Field Induced Anharmonicity and Dynamics of the Helix

Let us simulate an appearance of the higher harmonics and optical properties of the cholesteric structure with the following parameters typical of chiral materials based on the well-known nematic mixture E7 helical pitch 0.4 pm, elastic modulus K22 = 5 X 10 dyn (or 5 pN) principal dielectric permittivity values Sn = 20, 

The inset to Fig. 12.13 shows the calculated space dependence of the x-component of the director n z) within one period of the cholesteric structure. The voltage applied to the in-plane electrodes is either 0 or 200 V ( = 10 V/pm). As expected, at the field applied, the apices of the curve n z) for U = 200 V become very flat. The main plot of Fig. 12.13 represents the Fourier transform of the director component nj qlln). In zero field, on the wavevector axis, the helix is represented 

The appearance of the high harmonics in the director distribution results in considerably faster electro-optical switching. The dynamics of the cholesteric helix in the electric field is described by the balance of viscous, elastic and electric torques in the infinitely thick sample is given by 

A low field only slightly changes the angle cp keeping only the first harmonic of the structure with wavevector IntPo. Then, as soon as the field is switched off, the helical structure cp (z) would relax to the field-off structure according to the same equation (12.31) without the field term. With 3cp/3z = qo we find solution 

Note that in contrast to nematics Tj is controlled by the helical pitch Po = 2nlqo and not by cell thickness d. At a strong field, the distortion involves several harmonics with number m and wavevectors q = 2nm/Po and each harmonic relaxes with its 

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