The two substrates were assembled using epoxy butanol at a concentration of 3 wt. %. The solution was spin coated onto the substrates. Then, the film glue and uniformly separated by 5 µm, 10 µm and 15 µm thick glass spacers. All cells were filled with was baked at 80 °C for 1 hour to remove residual solvent. The two substrates were assembled using the experimental LCs’ mixture having negative dielectric anisotropy described below. epoxy glue and uniformly separated by 5 µm, 10 µm and 15 µm thick glass spacers. All cells were filled with the experimental LCs’ mixture having negative dielectric anisotropy described below.

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2.3.2.3. Liquid Liquid Crystal Crystal Formulation Formulation 2.3. Liquid Crystal Formulation A high number of excellent nematic mixtures having positive dielectric anisotropy and high AA high high number number of of excellent excellent nematic nematic mixtures mixtures having having positive positive dielectric dielectric anisotropy anisotropy and and high high chemical stability have been formulated. However, very few mixtures with negative dielectric chemicalchemical stability stability have have been been formulated. formulated. However,However, veryvery fewfew mixtures mixtures with with negative negative dielectric dielectric anisotropy have been developed. Commercially available stable nematic materials for VAN displays anisotropyanisotropy have have been been developed. developed. Commercially Commercially available available stable stable nematic nematic materials materials for for VAN VAN displays displays are mainly 1,2-difluorobenzene derivatives having Δn around 0.09. Efficient depolarizer based on the areare mainly mainly 1,2-difluorobenzene 1,2-difluorobenzene derivatives derivatives having having∆ nΔn around around 0.09. 0.09. E Efficientfficient depolarizer depolarizer based based on on the the PVAN configuration requires sufficient retardance in the generated domains upon switching. In this PVANPVAN configuration configuration requires requires su sufficientfficient retardance retardance in in the the generated generated domains domains upon upon switching. switching. In In this this case, LCs material with a relatively high birefringence will be needed, in order to achieve sufficient case,case, LCs LCs material material with with a a relatively relatively high high birefringence birefringence will will be be needed, needed, in in order order to to achieve achieve su sufficientfficient retardance at leastπ π + 2π mπ for linear polarization πand π/2π + mπ for , for retardanceretardance at at least least+ π2 + m 2 mforπ linearfor linear polarization polarization and and/2 + mπ/2 +for m circularπ for circular polarization, polarization, for m = 0,for m = 0, 1,… [15]. As the potential exploitation of this device is related to LC properties, methods of 1,m... = 0,[15 1,…]. As [15]. the As potential the potential exploitation exploitation of this of device this device is related is related to LC properties,to LC properties, methods methods of their of their syntheses and performance improvements related to cell manufacturing are important. The LC synthesestheir syntheses and performance and performance improvements improvements related to rela cellted manufacturing to cell manufacturing are important. are important. The LC mixture The LC mixture used in this work is an experimental mixture under code name of 2050 prepared by Military usedmixture in this used work in isthis an work experimental is an experimental mixture under mixture code under name ofcode 2050 name prepared of 2050 by prepared Military Universityby Military University of Technology of Warsaw, Poland. This mixture has been prepared through a three- ofUniversity Technology of of Technology Warsaw, Poland. of Warsaw, This mixture Poland. has This been mixture prepared has through beena prepared three- component through eutectica three- component eutectic mixture (see Table1). To increase birefringence, we selected laterally difluoro- mixturecomponent (see Tableeutectic1). Tomixture increase (see birefringence, Table1). To weincrease selected birefringence, laterally difluoro-substituted we selected laterally terphenyls difluoro- substituted terphenyls Compound (I) [23,24]. They have fully aromatic structure with a negative Compoundsubstituted (I) terphenyls [23,24]. They Compound have fully (I) aromatic [23,24]. They structure have with fully a negativearomatic dielectricstructure anisotropywith a negative and dielectric anisotropy and exhibit excellent chemical and photochemical stability. Compounds (II) and exhibitdielectric excellent anisotropy chemical and andexhibit photochemical excellent chemical stability. and Compounds photochemical (II)and stability. (III) are Compounds very convenient (II) and (III) are very convenient components to decrease the melting point of three ring eutectic mixtures. components(III) are very to convenient decrease the components melting point to decrease of three ringthe melting eutectic point mixtures. of three ring eutectic mixtures.

TableTable 1. 1.General General molecular molecular structures structures of of compounds compounds used used to to form form the the investigated investigated 2050 2050 nematic nematic Table 1. General molecular structures of compounds used to form the investigated 2050 nematic mixturemixture and and their their weight weight %. %. mixture and their weight %. Components Chemical Structure Weight % Components ComponentsChemical Chemical Structure Weight % Weight % I F F I F F

R1 R2 34.1 I R1 R2 34.1 34.1

R1 and R2 = alkyl (CH3-C5H11) R1R1 andand R2R2= = alkylalkyl (CH(CH33-C5H1111)) II II C H OCH 18.6 II C3H7 OCH3 18.6 18.6 C3H7 OCH3 18.6

