Kerr effects

According to the Kerr effect, the induced birefiingence is proportional to the quadratic electric field as described by 

A coordinate showing the refractive index ellipsoid and the direction of applied 

The first term in Equation (14.6) is related to initial refractive indices of the medium at three primary directions, n, Uy, n. The second term refers to the linear electro-optic effect, which is known as the Pockels effect, and the third term refers to the quadratic electro-optic effect, known as the Kerr effect. Here, and Sjj are electro-optic tensors for the linear and quadratic electro-optic effects, respectively. The second-order Kerr effect is small as compared to the first-order linear effect, so it is usually neglected in the presence of linear effect. However, in crystals with centro-symmetric point groups, the linear effect vanishes and then the Kerr effect becomes dominant. 

Under these circumstances, the electric field components in x and y directions are both zero  

In Equation (14.7), the linear term vanishes and only the Kerr effect term survives. The electrooptic tensor for the Kerr effect varies with different molecular stmcture. For an isotropic Uquid, its quadratic electro-optic effect coefficients can be represented by the following matrix  

In electric fields, liquid crystals react by reflecting light to display certain colors. This is the basis for the manufacturing of liquid-crystal display screens in the electronics industry. This phenomenon can be explained in terms of the Kerr effect. 

In 1875, J. Kerr observed that if a transparent isotropic substance is placed in a stationary electric field, it becomes optically anitotropic and doubly reflecting because the electric field tends to bring about a definite orientation of the molecules. 

The Kerr effect may be described as follows. Let b, b2, and b-j be the three imaginary principal axes at right angles. The mean molar polarizability of the molecule ot is defined as 

The anisotropy of liquid crystals is related to the constant K, now called the Ken-constant  

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H) RAMAN INDUCED KERR EFFECT SPECTROSCOPY (RIKES)... 

Heiman D, Hellwarth R W, Levenson M D and Martin G 1976 Raman-induced Kerr effect Rhys. Rev. Lett. 36 189-92... 

Rikes. See Raman-induced Kerr-effect spectroscopy. 

Fig. 8. Principle of the magnetooptical read-out of domain patterns by the polar Kerr effect. The polarisation plane of the incoming laser beam is rotated clock- or counterclockwise according to the orientation (up or down) of the magnetic moments.

From the write and read process sketched so far, some requirements for MO media can be derived (/) a high perpendicular, uniaxial magnetic anisotropy K in order to enable readout with the polar Kerr effect (2) a magnetoopticady active layer with a sufficient figure of merit R 0- where R is the reflectivity and the Kerr angle (T) a Curie temperature between 400 and 600 K, the lower limit to enable stable domains at room temperature and the upper limit because of the limited laser power for writing. 

Nonlinear refraction phenomena, involving high iatensity femtosecond pulses of light traveling in a rod of Tfsapphire, represent one of the most important commercial exploitations of third-order optical nonlinearity. This is the realization of mode-locking ia femtosecond Tfsapphire lasers (qv). High intensity femtosecond pulses are focused on an output port by the third-order Kerr effect while the lower intensity continuous wave (CW) beam remains unfocused and thus is not effectively coupled out of the laser. 

The dynamic Kerr effect (DKE) is the third-order analogue of the second-order Pockel s effect. DKE also gives rise to phase shifts given by... 

In an effort to identify materials appropriate for the appHcation of third-order optical nonlinearity, several figures of merit (EOM) have been defined (1—r5,r51—r53). Parallel all-optical (Kerr effect) switching and processing involve the focusing of many images onto a nonlinear slab where the transmissive... 

Experimental determinations are far from straightforward, especially if the molecule has little or no symmetry. The mean value can be deduced from the refractive index of a gas, whilst Kerr effect experiments give some idea of the anisotropy. 

As was proven later by Bishop [19], the coefficient A in the expansion (73) is the same for all optical processes. If the expansion (73) is extended to fourth-order [4,19] by adding the term the coefficient B is the same for the dc-Kerr effect and for electric field induced second-harmonic generation, but other fourth powers of the frequencies than are in general needed to represent the frequency-dependence of 7 with process-independent dispersion coefficients [19]. Bishop and De Kee [20] proposed recently for the all-diagonal components yaaaa the expansion... 

Table 1 Coefficients for 7[ (a ) for third harmonic generation (THG), degenerate four wave mixing (DFWM), electric field induced second harmonic generation (ESHG), and Kerr effect in methane at the experimental geometry rcH = 2.052 a.u. A CCSD wavefunction and the t-aug-cc-pVDZ basis were used. (Results given in atomic units, the number in parentheses indicate powers of ten.)...

The present study demonstrates that the analytic calculation of hyperpolarizability dispersion coefficients provides an efficient alternative to the pointwise calculation of dispersion curves. The dispersion coefficients provide additional insight into non-linear optical properties and are transferable between the various optical processes, also to processes not investigated here as for example the ac-Kerr effect or coherent anti-Stokes Raman scattering (CARS), which depend on two independent laser frequencies and would be expensive to study with calculations ex-plictly frequency-dependent calculations. 

For the application of QDs to three-dimensional biological imaging, a large two-photon absorption cross section is required to avoid cell damage by light irradiation. For application to optoelectronics, QDs should have a large nonlinear refractive index as well as fast response. Two-photon absorption and the optical Kerr effect of QDs are third-order nonlinear optical effects, which can be evaluated from the third-order nonlinear susceptibility, or the nonlinear refractive index, y, and the nonlinear absorption coefficient, p. Experimentally, third-order nonlinear optical parameters have been examined by four-wave mixing and Z-scan experiments. 

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