Electrically tunable two-dimensional liquid crystals gratings induced by polarization holography

Abstract

Two-dimensional (2D) gratings made up of an array of differently twisted nematic structures are obtained by crossed assembling of 1D polarization holograms recorded at the photoaligning substrates. The rotating linear polarization pattern, produced by the interference of two opposite circularly polarized beams, is recorded on the azo-dye doped polyimide aligning layers. The 2D gratings diffract light in different directions with different polarization states, that can be optically controlled. Orthogonal circularly and linearly polarized diffraction orders are simultaneously obtained irradiating the grating with a linearly polarized beam. An external ac voltage allows to completely control the diffracted energy distribution.

Polarization-gratings approach to deformed-helix ferroelectric liquid crystals with subwavelength pitch

“…[27,28] for stratified anisotropic media. Mathematically, in this approach, the key formulas (37) and (38) give the transmission and reflection matrices of diffraction orders, T n and R n , expressed in terms of the linking matrix (33) which is related to the evolution operator (20) of the system of matrix equations (16) for the Floquet harmonics (14) derived from the Maxwell's equations for the lateral components of the electric and magnetic fields (10).…”

“…[27,28], relate these matrices and the evolution operator given by Eq. (20). To this end, we use the boundary conditions requiring the tangential components of the electric and magnetic fields to be continuous at the boundary surfaces…”

“…and apply the relation (20) to the anisotropic layer of the thickness D to yield the following result:…”

“…According to the computational procedure developed in the previous section, after inserting the above parameters into the matrices of the system (16) for the Floquet harmonics, we need to find the evolution operator by solving the initial value problem (20). Then computing the transmission and the reflection matrices (30) involve the following steps: (a) evaluation of the linking matrix (33); (b) calculation of the efficiency matrices (35) by solving the system of linear equation (34); (c) computing the matrices T n and R n from the formulas (37) and (38), respectively.…”

“…The holographic technique has been extensively used to create PGs in liquid crystal (LC) cells with photosensitive aligning substrates such as linear photopolymerizable polymer layers [16,17], azo-dye films [18], azo-dye doped polyimide [19,20], and azobenzene side-chain polymer layers [21].…”