Flexoelectro-optic effect and two-beam energy exchange in a hybrid photorefractive cholesteric cell with a short-pitch horizontal helix

We develop a theoretical model to describe two-beam energy exchange in a hybrid photorefractive cholesteric cell with a short-pitch helix oriented parallel to the cell substrates (so-called uniformly lying helix configuration). Weak and strong light beams incident on the hybrid cell interfere and induce a periodic space-charge field in the photorefractive substrate of the cell, which penetrates into the cholesteric liquid crystal (LC). Due to the flexoelectro-optic effect an interaction of the photorefractive field with the LC flexopolarization causes the spatially periodic modulation of the helix axis in the plane parallel to the cell substrates. Coupling of a weak signal beam with a strong pump beam at the LC permittivity grating, induced by the periodically tilted helix axis, leads to the energy gain of the weak signal beam. Dependence of the signal beam gain coefficient on the parameters of the short-pitch cholesteric LC is studied.

Figure 1

Cholesteric LC cell with the initial helix axis directed along the $x$ axis, showing light beams incident from the photorefractive medium, together with associated wave and polarization vectors; $\alpha$ is an angle of refraction.

Figure 2

Dependence of the function $|\beta \left(L_1\right)|/2r_0$ on the transverse CLC cell dimension $L_1$ for grating spacing $\mathrm{\Lambda }=1\mu \mathrm{m}$ (solid line), $2\mu \mathrm{m}$ (dashed line), and $4\mu \mathrm{m}$ (dot-dashed line). The cell thickness is $L=5\mu \mathrm{m}$.

Figure 3

Magnitude $\varphi \left(z\right)$ of the helix axis rotation angle versus grating spacing. $z/L=-0.5$ (solid curve), −0.45 (dashed curve), and −0.4 (dash-dotted curve); ratio of flexoelectric coefficient to elastic constant $r_0=1\mathrm{C}{\mathrm{m}}^{-1}{\mathrm{N}}^{-1}$, cholesteric pitch $p=0.3\mu \mathrm{m}$, and the transverse CLC cell dimension $L_1=0.1\mu \mathrm{m}$.

Figure 4

Gain coefficient $\mathrm{\Gamma }$ versus grating spacing $\mathrm{\Lambda }$ in a hybrid photorefractive cell containing cholesteric LC mixture BL038/CB15. Cholesteric pitch $p=0.25\mu \mathrm{m}$; ratio of flexoelectric coefficient to elastic constant in the case of horizontal helix axis (solid line) $r_0=1\mathrm{C}{\mathrm{m}}^{-1}{\mathrm{N}}^{-1}$; the ratios of flexoelectric to elastic moduli in the case of vertical helix axis (dashed line) are those describing the experimental results in [13] and have an order of magnitude $\sim 1\mathrm{C}{\mathrm{m}}^{-1}{\mathrm{N}}^{-1}1$.

Figure 5

Gain coefficient $\mathrm{\Gamma }$ versus grating spacing $\mathrm{\Lambda }$ for CLC with horizontal helix axis; (a) different values of the ratio of flexoelectric coefficient to elastic constant: $r_0=1$ (dash-dotted line), 3 (dashed line), 5 (solid line), $p=0.3\mu \mathrm{m}$; (b) different values of the cholesteric pitch: $p=0.2\mu \mathrm{m}$ (dash-dotted line), $p=0.3\mu \mathrm{m}$ (dashed line), $p=0.4\mu \mathrm{m}$ (solid line); $r_0=3$.