III III III C3H7 OC2H5 47.3 47.3 C3H7 OC2H5 47.3 3 7 2 5

The resulting mixture 2050 has negative dielectric anisotropy and exhibits the following optical The resulting mixture 2050 has negative dielectric anisotropy and exhibits the following optical The resulting mixtureλ 2050 = 589 has negative dielectric anisotropy and exhibits the following optical parameters measured at λ = 589 nm: ordinary index no = 1.5006, extraordinary index ne = 1.6273 and parameters measured at λ = 589 nm: ordinary index no = 1.5006, extraordinary index ne = 1.6273 and parametersbirefringence measured Δn = 0.1273. at λ =The589 phase nm: sequence ordinary as index a function no = 1.5006, of the temperature extraordinary of the index nematic ne = mixture1.6273 birefringence Δn = 0.1273. The phase sequence as a function of the temperature of the nematic mixture andis Cr birefringence 0 < N <51.4∆ n°C= Iso.0.1273. Temperature The phase of sequence phase transition as a function between of the isotropic temperature andof nematic the nematic phase is Cr 0 < N <51.4 °C Iso. Temperature of phase transition between isotropic and nematic phase mixture(clearing is Crtemperature) 0 < N <51.4 is◦ Caround Iso. Temperature 51.4 °C. of phase transition between isotropic and nematic phase (clearing temperature) is around 51.4 °C. (clearingDielectric temperature) spectroscopy is around was 51.4 performed◦C. to confirm the negative electric anisotropy of the Dielectric spectroscopy was performed to confirm the negative electric anisotropy of the proposedDielectric mixture. spectroscopy The procedure was performed of this tomeasurement confirm the negative is described electric in anisotropyreference [25]. of the The proposed electric proposed mixture. The procedure of this measurement is described in reference [25]. The electric mixture.anisotropy The measured procedure at of thisroom measurement temperature is (25 described °C) and in referenceat the frequency [25]. The electricof 1 kHz anisotropy is about anisotropy measured at room temperature (25 °C) and at the frequency of 1 kHz is about measuredΔε = −0.8. atThis room LC mixture temperature shows (25 a very◦C) and low atdielectric the frequency anisotropy of 1 since kHz isconstituent about ∆ε compounds= 0.8. This of LC the Δε = −0.8.This LC mixture shows a very low dielectric anisotropy since constituent compounds− of the mixturemixture shows do not a contain very low strong dielectric polar anisotropy groups like since -CN constituentor -NCS. compounds of the mixture do not mixture do not contain strong polar groups like -CN or -NCS. contain strong polar groups like -CN or -NCS. 3. Electro-Optic Measurements 3.3. Electro-Optic Electro-Optic Measurements Measurements Polarimetric and crossed polarizers set-ups were used to study depolarization properties of PolarimetricPolarimetric and and crossed crossed polarizers polarizers set-ups set-ups were were used used to to study study depolarization depolarization properties properties of of manufactured PVAN cells. Both were integrated to use the same light source what was schematically manufacturedmanufactured PVAN PVAN cells. cells. Both Both were were integrated integrated to to use use the the same same light light source source what what was was schematically schematically presented in Figure 2. This set-up consists of spatial filter module (SF—Thorlabs), SOP generator presentedpresented in in Figure Figure2. 2. This This set-up set-up consists consists of of spatial spatial filter filter module module (SF—Thorlabs), (SF—Thorlabs), SOP SOP generator generator (PSG—Thorlabs), beam splitter (BS—Thorlabs), mirror M, a pair of SOP analyzers PSA1 and PSA2 (PSG—Thorlabs),(PSG—Thorlabs), beam beam splitter splitter (BS—Thorlabs), (BS—Thorlabs), mirror mirror M, M, a a pair pair of of SOP SOP analyzers analyzers PSA1 PSA1 and and PSA2 PSA2 (PAX5710VIS, Thorlabs), CCD camera (DMK 72AUC02, The Imaging Source) and function generator (PAX5710VIS,(PAX5710VIS, Thorlabs), Thorlabs), CCD CCD camera camera (DMK (DMK 72AUC02, 72AUC02, The The Imaging Imaging Source) Source) and and function function generator generator (FG-Agilent), and personal computer (PC) as a control unit. (FG-Agilent),(FG-Agilent), and and personal personal computer computer (PC) (PC) as as a controla control unit. unit.

