Kerr effect, field-induced birefringence

A birefringence with the induced optical axis parallel to E can be also induced in any isotropic medium if a uniform electric field is applied at right angles to the light beam. This is the so-called Kerr effect. The induced birefringence is proportional to E, and it is customary to express it as ... 

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... 

In electric-field-induced birefringence (or electrical birefringence, quadratic electrooptic effect, Kerr effect), an isotropic transparent substance becomes birefringent when placed in an electric field . The sample assumes the characteristics of a uniaxial crystal, the optical axis of which is parallel to the direction of the applied field. When the sample is illuminated normal to , the resulting two indices, and wj (which can be thought of as He and ), are associated with the parallel and perpendicular orientations, respectively. 

The optical Kerr effect is a phenomenon of the optical field-induced birefringence and refers to the linear birefiingence induced by a linearly polarized optical field. The pump and probe beams are polarized 45 to each other in optical Kerr effect experiments. The probe beam may be composed of two orthogonal linearly polarized beams, and the polarization of one beam is parallel to that of the pump beam. According to third-order optical nonlinearity, the pump beam-induced linear birefringence is given by [46]. 

A well-known nonlinear process taking place in the liquid state of anisotropic molecules is the optical-field induced birefringence (optical Kerr effect ). This nonlinearity results from the reorientation of the molecules in the electric field of a light beam. In the isotropic phase the optical field perturbs the orientational distribution of the molecules. In the perturbed state more molecules are aligned parallel to the electric field than perpendicularly to it and as a consequence the medium becomes birefringent. On the other hand in liquid crystals the orientational distribution of the molecules is inherently anisotropic. The optical field, just as a d.c. electric or magnetic field, induces a collective rotation of the molecules. This process can be described as a reorientation of the director. 

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. 

On the assumption of total symmetry of the tensor of third-order nonlinear polarizability c(— co coi, cog, cog), its non-zero and independent elements are the same as those of Table 12. Direct theoretical calculations of c = c(0 0,0,0) have been performed for the atoms of inert gases and some simple molecules. Values of the tensor elements = c(— cu cu, 0,0) have been determined for numerous molecules from static Kerr effect studies and values of c = c(— cd ot>,coi — col) from measurements of optical birefringence induced by laser li t. Measurements of second-harmonic generation by gases in the presence of a static electric field yield the tensor elements c " = c( — 2co co, to, 0), which can also be obtained from second-harmonic scattering in centro-symmetric liquids. The elements of the tensor c = c(— 3co co, co, co)... 

The clasdcal fundamentals of the theory of the Kerr effect are due to Voigt in terms of dectron theory of the atom as an anharmonic oscillator and to Langevin in terms of statistical optical reorioitation of anisotropic molecules in a static dectric fidd. Buckingham proposed a theory and method of measurement of the optical birefringence induced by the gradient of a static electric field permitting the determination of electric quadrupole moments. 

Empirical models of the induced anisotropy have also been obtained from measurements of the pressure- and field-induced optical birefringence (Kerr effect) [20]. While these are not spectroscopic procedures, we include such references here because of their significance for CILS [20, 24-26, 52, 53]. Other modeling attempts are based on measurements of depolarization ratios as a function of pressure [163, 178, 179]. In recent work satisfactory consistency of the anisotropies derived from second virial Kerr coefficients, pressure-induced depolarization ratios, and depolarized CILS has been reported [11, 80]. We note that the confusion that has existed in the early years of CILS studies is now understood to have been due to the previous lack... 

Electro-optic effects refer to the changes in the refractive index of a material induced by the application of an external electric field, which modulates their optical properties [61, 62], Application of an applied external field induces in an optically isotropic material, like liquids, isotropic thin films, an optical birefringence. The size of this effect is represented by a coefficient B, called Kerr constant. The electric field induced refractive index difference is given by... 

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. 

We have seen that molecules may be oriented in an electric field. If these molecules are anisotropic, such orientation produces birefringence. This is the Kerr effect. The orientation may occur because molecules have a permanent dipole moment, or else they may arise because of an anisotropic induced dipole moment with molecules having anisotropic polarizabilities. 

Optical Kerr Effect. Another important method used to characterize polymers is the optical Kerr effect (OKE). The optical Kerr effect differs from the quadratic electrooptic effect in that the birefringence effects are induced solely by an optical field (37). In this measurement, an intense linearly polarized pump pulse induces birefringence in the nonlinear sample through an intensity-dependent refractive index change. The sample is placed between crossed polarizers and a weak, typically tunable, continuous wave (cw) probe laser (usually at a different wavelength and polarized at 45° to the pump pulse) overlaps the pumped region. The increased transmission of the probe beam when the pump pulse arrives is proportional to (Xeff), a combination of elements of the tensor. Many... 

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