Static One-Dimensional Distortions in Cholesteric Liquid Crystals

We report new experimental observations on a cholesteric planar texture of pitch $P$ and thickness $L$ submitted to a static magnetic $\overrightarrow{\mathrm{H}}$ or a high-frequency electric field $\overrightarrow{\mathrm{E}}$. Two configurations are considered: (a) $\overrightarrow{\mathrm{H}}$ parallel to the helical axis: if ${\chi }_a>0\mathrm{}$, $L\sim P$, an array of stripes is observed at threshold. This is to be compared to the case ${\chi }_a>0\mathrm{}$, $L\gg P$, where a square gridlike pattern is nucleated in the same conditions. (b) $\overrightarrow{\mathrm{E}}$ perpendicular to the helical axis: if ${\epsilon }_a<0\mathrm{}$, $L\gg 0$, a static array of stripes is again observed, the stripes being perpendicular to $\overrightarrow{\mathrm{E}}$. This configuration is equivalent to the configuration ${\chi }_a<0\mathrm{}$, $\overrightarrow{\mathrm{H}}$ perpendicular to the helical axis. The threshold conditions derived by Helfrich and Hurault in the case $L\gg P$, ${\chi }_a>0\mathrm{}$, $\overrightarrow{\mathrm{H}}$ parallel to the helical axis seem to be also valid in those two cases. A more detailed theoretical treatment is devoted to the second geometry.