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Figure 2. Integrated polarimetric and crossed polarizers’ set-ups for depolarization properties Figure 2. Integrated polarimetric and crossed polarizers’ set-ups for depolarization properties characterization of a PVAN cell. SF—spatial filter module, PSG—SOP generator, BS—beam splitter, characterization of a PVAN cell. SF—spatial filter module, PSG—SOP generator, BS—beam splitter, PSA1—polarimeter as a SOP analyzer, M—mirror, PSA2—SOP analyzer as a linear with PSA1—polarimeter as a SOP analyzer, M—mirror, PSA2—SOP analyzer as a linear polarizer with vertical orientation, FG—function generator, PC—personal computer. vertical orientation, FG—function generator, PC—personal computer. Laser light (He-Ne λ = 633 nm) illuminates the spatial filter module (SF) first. A Gaussian linearly Laser light (He-Ne λ = 633 nm) illuminates the spatial filter module (SF) first. A Gaussian linearly polarized mode of He-Ne laser is transformed by SF to obtain light beam with homogeneous intensity polarized mode of He-Ne laser is transformed by SF to obtain light beam with homogeneous intensity and by using lenses and diaphragm the beam size is adjusted up to around 5mm of its outer diameter. and by using lenses and diaphragm the beam size is adjusted up to around 5mm of its outer diameter. Such beam passes through a SOP generator (PSG) which was assembled with a linear polarizer and Such beam passes through a SOP generator (PSG) which was assembled with a linear polarizer and a quarter . By using PSG, the manual adjustment of demanded input SOPs is possible. a quarter waveplate. By using PSG, the manual adjustment of demanded input SOPs is possible. Light Light beam with selected SOP is next transmitted through the PVAN cell and polarization changes beam with selected SOP is next transmitted through the PVAN cell and polarization changes are are measured by a SOP analyzer PSA1. Micrographs of the tested sample texture are taken by CCD measured by a SOP analyzer PSA1. Micrographs of the tested sample texture are taken by CCD camera after sequence reflections of a light beam from BS and M, and its passing through the second camera after sequence reflections of a light beam from BS and M, and its passing through the second SOP analyzer PSA2. In the polarimetric part of the set-up as PSA1 the commercial PAX5710VIS SOP analyzer PSA2. In the polarimetric part of the set-up as PSA1 the commercial PAX5710VIS polarimetric head (ThorLabs) was applied. PSG and PSA2 form the crossed polarizers’ part of the polarimetric head (ThorLabs) was applied. PSG and PSA2 form the crossed polarizers’ part of the set- set-up because PSA2 is a simple linear analyzer. Function generator (FG) drives the tested LC cell to up because PSA2 is a simple linear analyzer. Function generator (FG) drives the tested LC cell to obtain its electro-optic characteristics. PC was used to operate FG, CCD and PSA1. obtain its electro-optic characteristics. PC was used to operate FG, CCD and PSA1. Voltage changes of the FG signal allow to induce an electric field inside the LC cell to reach Voltage changes of the FG signal allow to induce an electric field inside the LC cell to reach birefringence spatial modulation [17]. Then, measured by PSA1 Stokes vector is a spatial integration of birefringence spatial modulation [17]. Then, measured by PSA1 Stokes vector is a spatial integration all SOPs present in the cross-section of the transmitted beam. Since this beam carries mixed SOPs the of all SOPs present in the cross-section of the transmitted beam. Since this beam carries mixed SOPs measured Stokes vector shows this light beam as a depolarized one. the measured Stokes vector shows this light beam as a depolarized one. For proper validation of depolarization properties of a PVAN cell in all further experiments as For proper validation of depolarization properties of a PVAN cell in all further experiments as a driven signal was used square waveform with a 1 kHz frequency and its voltage was changed a driven signal was used square waveform with a 1 kHz frequency and its voltage was changed within the range of 0–10 V with an increment of 50 mV. Additionally, thickness of the PNAN cell within the range of 0–10 V with an increment of 50 mV. Additionally, thickness of the PNAN cell was was taken into account and there were tested samples with thicknesses of 5 µm, 10 µm and 15 µm. taken into account and there were tested samples with thicknesses of 5 μm, 10 μm and 15 μm. In each In each measurement, the tested sample was illuminated first by linear horizontal (H) SOP and full measurement, the tested sample was illuminated first by linear horizontal (H) SOP and full polarization characterization of this device another specific input SOPs were generated, i.e., another polarization characterization of this device another specific input SOPs were generated, i.e. another three linearly polarized with azimuth: vertical (V), at 45 and at 45 , and two circularly polarized three linearly polarized with azimuth: vertical (V), at 45°◦ and at −−45°,◦ and two circularly polarized with right (R) and left (L) handedness. with right (R) and left (L) handedness. The above measurements allow to obtain Mueller matrices for full characterization of tested samples. However, as the first validation of PVAN cells’ principles of work, DOP changes for two representative input SOPs, i.e., H and R were presented in Figure3, respectively. The above presented DOP properties as a function of the applied voltage for LC response prove that PVAN cells are the effective depolarizers at certain values of voltages. This effectiveness has periodic character and with increasing thickness of the cell, the number of extremes increases proportionally. Number of minima doubles for circular R SOP (Figure3b) comparing to H SOP (Figure3a). However, DOP for linear SOP reaches lower values of minima than the circular one. This effect is related to induced by applied voltage linear birefringence of the used PVAN and is similar to results presented in [17]. As it was mentioned above, the DNA-surfactant film is expected as a promising homeotropic alignment film with rubbing-free. As result of the anchoring strength of homeotropic alignment is weak, therefore Freedericksz(a) transition is soften to around 2 V [26]. (b) Figure3a,b shows that dynamics of DOP changes above this voltage increases su fficiently with μ LC thickness.Figure 3. DOP For theas a samplefunction with of the a voltage thickness for ofPVAN 5 µm cells (Figure with3 thicknesses: green dotted 5 m line) (green the dotted e ffectiveness line), of μ μ depolarization10 m (blue is dashed the lowest line) and and 15 it hasm (red only dot-dashed one minimum line) for for input linear SOP: polarization (a) linear Hand and DOP(b) circular is around 18% atR. 2.65 V (Figure3a). For samples with thicknesses of 10 µm and 15 µm first minima appear just

Crystals 2018, 8, x FOR PEER REVIEW 5 of 13

Figure 2. Integrated polarimetric and crossed polarizers’ set-ups for depolarization properties characterization of a PVAN cell. SF—spatial filter module, PSG—SOP generator, BS—beam splitter, PSA1—polarimeter as a SOP analyzer, M—mirror, PSA2—SOP analyzer as a linear polarizer with vertical orientation, FG—function generator, PC—personal computer.

