Birefringence electrically induced

Kerr effect - An electrooptical effect in which birefringence is induced in a liquid or gas when a strong electric field is applied perpendicular to the direction of an incident light beam. The Kerr constant k is given by = k F , where X is the wavelength, E is the electric field strength, and and are the indices of refraction of the ordinary and extraordinary rays, respectively. 

To find the value of the elastic moduli ratio Kss/Ku it is also possible to measure either the birefringence 6 = And/X And is the optical path difference and the A is the wavelength of light), or the capacitance C versus voltage U curve in the electrically induced Frederiks transition [55]. 

This effect has been observed experimentally in comparatively thick cells (d 50 /xm) [113]. In cells with d 20 /xm, the final twisted state (in the field) proves to be insufficiently stable and the nematic liquid crystal layer is gradually transformed into a planar structure. The addition of small quantities of cholesteric liquid crystals to the initial nematic mixture enables a stable twisted structure to be achieved with the application of a field and improves the electrooptical characteristics of the device. The electrooptical response of electrically induced twist nematic cells includes intensity oscillations observed both in the switching on and switching off regimes [114]. These oscillations take place due to the variation of birefringence, which are not important in the usual twist effect. 

A birefringence is induced in an ordinary liquid if a uniform electric field is applied at right angles to the direction of a beam passing through the cell its value is related to the field strength E through... 

Electric field is also expected as an effective external field to drive finite and fast deformation in LCEs, because, as is well known for low molecular mass LCs (LMM-LCs), an electric field is capable of inducing fast rotation of the director toward the field direction [6]. This electrically driven director rotation results in a large and fast change in optical birefringence that is called the electro-optical (EO) effect. The EO effect is a key principle of LC displays. Electrically induced deformation of LCEs is also attractive when they are used for soft actuators a fast actuation is expected, and electric field is an easily controlled external variable. However, in general, it is difficult for LCEs in the neat state to exhibit finite deformation in response to the modest electric fields accessible in laboratories. Some chiral smectic elastomers in the neat state show finite deformation stemming from electroclinic effects [7,8], but that is beyond the scope of this article we focus on deformation by director rotation. 

The main part of this chapter will deal with birefringence caused by flow (streaming birefringence). Other possibilities i.e. magnetically and electrically induced birefringence) are also possible, but will not be discussed. 

Commonly known as the Kerr Effect, this is the best known electro-optic phenomenon. Although initially studied in glasses by John Kerr (J) in 1875, who considered the birefringence to be related to electrically induced strain in the material, it is now used widely to follow the alignment due to orientation and deformation of macro-particles in solution and suspension (2—4). It owes its origin to anistropy of the refractive indices associated with the major geometric axes of the molecules. 

The first and third order terms in odd powers of the applied electric field are present for all materials. In the second order term, a polarization is induced proportional to the square of the applied electric field, and the. nonlinear second order optical susceptibility must, therefore, vanish in crystals that possess a center of symmetry. In addition to the noncentrosymmetric structure, efficient second harmonic generation requires crystals to possess propagation directions where the crystal birefringence cancels the natural dispersion leading to phase matching. 

The Kerr effect is the birefringence induced in a medium by an external electric field (12). From such an experiment we deduce the molar Kerr constant mK, thus... 

Theory. In the general case where rigid revolution ellipsoidal particles in solution possess both a permanent and an induced dipolar moment colinear with the particle optical axis, the theory derived by Tinoco predicts the following behaviour of the solution birefringence An(t) in the limit of weak electric field (6). 

Dynamic behaviour. Time dependent curves of the birefringence An(t) induced by applying successively a positive and a negative electric... 

Here, cfy (co) is the linear polarisability tensor at frequency co and describes the linear variation of the induced dipole with the electric field. The resulting oscillation in the polarisation (oscillating dipole) is, in effect, a moving charge, and will therefore emit radiation of the same frequency as the oscillation. This gives rise to linear optical effects such as birefringence and refraction. 

Variable retardation can also be achieved using electric birefringence induced in liquid layers. Commercial devices are available that use this method. 

The usefulness of electrical response measurements of solutions is not limited to effects linear in applied field. Transient birefringence induced by polarizing electric fields (the transient or dynamic Kerr effect) has given valuable information about biopolymers in solution the effect must by symmetry be an even function of E(t), beginning with terms in E (t). In both cases, a response theory treatment of transient behavior meets with difficulties not encountered in linear problems, but recent progress in deriving correlation function expressions for such effects is described in III. 

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