Polarization of light by a polymer film containing elongated drops of liquid crystal with inhomogeneous interfacial anchoring

Polarization, transmission, and small-angle scattering of light by a polymer film with elongated droplets of nematic liquid crystal

“…The relaxation method of minimizing the free energy volume density was applied to simulate the LC director configuration (a distribution of local optical axes) inside droplets. The anomalous diffraction approximation was used to determine the elements of the amplitude scattering matrix [14,19,22,[26][27][28]. The calculations were carried out for the monodisperse LC droplets in a polymer film (matrix).…”

“…Using the Foldy-Twersky approximation [14][15][16][17][18][19], we can write the expressions for the coherent (directed) transmission coefficient and polarization degree P c of the forward-c np T transmitted light (the polarizing ability of layer for forward-transmitted light):…”

“…Here T || с and T  с are the coefficients of coherent transmission for the components of incident light polarized parallel and orthogonal to the stretching axis; γ 2 and γ 1 are the corresponding extinction coefficients of the layer; c v is the volume filling factor of layer (the ratio of volume of all LC droplets to the volume of PDLC layer); Q e  and Q o  are the extinction efficiency factors [20] for the extraordinary and ordinary waves, averaged over the droplet sizes; S 2f is the two-dimensional order parameter of PDLC layer; k=2πn p /λ, λ is the wavelength of incident light, n p is the refractive index of polymer matrix;  y =b/a and  z =c/a are the parameters of droplet's anisometry; ReS 0 2,1  are the averaged real parts of the diagonal elements of amplitude scattering matrix for the strictly forward direction of scattering [14]; the angle brackets … mean the average over the a semiaxis of droplets along the film normal; P(a) is the normalized probability density of a semiaxes distribution along the film normal;  m is the maximal angle of droplet optical axes deviation relatively to the stretching axis. At  m =0 the optical axes of droplets are entirely oriented along the stretching axis (S 2f =1).…”

“…At stretching, the layer thickness l and the semiaxes a, b, c of droplets are related by the expressions [6,14]:…”

“…Unidirectional mechanical stretching of PDLC film doped with the ionic surfactants allows obtaining the LC director configuration (distribution of local optical axes) within the droplet volume close to homogeneous (monodomain) [12,13]. Thus, it gives an opportunity to achieve simultaneously the limit polarization characteristics for unpolarized incident light: the coherent transmission coefficient equal to 0.5 and the polarization degree of forward-transmitted light equal to 1 in the wide spectral range [14].…”