Laser light (He-Ne λ = 633 nm) illuminates the spatial filter module (SF) first. A Gaussian linearly polarized mode of He-Ne laser is transformed by SF to obtain light beam with homogeneous intensity and by using lenses and diaphragm the beam size is adjusted up to around 5mm of its outer diameter. Such beam passes through a SOP generator (PSG) which was assembled with a linear polarizer and a quarter waveplate. By using PSG, the manual adjustment of demanded input SOPs is possible. Light beam with selected SOP is next transmitted through the PVAN cell and polarization changes are measured by a SOP analyzer PSA1. Micrographs of the tested sample texture are taken by CCD camera after sequence reflections of a light beam from BS and M, and its passing through the second SOP analyzer PSA2. In the polarimetric part of the set-up as PSA1 the commercial PAX5710VIS polarimetric head (ThorLabs) was applied. PSG and PSA2 form the crossed polarizers’ part of the set- up because PSA2 is a simple linear analyzer. Function generator (FG) drives the tested LC cell to obtain its electro-optic characteristics. PC was used to operate FG, CCD and PSA1. Voltage changes of the FG signal allow to induce an electric field inside the LC cell to reach birefringence spatial modulation [17]. Then, measured by PSA1 Stokes vector is a spatial integration of all SOPs present in the cross-section of the transmitted beam. Since this beam carries mixed SOPs theCrystals measured2019, 9, 387 Stokes vector shows this light beam as a depolarized one. 6 of 12 For proper validation of depolarization properties of a PVAN cell in all further experiments as a driven signal was used square waveform with a 1 kHz frequency and its voltage was changed µ withinabove thethe thresholdrange of 0–10 voltages V with for an both increment input polarizations. of 50 mV. Additionally, And for a 10 thicknessm sample of the (blue PNAN dashed cell lines) was takenDOP reachesinto account its global and minimathere were for bothtested input samples SOP, with i.e.,4.4% thicknesses at 2.1 V of for 5 horizontalμm, 10 μm andand 8% 15 atμm. 1.95 In Veach for µ measurement,right circular. In the contrast tested for sample the sample was with illuminated a thickness first of 15by mlinear these horizontal minima are (H) of 7% SOP at 2.65 and V andfull µ 11%polarization at 3 V. These characterization values suggest of thatthis device the PVAN another cell with specific a 10 inputm thickness SOPs were is the generated, most effective i.e. another among µ threeanalyzed linearly samples. polarized Moreover, with azimuth: these measurement vertical (V), data at 45° show and that at PVAN−45°, and cell two with circularly a 5 m thickness polarized is withtoo thin right to (R) be usedand left as an(L) e handedness.ffective depolarizer and in further analysis this sample was excluded.

(a) (b) μ Figure 3. DOPDOP as as a a function function of of the the voltage voltage fo forr PVAN PVAN cells with thicknesses: 5 5 µmm (green (green dotted dotted line), line), μ μ 10 µm (blue dashed line)line) andand 1515µ mm (red(red dot-dashed dot-dashed line) line) for for input input SOP: SOP: (a ()a linear) linear H H and and (b )(b circular) circular R. R. However, an extended analysis of depolarization properties requires measurement of Mueller matrices of a PVAN cell. Mueller matrix of an LCC sample allows to characterize losses, dichroism, birefringence, and depolarization [4,27]. In this paper, the first of these parameters was excluded from consideration because above Fréedericksz transition, all manufactured samples exhibit small total losses around 0.5 dB. Due to the fact that random orientation of molecules in such type of LCC induces a random fluctuation of the , the light scattering capability of the cell has to be investigated [28]. This effect was described as a small angle light scattering in [29], and its influence on depolarization properties of the PVAN cell is discussed at the end of this paper. To obtain information about next three parameters, the polar decomposition method was used [4,27,30]. The normalized experimentally Mueller matrix M in this model is a concatenation of three matrices MD, MR and M∆ which carries information about dichroism, birefringence and depolarization, respectively. This takes the following mathematical form of: M = M∆ MRMD (1) Depolarization properties of optical element beads on Mueller matrix can be calculated based on Matrix M∆ or directly from the experimental matrix M as average DOP (AvDOP) [4,27] and anisotropic depolarization degree (Add) [4]. In the paper, direct model and mentioned parameters are calculated by the following equations:

Z π Z π 1 4 AvDOP = DOP(α, ε) cos 2εdαdε (2a) 4π 0 π − 4 q  1  2 2 2   S0 (α, ε) + S0 (α, ε) + S0 (α, ε)   1 2 3  cos α cos ε  DOP(α, ε) = if S0 = M S and S =   (2b) S (α, ε)  sin α cos ε  0    sin ε 

