Influence of the magnetic and laser fields on the director structures of a ferrocholesteric liquid crystal in homeotropic cells

We study the influence of the magnetic and laser fields on the director structures of a ferrocholesteric liquid crystal in homeotropic cells. Using the analytical method based on the Euler-Lagrange equations, we find a correlation between the fields intensities and the confinement ratio r=d/p, (d is the cell thickness and p is the cholesteric pitch) at the limit of the transition from the homeotropic alignment to the translationally invariant configuration (TIC) with uniform in plane twist. We discuss this correlation as a function of the sign of the magnetic and dielectric anisotropies. If both anisotropies are positive and the magnetic field and the laser beam are perpendicular to the cell walls, the magnetic field preserves the homeotropic alignment while the laser beam pushes the system towards the TIC. The control parameters of the transition are the laser beam intensity and the confinement ratio. If the magnetic anisotropy is negative and the dielectric one is positive both fields concur in driving the system towards the TIC. The spinodal surface separating the metastable homeotropic configuration from the instable TIC is an ellipsoid whose halfaxes are smaller that in the case of a pure liquid crystal by a factor depending on the material constants and the cell thickness. We find also the total twist angle across the sample witch can be varied between a lower and an upper limit by changing the light intensity or the magnetic field strength. Our results can be useful in designing magneto-optical devices.