Spectral and polarization structure of field-induced photonic bands in cholesteric liquid crystals

Transmission of planar layers of cholesteric liquid crystals is studied in pulsed electric fields perpendicular to the helix axis at normal incidence of both linearly polarized and unpolarized light. Spectral and light polarization properties of the primary photonic band and the field-induced bands up to fourth order of Bragg selective reflection are studied in detail. In our experiments we have achieved an electric field strength several times higher than the theoretical values corresponding to the critical field of full helix unwinding. However, the experiments show that despite the high strength of the electric field applied the helix does not unwind, but strongly deforms, keeping its initial spatial period. Strong helix deformation results in distinct spectral band splitting, as well as very high field-induced selective reflectance that can be applied in lasers and other optoelectronic devices. Peculiarities of inducing and splitting the bands are discussed in terms of the scattering coefficient approach. All observed effects are confirmed by numerical simulations. The simulations also show that liquid crystal surface anchoring is not the factor that prevents the helix unwinding. Thus, the currently acknowledged concept of continuous helix unwinding in the electric field should be reconsidered.

Figure 1

Scheme of experimental LC cell: (1) aluminum electrodes; (2, 3) glass substrates; (4) CLC layer; (5) Teflon gaskets; (6) polyimide films.

Figure 2

Transmittance spectra of CLC (a) with helix pitch 590 nm (primary and second-order photonic bands) and (b) with helix pitch 1075 nm (photonic bands of second, third, and fourth order) in unpolarized light at different electric field strengths: 1, $0\mathrm{V}/\mu \mathrm{m}$; 2, $1.7\mathrm{V}/\mu \mathrm{m}$; 3, $2.6\mathrm{V}/\mu \mathrm{m}$; 4, $5.2\mathrm{V}/\mu \mathrm{m}$.

Figure 3

Transmittance spectra of CLC layer with a helix pitch of 590 nm (first- and second-order photonic bands) for (a) $\mathbf{e}\parallel \mathbf{E}$ and (b) $\mathbf{e}\perp \mathbf{E}$ at different electric field strengths: 1, $0\mathrm{V}/\mu \mathrm{m}$; 2, $1.7\mathrm{V}/\mu \mathrm{m}$; 3, $2.6\mathrm{V}/\mu \mathrm{m}$; 4, $5.2\mathrm{V}/\mu \mathrm{m}$.

Figure 4

Transmittance spectra of CLC layer with helix pitch 1075 nm (photonic bands of the second, third, and fourth order) for (a) $\mathbf{e}\parallel \mathbf{E}$ and (b) $\mathbf{e}\perp \mathbf{E}$ at different electric field strengths: 1, $0\mathrm{V}/\mu \mathrm{m}$; 2, $1.7\mathrm{V}/\mu \mathrm{m}$; 3, $2.6\mathrm{V}/\mu \mathrm{m}$; 4, $5.2\mathrm{V}/\mu \mathrm{m}$.

Figure 5

Transmittance spectra of CLC layer with helix pitch 590 nm (first- and second-order photonic bands) for (a) $\phi =+{45}^{\circ }$ and (b) $\phi =-{45}^{\circ }$ at different electric field strengths: 1, $0\mathrm{V}/\mu \mathrm{m}$; 2, $1.7\mathrm{V}/\mu \mathrm{m}$; 3, $2.6\mathrm{V}/\mu \mathrm{m}$; 4, $5.2\mathrm{V}/\mu \mathrm{m}$.

Figure 6

Simulated distribution of the director field in the CLC layer (the parameters correspond to the experimental sample with a pitch of $1.075\mu \mathrm{m}$) (a) in the absence of the electric field and (b) at $E_x=5.2\mathrm{V}/\mu \mathrm{m}$; simulation is performed for negligible LC surface anchoring $(W_a=W_z={10}^{-9}\mathrm{J}/{\mathrm{m}}^2)$. At the right side the schematic representation of the non-disturbed and field-distorted helix is shown.

Figure 7

Transmittance spectra of the CLC layer in unpolarized light simulated for different electric field strengths. The CLC parameters correspond to the experimental sample [see Fig. 2]. The CLC layer thickness equals 11 pitches with $P_0=1075\mathrm{nm}(d=11.875\mu \mathrm{m})$. Curves: (1) $E_x=0$; (2) $E_x=1.7\mathrm{V}/\mu \mathrm{m}$; (3) $E_x=5.2\mathrm{V}/\mu \mathrm{m}$. Simulations performed for negligible surface anchoring $W_a=W_z={10}^{-9}\mathrm{J}/{\mathrm{m}}^2$.

Figure 8

A scheme illustrating the spectral splitting of the field-induced second-order photonic band. One pitch of CLC helix deformed by an electric field applied along the $x$ axis is shown inside the solid box. The dashed box confines free space. The standing waves which are due to the interference of forward and Bragg-reflected backward waves with wave vectors $k=\pm 4p/P$ inside the CLC medium are drawn at the box edges, and they have different wavelengths $n_{x}P/2$ and $n_{y}P/2$ respectively for $x$- and $y$- polarized light in the free space.