AvDOPmax AvDOP Add = − min (2c) AvDOPmax + AvDOPmin where: α and ε are azimuth and ellipticity of input SOP represented by Stokes vector S. Crystals 2019, 9, 387 7 of 12 Crystals 2018, 8, x FOR PEER REVIEW 7 of 13

depolarizingAvDOP isoptical an integral element of DOP has calculatedAvDOP = from1 and output it is 0 Stokes for totally vector depolarizingS0 which depends element. on generalPartial SOPdepolarizing of the input devices Stokes have vector intermediateS and Mueller values. matrix In MFigureof the 4a tested these optical parameters element. for Non-depolarizingthe tested PVAN opticalcell with element a thickness has AvDOP of 10 μ=m 1and and 15 itμ ism 0 were for totally presented. depolarizing Add parameter element. is Partial a cumulative depolarizing information devices haveabout intermediate anisotropy of values. the average In Figure DOP4a thesecalculated parameters as a relative for the testeddifference PVAN of cellmaximal with a and thickness minimal of 10valuesµm andof AvDOP. 15 µm were Due presented. to the fact Add that parameter DOP char isacteristics a cumulative presented information in Figure about anisotropy3 have different of the averagelocations DOP of minima calculated and asmaxima a relative for dilinearfference and of circular maximal input and SOPs minimal on a values voltage of scale, AvDOP. it is Due expected to the factthat thattested DOP samples characteristics can be presentedconsidered in Figureas at leas3 havet partially di fferent anisotropic locations of elem minimaent. andTherefore, maxima it foris linearreasonable and circularto calculate input Add SOPs parameter. on a voltage In this scale, case it is Add expected = 0 means that tested that the samples depolarizer can be is considered isotropic asand at Add least = partially 1 means anisotropic that it is totally element. anisotropic. Therefore, In it Figure is reasonable 4b Add to parameters calculate Add of the parameter. tested samples In this caseare presented. Add = 0 means that the depolarizer is isotropic and Add = 1 means that it is totally anisotropic. In FigureAnalyses4b Add of parametersplots presented of the in tested Figure samples 4a show are th presented.at both tested elements have relatively high valuesAnalyses of AvDOP of plotsparameter presented because in Figure the minima4a show are that of around both tested 0.35 and elements it is far have from relatively the measured high valuesDOP presented of AvDOP in parameterFigure 3. However, because the informatio miniman are about of around AvDOP 0.35 gives and general it is far information from the measured on how DOPstrong presented attention inneeds Figure to3 .be However, taken to informationapply proper about voltage AvDOP to a givesknown general input informationSOP or how onto howtune strongvoltage attention to minimize needs toDOP be taken if input to apply SOP proper is unknown. voltage to Unfortunately, a known input SOPanisotropic or how toproperties tune voltage of todepolarization minimize DOP of iftested input samples SOP is unknown. presented Unfortunately,in Figure 4b in anisotropic this form propertiesdo not allow of depolarization to apprehend ofif testedhigh or samples low value presented of Add in Figureis preferable4b in this or formnot for do notthis allowdevice. to apprehendTherefore, iffollowing high or low the valuemethod of Addpresented is preferable in [31], orthe not 2D for map this of device. AvDOP Therefore, as a function following of input the method SOP parameters presentedα in and [31 ε], is the shown 2D map in ofFigure AvDOP 5. Voltage as a function values of selected input SOP for parametersthese plotsα wereand εtakenis shown as minima in Figure of5 linear. Voltage and values circular selected input forSOPs, these respectively. plots were taken as minima of linear and circular input SOPs, respectively.

(a) (b)

Figure 4. CalculatedCalculated (a ()a AvDOP) AvDOP and and (b ()b Add) Add as asa function a function of the of theapplied applied voltage voltage for PVAN for PVAN cells with cells withthicknesses thicknesses of 10 ofμm 10 (blueµm dotted (blue dotted line) and line) 15 and μm 15(dot-dashedµm (dot-dashed line). AvDOP—average line). AvDOP—average DOP, Add— DOP, Add—anisotropicanisotropic depolarization depolarization degree. degree.

The above 2D maps show zones labeled by AvDOPAvDOP values.values. Red zones point maxima while blue zones point minima minima of of this this parame parameter.ter. Proper Proper selection selection of ofvoltage voltage allows allows to reach to reach minimum minimum DOP DOP for fora certain a certain input input SOP SOP (Figure (Figure 3),3 ),but but the the above above 2D 2D ma mapp allows allows to to access access the influenceinfluence ofof changeschanges ofof input SOPSOP onon measuredmeasured DOP.DOP. Thus, Thus, if if the the input input SOP SOP is is linear linear H H as as in in Figure Figure5a,c, 5a,c, for for both both samples samples it is it necessaryis necessary to keepto keep SOP linearSOP linear to be into or be close in toor theclose DOP to globalthe DOP minimum. global Inputminimum. circular Input polarizations circular [seepolarizations Figure5a,d] [see have Figure higher 5a,d] AvDOP have higher and their AvDOP behavior and intheir both behavior samples in is both opposite samples to previous is opposite plots. to Hereprevious minima plots. are Here close minima to circular are SOPs close and to changescircular ofSOPs input and SOP changes in the linear of input polarization SOP in directionsthe linear locatepolarization maxima directions around thelocate linear maxima V SOP. around the linear V SOP. In the next step of the analysis the polar decomposition defined by relations (1) was used to extract information about dichroism and birefringence of the tested PVAN cell. Voltage changes of representative, cumulative parameters for mentioned above effects as diattenuation and retardance [30] are presented in Figure6.

Crystals 2018, 8, x FOR PEER REVIEW 8 of 13

Crystals 2019, 9, 387 8 of 12 Crystals 2018, 8, x FOR PEER REVIEW 8 of 13

(a) (b)

(a) (b)

(c) (d)

Figure 5. Calculated AvDOP maps for PVAN cells with thicknesses: 10μm (a) & (b) and 15 μm (c) & (d) for following voltages and input SOPs (a) 1.95 V & circular R, (b) 2.1 V & linear H, (c) 2.1 V & linear H and (d) 3 V & circular R.

