Electric field birefringence

In an electrooptic material the phase retardation angle is controlled by altering birefringence, which is in turn controlled by the potential of an apphed electric field. An electrooptic device thus acts as a variable phase optical retardation plate, and can be used to modulate the wavelength or intensity of an incident beam. 

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). 

The rise of the birefringence following the setting-up of the electric field is given by ... 

The transient regime following electric field inversion aJ.lows more precise determination of the P/Q ratio to be achieved. If the particle does not possess any permanent dipole (P/Q = O) the birefringence remains stationary upon field inversion. If there is a contribution of permanent dipole, then An reaches a minimum An. related at low fields with P/Q according to ... 

Information about absolute values of electrical and optical parameters of the particle are provided by the behaviour of the steady state birefringence An versus the square of the electric field E An is given by (8) ... 

A single exponential curve (cf. "Equation U") has been fitted to the birefringence decay curve after removal of the electric field the agreement is good for Cq = 0.5 at 25°C (Fig.l) and moderately good for Cq = 1.6 at 60°C (Fig.2b).The fits lead to the relaxation times Tj = 1/6 Dj reported in Table I. As to the other cases, the agreement is very poor (Fig.2a) a two exponential curve is then necessary to describe the decay curves behaviour.The two-time constants are reported in Table I. 

Steady-state birefringence. The investigation of the steady-state birefringence variation versus the squared electric field leads to the knowledge of the Kerr constant the electrical parameters... 

As this variation is close to linearity in the whole electric field range investigated the P/Q ratio deduced from the birefringence... 

Figure 2. Time dependence of the "birefringence decay signal, at the removal of the electric field, of a PVC solution at C = 10" g cm and for a quenching concentration of 1.6 10 g cm . Temperatures are T = 25°C (Fig,2a) and T = 60°C (Fig.2b). Dotted lines represent the single exponential curves deduced from the "best fit of Equation 8 to the experimental curves. Residues (i.e. difference between these two curves) are plotted below.

Three common types of electrooptic effects are illustrated in Figure 8 i.e, quadratic and linear birefringence and memory scattering. Also included in the figure is a typical setup required for generating each effect along with the observed behavior shown in terms of light intensity output (I) as a function of electric field (E). 

A second type of behavior existing in the PLZT s is the linear (Pockels) effect which is generally found in high coercive field, tetragonal materials (composition 3), This effect is so named because of the linear relationship between An and electric field. The truly linear, nonhysteretic character of this effect has been found to be intrinsic to the material and not due to domain reorientation processes which occur in the quadratic and memory materials. The linear materials possess permanent remanent polarization however, in this case the material is switched to its saturation remanence, and it remains in that state. Optical information is extracted from the ceramic by the action of an electric field which causes linear changes in the birefringence, but in no case is there polarization reversal in the material. 

Physical properties of liquid crystals are generally anisotropic (see, for example, du Jeu, 1980). The anisotropic physical properties that are relevant to display devices are refractive index, dielectric permittivity and orientational elasticity (Raynes, 1983). A nematic LC has two principal refractive indices, Un and measured parallel and perpendicular to the nematic director respectively. The birefringence An = ny — rij is positive, typically around 0.25. The anisotropy in the dielectric permittivity which is given by As = II — Sj is the driving force for most electrooptic effects in LCs. The electric contribution to the free energy contains a term that depends on the angle between the director n and the electric field E and is given by... 

Polarized light is obtained when a beam of natural (unpolarized) light passes through some types of anisotropic matter. In optical instruments this is usually a birefringent crystal which splits the incident unpolarized beam into two beams of perpendicular linear polarization, known as the ordinary and extraordinary beams. Anisotropy can also be created by the effect of an electric field, this being known as the Kerr effect. 

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