# Monochromatic Depolarizer Based on Liquid Crystal

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Technology of the PVAN Cell

#### 2.1. Preparation of Biopolymer Alignment Layer

^{+}present in DNA salt back bone are replaced by surfactant groups [15] as is presented in Figure 1.

#### 2.2. Manufacturing Process of the Cells

^{2}area was patterned in the ITO by photolithography process. DNA-DODMAC complex was dissolved in butanol at a concentration of 3 wt. %. The solution was spin coated onto the substrates. Then, the film was baked at 80 °C for 1 hour to remove residual solvent. The two substrates were assembled using 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.

#### 2.3. Liquid Crystal Formulation

_{o}= 1.5006, extraordinary index n

_{e}= 1.6273 and birefringence Δn = 0.1273. The phase sequence as a function of the temperature of the nematic mixture is Cr 0 < N <51.4 °C Iso. Temperature of phase transition between isotropic and nematic phase (clearing temperature) is around 51.4 °C.

## 3. Electro-Optic Measurements

**M**in this model is a concatenation of three matrices

**M**,

_{D}**M**and

_{R}**M**which carries information about dichroism, birefringence and depolarization, respectively. This takes the following mathematical form of:

_{Δ}**M**or directly from the experimental matrix

_{Δ}**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:

**M**of the tested optical element. Non-depolarizing optical element has AvDOP = 1 and it is 0 for totally depolarizing element. Partial depolarizing devices have intermediate values. In Figure 4a these parameters for the tested PVAN cell with a thickness of 10 μm and 15 μm were presented. Add parameter is a cumulative information about anisotropy of the average DOP calculated as a relative difference of maximal and minimal values of AvDOP. Due to the fact that DOP characteristics presented in Figure 3 have different locations of minima and maxima for linear and circular input SOPs on a voltage scale, it is expected that tested samples can be considered as at least partially anisotropic element. Therefore, it is reasonable to calculate Add parameter. In this case Add = 0 means that the depolarizer is isotropic and Add = 1 means that it is totally anisotropic. In Figure 4b Add parameters of the tested samples are presented.

**M**matrices has very small fluctuations and in this case both tested samples are dichroism free. However, calculated total retardance (Figure 6b) based on matrices

_{D}**M**includes information about cumulative birefringence of the PVAN cell. These calculations prove that depolarization properties 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 thicknesses of 10 μm and 15 μm, respectively and these values fully correspond with data mentioned in Table 1 of the previous paragraph.

_{R}## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**DNA structure with a surfactant DODMAC, where: A, T, G and C—four nitrogen-containing nucleobases and hydrogen bonds bind the nitrogenous bases of the two separate polynucleotides.

**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.

**Figure 3.**DOP as a function of the voltage for PVAN cells with thicknesses: 5 μm (green dotted line), 10 μm (blue dashed line) and 15 μm (red dot-dashed line) for input SOP: (

**a**) linear H and (

**b**) circular R.

**Figure 4.**Calculated (

**a**) AvDOP and (

**b**) Add as a function of the applied voltage for PVAN cells with thicknesses of 10 μm (blue dotted line) and 15 μm (dot-dashed line). AvDOP—average DOP, Add—anisotropic depolarization degree.

**Figure 5.**Calculated AvDOP maps for PVAN cells with thicknesses: 10 μm (

**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.

**Figure 6.**Calculated: (

**a**) diattenuation and (

**b**) retardance of tested PVAN cells with thicknesses of 10 μm (blue dotted line) and 15 μm (dot-dashed line).

**Figure 7.**Microphotographs of 2050 LC domains on the DODA biofilm observed under crossed polarizers for input linear horizontal SOP and under voltage of 2.15 V applied to the cell in three time intervals of the samples with thickness of 10 μm after (

**a**) 25 s, (

**b**) 150 s (

**c**) 300 s and 15 μm after (

**d**) 25 s, (

**e**) 150 s, (

**f**) 300 s.

**Figure 8.**Time evolution of measured DOP at different applied voltages to PVAN cells with thickness of: (

**a**) 10 μm and (

**b**) 15 μm. The SOP of the incident light is linearly H polarized.

**Figure 9.**Spectral intensity distribution of a focused beam transmitted by cells of thickness of 5 μm, 10 μm and 15 μm when the cells are driven with the voltage of V = 2.65 V, 2.15 V and 2.15 V, respectively. (

**a**,

**e**,

**i**) represent the focused condition at V = 0. The images of scattered beam are recorded by a CCD camera placed at Fourier plan after different times’ lag detection. The SOP of the incident light is linear H polarized.

**Table 1.**General molecular structures of compounds used to form the investigated 2050 nematic mixture and their weight %.

Components | Chemical Structure | Weight % |
---|---|---|

I | R1 and R2 = alkyl (CH _{3}-C_{5}H_{11}) | 34.1 |

II | 18.6 | |

III | 47.3 |

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**MDPI and ACS Style**

Marć, P.; Bennis, N.; Spadło, A.; Kalbarczyk, A.; Węgłowski, R.; Garbat, K.; Jaroszewicz, L.R. Monochromatic Depolarizer Based on Liquid Crystal. *Crystals* **2019**, *9*, 387.
https://doi.org/10.3390/cryst9080387

**AMA Style**

Marć P, Bennis N, Spadło A, Kalbarczyk A, Węgłowski R, Garbat K, Jaroszewicz LR. Monochromatic Depolarizer Based on Liquid Crystal. *Crystals*. 2019; 9(8):387.
https://doi.org/10.3390/cryst9080387

**Chicago/Turabian Style**

Marć, Paweł, Noureddine Bennis, Anna Spadło, Aleksandra Kalbarczyk, Rafał Węgłowski, Katarzyna Garbat, and Leszek R. Jaroszewicz. 2019. "Monochromatic Depolarizer Based on Liquid Crystal" *Crystals* 9, no. 8: 387.
https://doi.org/10.3390/cryst9080387