(c) (d) In the next step of the analysis the polar decomposition defined by relations (1) was used to extractFigureFigure information 5. 5.Calculated Calculated about AvDOP AvDOP dichroism maps maps for for and PVANPVAN birefringence cellscells withwith thicknesses:thicknesses:of the tested 10 10 PVANμµmm (a ()a &)&(cell. (b)b Voltageand) and 15 15 μ mchangesµ m(c)( c&)& of representative,(d)(d for) for following following cumulative voltages voltages and parameters and input input SOPs SOPs for (a mentione) ( 1.95a) 1.95 V &Vd circular& above circular R,effects (R,b) ( 2.1b )as 2.1 V diattenuation & V linear & linear H, (H,c) and 2.1(c) V2.1 retardance & V linear & [30]H linear andare presented (d H) 3and V & (d circular) in 3 VFigure & circular R. 6. R.

In the next step of the analysis the polar decomposition defined by relations (1) was used to extract information about dichroism and birefringence of the tested PVAN cell. Voltage changes of representative, cumulative parameters for mentioned above effects as diattenuation and retardance [30] are presented in Figure 6.

(a) (b)

FigureFigure 6. Calculated:6. Calculated: ( a(a)) diattenuationdiattenuation and and (b (b) )retardance retardance of oftested tested PVAN PVAN cells cells with with thicknesses thicknesses of 10 of μ μ 10 µmm (blue(blue dotted line) line) and and 15 15 µmm (dot-dashed (dot-dashed line). line).

DiattenuationDiattenuation presented presented in Figurein Figure6a calculated 6a calculated basing basing on MD onmatrices MD matrices has very has small very fluctuations small andfluctuations in this case bothand in tested this(a) samplescase both are tested dichroism samp free.les are However, dichroism calculated free. However,(b) total retardance calculated (Figure total6 b) based onFigure matrices 6. Calculated:MR includes (a) diattenuation information and ( aboutb) retardance cumulative of tested birefringence PVAN cells with of thethicknesses PVAN of cell. 10 These calculationsμm (blue prove dotted that line) depolarization and 15 μm (dot-dashed properties line). of these devices are strongly connected with mean birefringence. Calculated birefringence [30] from retardances of both samples are of 0.116 and 0.111 for thicknessesDiattenuation of 10 µm andpresented 15 µm, in respectively Figure 6a andcalculated these values basing fully on correspondMD matrices with has data very mentioned small influctuations Table1 of the and previous in this paragraph. case both tested samples are dichroism free. However, calculated total

Crystals 2018, 8, x FOR PEER REVIEW 9 of 13

retardance (Figure 6b) based on matrices MR includes information about cumulative birefringence of Crystalsthe PVAN2019, 9 ,cell. 387 These calculations prove that depolarization properties of these devices are strongly9 of 12 connected with mean birefringence. Calculated birefringence [30] from retardances of both samples are of 0.116 and 0.111 for thicknesses of 10 μm and 15 μm, respectively and these values fully Spatial and time domain electro-optic characteristics of the tested PVAN cells were characterized correspond with data mentioned in Table 1 of the previous paragraph. based on microphotographs observed under crossed polarizers’ configuration of the experimental Spatial and time domain electro-optic characteristics of the tested PVAN cells were characterized set-upbased from on microphotographs Figure2 and were observed presented under in Figure crosse7.d polarizers’ configuration of the experimental set-upMicroscopic from Figure textures 2 and were of a conventionalpresented in Figure PVAN 7. cell show that in this VAN nematic LC with null pretilt,Microscopic upon switching textures by externalof a conventional electric field, PVAN the cell field show causes that continuousin this VAN deformations nematic LC with of the null LCs’ molecules.pretilt, upon As switching result of the by conflictexternal betweenelectric field, different the field orientations causes continuous of the molecules, deformations topological of the LCs’ defects aremolecules. produced. As Furthermore, result of the conflict disclinations between appear different where orientations the local orientationof the molecules, of LC topological director is undefined.defects Onare the produced. other hand, Furthermore, it can be supposed disclinations that theappear domain where formation the local originates orientation from of the LC occurrence director is due toundefined. undefined On switching the other direction hand, ofit can the molecules’be supposed director. that the This domain domains’ formation behavior originates is characteristic from the for theoccurrence formation due of to numerous undefined umbilical switching defects direction induced of the bymolecules’ applied director. electric fieldThis todomains’ the nematic behavior liquid crystalis characteristic with negative for the dielectric formation anisotropy, of numerous confined umbilical in cells defects with induced homeotropic by applied boundary electric conditions. field to Inthe this nematic case only liquid one crystal integer with strength negative type dielectric of director anisotropy, field deformations confined in cancells bewith formed homeotropic which are regionsboundary where conditions. the in-plane In this component case only one of theinteger director strength rotates type through of director2 fieldπ (s =deformations1) [32], resulting can be in ± ± spatialformed distribution which are regions of birefringence where the in in-plane a PVAN component cell under of voltage the director action rotates (see Figurethrough7). ± These 2π (s = defects ± 1) are[32], important resulting in in practical spatial distribution applications, of birefringence such as depolarization in a PVAN ofcell polarized under voltage light. action Moreover, (see Figure we have observed7). These that defects the morphologyare important of in such practical textures applications, changes insuch time as duedepolarization to umbilical of defect polarized annihilation light. overMoreover, time where we have defects observed of opposite that the sign morphology and equal of strengthsuch textures attract changes each otherin time and due annihilate, to umbilical thus defect annihilation over time where defects of opposite sign and equal strength attract each other and reduce the number of observed defects with time [33]. Similar results have been observed in our annihilate, thus reduce the number of observed defects with time [33]. Similar results have been experiment as it is shown in the sequences of Figure7a to Figure7b and to Figure7c for 10 µm thick observed in our experiment as it is shown in the sequences of Figure 7a to Figure 7b and to Figure 7c sample and next Figure7d–f for 15 µm thick cell. The annihilation dynamics of nematic umbilical for 10 μm thick sample and next Figure 7d–f for 15 μm thick cell. The annihilation dynamics of defects, induced by electric field application to homeotropically oriented liquid crystal samples of nematic umbilical defects, induced by electric field application to homeotropically oriented liquid negativecrystal samples dielectric of anisotropy,negative dielectric were experimentally anisotropy, were investigated experimentally in [34 investigated]. in [34].

