Nanooptics and photonics
Statistical analysis of polarization-microscopic textures of imperfectly oriented planar cholesteric cells
Dudok T.H.1, Krupych O.M.1, Nastishin Yu.A.2
1 Vlokh Institute of Physical Optics of Physics of the Ministry of Education of UkraineDragomanova, 23, Lviv-79005, Ukraine. 
E-mail: j007@ifo.lviv.ua
2 Hetman Petro Sahaidachnyi National Army Academy, Heroes of Maidan, 32, Lviv-79026, Ukraine.

To set on a quantitative basis the quality of the alignment in imperfectly aligned planar cholesteric cells used for laser generation [1], we have performed the statistical analysis of the distribution of the ellipticity of light for an array of elementary beams passing through the cell. The thickness of the cells is of 25 microns with glance and frosted glass substrates. Measurement of the distribution of the orientation of the axes of elliptic polarization and the ellipticity angles was performed following the method described in [2].
The distribution of the optical phase retardation is well approximated by the Lorentz distribution function. The statistical distribution of the orientation of the optical indicatrix in the field of the image is well approximated by the Gaussian distribution function.
The difference in the statistical distribution of the optical phase difference for cells with frosted and glance substrates is clearly observed. A slightly smaller, though not less essential difference is observed between the statistical distributions of orientation of the optical indicatrix determined for cells with frosted and glance substrates.
Therefore, the analysis of the distribution of the orientation of the optical indicatrix and the phase retardation for an array of elementary rays passing through a cell with a liquid crystal allows one to quantify the degree of disorder in imperfectly aligned liquid crystal cells.

1.	Dudok T., Savaryn V.I., Krupych O.M., Fechan A.V., Lychkovskyy E., Cherpak V.V., Pansu B., Nastishin Yu.A. Lasing in imperfectly aligned cholesterics // Applied Optics – 2015. – 54. – P. 9644-9653.
2.	Gradient thermooptical effect in LiNbO3 crystals. / Vlokh R., Krupych O., Kostyrko M., Netolya V., Trach I. // Ukr. J. Phys. Opt. – 2001. – 2. – P. 154-158.