In this thesis, the homeotropic-planar transition of cholesteric liquid crystal (ChLC) is investigated.
Firstly, in order to understand the basic nature of reflection of light by the ChLC cells, we calculate the reflectance spectra as a function of cell thickness and inicident angle. We find that the cell should be thicker than about 10 $P_0$, to exhibit the unique selective reflection of ChLC, which imposes the condition of the minimum thickness on reflective ChLC displays. As the incident angle gets larger, the peak wavelength of the reflection spectrum moves towardd the shorter wavelength side, which means that the color of ChLC display varies with the viewing angle. We also investigate the photonic defect modes of ChLC as a photonic band gap material. It is found that, when the small portion of ChLC is replaced by an optically isotropic layer, the photonic defect mode is induced in the wavelength range of selective reflection, as in the conventional photonic crystals. The wavelength of the defect mode $\lambda_d$ depends linearly on the refractive index of the defect layer $n_d$, and lies at the center of the selective reflection band when the phase slip due to the defect layer is equal to odd multiples of $\frac{\pi}{2}$. The reflectance of the defect mode is also a function of $n_d$. We find that the reflectance of defect mode is zero when the optical path lengh of defect layer is the half multiples of $\lambda_d$, which is the condition for the total transmittance for the light incident on a thin film.
Secondly, we measure the reflection spectra of light by the ChLCs in the homeotropic-planar transitions. After a sudden removal of the external electric field, the amplitude of reflectance peak is increased at the wavelength around 640 nm which is different from the peak wavelength, 477 nm for the planar state. The polarization state of the reflected light is found to be circular, which shows that the director field is deformed helically. These indicate that the liquid crystal is under the homeotropictransient planar transition. After the transient planar state, the peak amplitude is lowered and peak wavelength is shortened to have 477 nm, the wavelength corresponding to the planar texture, and the viewing angle widended. These show that the focal conic texture in which the helical axes are distributed randomly and whose pitch is the natural one $P_0$ is being formed. After the focal conic texture, the peak intensity becomes stronger without any significant change in the peak wavelength, which shows that the directors reorient to have the planar texture. In summary, the transition procedure is as follows.
homeotropic → transient planar → focal conic → planar
And finally, we investigate theoretically why the transient planar state whose pitch is different from the natural one appears in the homeo-tropic - planar transition of ChLCs, in spite of energetically unfavorable situation. We obtain both the approximate analytic solutions and the numerical solutions of director motion of ChLC sandwiched between parallel substrates, assuming a coordinate eystem such that the xy planeis paralled to the substrates. When the amplitudes of the director components perpendicular to the helical axis, $n_x$ and $n_y$, are much smaller than 1 and are uniform in space, the analytic solutions of approximate dynamic equations show that the amplitudes of $n_x$ and $n_y$ decrease unless the spatial frequency of $n_x$(and $n_y$), q, is smaller than 2($k_{22}/k_{33})q_0$ ($q_0$=$\frac{2π}{P_0}$), and is a quadratic function of q which has maximum value at q=($\frac{K_22}{K_33}$)$q_0$, and also depends on the elastic constants of both twist and bend. Numerical solutions of exact dynamic equation show that the initial spatial frequency of $n_x$(and $n_y$) remains constant throughout the transition. These two results obtained from the analytic and the numerical solutions lead us to conclude that the pitch of transient planar texture should be larger than 0.5($\frac{K_33}{K_22}$)$P_0$, when the amplitude of $n_x$(and $n_y$) is uniform in space. Functional dependence of the growth rate on the elastic constants agrees well quantitatively with that of the numerical solution of exact dynamic equation.
Unfortunately, it has not been understood what determines the initial distributions of $n_x$ and $n_y$. So, we calculate numerically the evolution of director motion for two feasible initial distributions. For the initial distributions of $n_x$ and $n_y$ that are fluctuating randomly with small amplitudes, numerical calculations for homeotropic surface alignments show that the homeotropic state evolves to form the transient planar state having the pitch of ($\frac{K_33}{K_22}$)$P_0$ Random fluctuation is decomposed into white Fourier components which have no phase correlations to each other. And the analytic solution of dynamic equation says that the growth rate of the amplitude of $n_x$ (and $n_y$) is the highest when q=($\frac{K_22}{K_33}$)$q_0$. Thus, we can say that the transient planar texture is formed from the homeotropic texture because the Fourier component of q=($\frac{K_22}{K_33}$)$q_0$ grows faster than any other components including $q_0$, if, in the initial stages, $n_x$ and $n_y$ are fluctuating randomly with small amplitudes in space.
When the director distribution of the final steady-state of the fieldinduced planar-homeotropic transition is employed as an initial distribution, numerical solutions for planar atignments show that the pitch of the transient planar state is slightly shorter than $\frac{K_33}{K_22}$)$P_0$. On the way of the transition, the transient planar region and the homeotropic region is clearly separated, and the former expands from the substrates toward the center of the cell. It is found that, throughout the transition, the pitch at the interfaces of the transient planar and the homeotropic region is determined by the torque balance between the twist and the bend deformations: the former forces q to raise to $q_0$, while the latter to reduce to 0. It is also found that the pitch of the transient planarregion is frozen throughout the transition because of the lowering of q at the interfaces by the bend deformation energy. After the transition is completed, the pitch which is slightly shorter than $\frac{K_33}{K_22}$)$P_0$, remains forever due to the azimuthal anchoring at the substrates of the cell. Thus, we can say that the transient planar texture is formed fromthe homeotropic texure because the bend deformation energy forces q to have lower value than the initial one. Numerical calculations for various values of physical parameters of ChLC and cell show that the transition time of the homeotropic-transient planar transition is proportional to cell gap, and inversly proportional to $K_22$ and $q_0$
For homeotropic surface alignment, dynamic behaviours and the pitch of the transient planar texture are almost the same as those for planar surface alignment. But after the transient planar texture is formed over all region of the cell, the pitch relaxes very slowly to $P_0$ because there is no barrier to the rotation of $n_x$ and $n_y$ at the substrates of the cell.