0.84 mm 0.84 mm 0.84 mm

(a) (b) (c)

0.84 mm 0.84 mm 0.84 mm

(d) (e) (f)

FigureFigure 7. 7.Microphotographs Microphotographs of 2050of 2050 LC LC domains domains on the onDODA the DODA biofilm biofilm observed observed under crossedunder crossed polarizers forpolarizers input linear for horizontalinput linear SOP horizontal and under SOP voltage and under of 2.15 voltage V applied of 2.15 to V the applied cell in to three the cell time in intervals three time of the μ μ samplesintervals with of the thickness samples of with 10 µm thickness after (a) of 25 10 s, (bm) 150after s ( ac) 30025 s, s ( andb) 150 15 sµ (mc) after300 s( dand) 25 15 s, (em) 150after s, ( (ef)) 25 300 s. s, (f) 150 s, (g) 300 s. Figure8 shows time evolution of the measured DOP at di fferent applied voltages. Since the azimuthal tilting of the LC molecules is not defined, the measurement of DOP in 10 µm and 15 µm cells shows that it takes more than 200 s for the first case and 25s for the second to reach the stable DOP through the reorientation process. Similar results have been observed previously [35]. To study the light scattering capability of the cells with thickness of 5 µm, 10 µm and 15 µm, Fourier transform of scattered light has been adopted. This method has been developed as a sensitive Crystals 2019, 9, 387 10 of 12 one for studying this effect from inhomogeneous and dynamic structures [36]. The samples were illuminated using a parallel beam of He-Ne laser and placed behind the lens at a certain distance from the focal plane. We applied to each sample a voltage corresponding to minimum (DOP); V = 2.65 V, 2.15 V and 2.15 V in the case of 5 µm, 10 µm and 15 µm, respectively. We recorded the images of the scattered beams that are detected by CCD camera placed at Fourier plan after different times’ lag detection. Figure9 shows images of spectral intensities’ distributions of the focused beams after switching ON of the cells with voltages corresponding to the DOP minimum. The small angular scattering distribution has been detected in Fourier plane where the beam profile differs from the focused condition in OFF state (Figure9a,e,i) showing beam spot spreading. As results of a spatial and temporal changes of refractive index distribution due to annihilation of umbilical defects, a spatial reshapingCrystalsCrystals 20182018 of,, 88 the,, xx FORFOR beam PEERPEER spreading REVIEWREVIEW changes with time. Significant changes of the beam reshaping1010 ofof with 1313 time are observed in thicker cells (10 and 15 µm). However, in a thin cell of 5 µm, no significant changes FigureFigure 88 showsshows timetime evolutionevolution ofof thethe measuredmeasured DOPDOP atat differentdifferent appliedapplied voltages.voltages. SinceSince thethe in light spreading is observed. Correlation of scattering properties of the studied cellsμ with theirμ azimuthalazimuthal tiltingtilting ofof thethe LCLC moleculesmolecules isis notnot defined,defined, thethe measurementmeasurement ofof DOPDOP inin 1010 μmm andand 1515 μmm dynamic change of spatial refractive index distribution, thickness effect and temperature dependence cellscells showsshows thatthat itit takestakes moremore thanthan 200200 ss forfor thethe fifirstrst casecase andand 25s25s forfor thethe secondsecond toto reachreach thethe stablestable will be a subject of a further study. DOPDOP throughthrough thethe reorientationreorientation process.process. SimilarSimilar resultsresults havehave beenbeen observedobserved previouslypreviously [35].[35].

(a)(a) (b)(b)

FigureFigureFigure 8. 8.8.Time TimeTime evolution evolution evolution ofof of measuredmeasured measured DOPDOP at at different didifferentfferent appliedapplied voltages voltages to to PVAN PVAN PVAN cells cells cells with with with thickness thickness thickness μ μ of:of:of: ( a (()aa) 10) 1010µ mμmm and andand ( b((bb))) 15 1515µ μm.m.m. TheThe SOPSOP ofof thethe incident incident light light isis linearlylinearly HH H polarized.polarized. polarized.

OFFOFF statestate ON ON statestate 1 1 ss 25 25 ss 150 150 s s

μ 55 μmm

(a)(a) (b)(b) (c)(c) (d)(d)

μ 1010 μmm

(e)(e) (f) (f) (g) (g) (h) (h)

μ 1515 μmm

(i)(i) (j) (j) (k) (k) (l) (l) μ FigureFigureFigure 9. 9.9.Spectral SpectralSpectral intensity intensityintensity distribution distributiondistribution ofof aa focusedfocused beam beam transmitted transmitted byby by cellscells cells ofof of thicknessthickness thickness ofof of 55 5 μm,µm,m, μ μ 101010µ m μmm and andand 15 µ1515m μ whenmm whenwhen the cellsthethe cells arecells driven areare drivendriven with thewithwith voltage thethe vovo ofltageltage V = 2.65ofof VV V, == 2.15 2.652.65 V V,V, and 2.152.15 2.15 VV V, andand respectively. 2.152.15 V,V, respectively. Figure 9a,e,i represent the focused condition at V = 0. The images of scattered beam are (a,respectively.e,i) represent Figure the focused 9a,e,i represent condition the at focused V = 0. The cond imagesition at of V scattered = 0. The images beam are of recordedscattered beam by a CCD are recorded by a CCD camera placed at Fourier plan after different times’ lag detection. The SOP of the camerarecorded placed by a at CCD Fourier camera plan placed after di atff erentFourier times’ plan lag after detection. different The times’ SOP lag of detection. the incident The light SOP is of linear the incident light is linear H polarized. Hincident polarized. light is linear H polarized. μ μ μ ToTo studystudy thethe lightlight scatteringscattering capabilitycapability ofof thethe cellscells withwith thicknessthickness ofof 55 μm,m, 1010 μmm andand 1515 μm,m, FourierFourier transformtransform ofof scatteredscattered lightlight hashas beenbeen adopted.adopted. ThisThis methodmethod has has beenbeen developed developed as as a a sensitive sensitive oneone forfor studyingstudying thisthis effecteffect fromfrom inhomogeneouinhomogeneouss andand dynamicdynamic structuresstructures [36].[36]. TheThe samplessamples werewere illuminatedilluminated usingusing aa parallelparallel beambeam ofof He-NeHe-Ne laserlaser andand placedplaced behindbehind thethe lenslens atat aa certaincertain distancedistance fromfrom thethe focalfocal plane.plane. WeWe appliedapplied toto eacheach samplesample aa voltagevoltage correspondingcorresponding toto minimumminimum (DOP);(DOP); VV == μ μ μ 2.652.65 V,V, 2.152.15 VV andand 2.152.15 VV inin thethe casecase ofof 55 μm,m, 1010 μmm andand 1515 μm,m, respectively.respectively. WeWe recordedrecorded thethe imagesimages ofof thethe scatteredscattered beamsbeams thatthat areare detecteddetected byby CCDCCD camecamerara placedplaced atat FourierFourier planplan afterafter differentdifferent times’times’ laglag detection.detection. FigureFigure 99 showsshows imagesimages ofof spectralspectral inintensities’tensities’ distributionsdistributions ofof thethe focusedfocused beamsbeams afterafter switchingswitching ONON ofof thethe cellscells withwith voltagesvoltages correspondingcorresponding toto thethe DOPDOP minimum.minimum. TheThe smallsmall angularangular scatteringscattering distributiondistribution hashas beenbeen detecteddetected inin FourierFourier planeplane wherewhere thethe beambeam profileprofile differsdiffers fromfrom thethe focusedfocused conditioncondition inin OFFOFF statestate (Figure(Figure 9a,e,i)9a,e,i) showinshowingg beambeam spotspot spreading.spreading. AsAs resultsresults ofof aa spatialspatial

Crystals 2019, 9, 387 11 of 12

4. Conclusions Depolarization of a monochromatic laser beam based on a pure vertically aligned nematic LC has been proposed. The alignment properties of DNA-based biopolymer were adopted to produce PVAN in order to design a high quality active pseudo-depolarizer. One of electro-optical properties of the tested PVAN cell is the ability to control the DOP level using relatively low voltages. Depolarization level of this device depends strongly on input SOP and generally has the anisotropic character. Polar decomposition method applied to experimental Mueller matrices shows that for tested devices voltage applied to the cell induces birefringence domains in addition the calculated mean values of retardance are at the level of 0.11. This value is in good correspondence with data from the refractometer measurement of the used LC. Furthermore, they are dichroism free. The small angular scattering distribution has been detected at Fourier plane after switching ON of the cells with voltage corresponding to the DOP minimum. As a result, a spatial reshaping of the beam spreading is changing with time due to annihilation of the umbilical defect.

Author Contributions: P.M. and N.B. analyzed measurement data and prepared manuscript, A.S. prepared and described the biopolymer of alignment layer, A.K. measured PVAN cells, R.W. manufactured PVAN cells, K.G. formulated the LC crystal mixture, L.R.J. analyzed and interpreted measurement data. Funding: This work was supported by the Ministry of National Defense by research grants: GBMON/13-995/2018/WAT and Ministry of Higher Education as a statutory activity project PBS -23 - 898. Acknowledgments: We would like to thank Anna Pakuła and Tomasz Jankowski from Virtual Reality Techniques Division of the Warsaw University of Technology for the scattering measurement. Conflicts of Interest: The authors declare no conflict of interest.

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