Kerr coefficient

Kerr coefficient -for electrooptic materials [CERAMICS - NONLINEAROPTICAL AND ELECTKOOPTIC CERAMICS] (Vol 5)... 

The constants ryk and fyk are the Pockels electro-optic coefficients, and Rijkl and gyki the Kerr coefficients. They are related as follows ... 

This time dependent phase shift leads to a frequency modulation that is proportional to the time derivative of the self induced phase shift fused silica with its positive Kerr coefficient rio = 2.5 x 10 16 cm2/W [28] the leading edges of the pulses are creating extra frequencies shifted to the red ( jvi(t) < 0) while the trailing edges causes blue shifted frequencies to emerge. Self-phase modulation modifies the envelope function according to... 

The low temperature refractive properties of the He gas have not been studied extensively. However, the second virial Kerr coefficient can be related to the zeroth moment of the polarized Raman spectrum, and thus deduced from the Raman experiment. For the helium gas at the liquid nitrogen temperature the experiment gives 1.46 a.u.416, the full quantum calculation 1.45328, while the classical result computed according to Eq. (1-260) gives 1.63 328. This shows that also for the Kerr effect the quantum corrections are important. A systematic study of these corrections and of the convergence of the semiclassical expansion has not been reported thus far, even though all necessary expressions are derived328. 

Measurements. The anisotropy of the pair polarizability has been determined from three types of measurements depolarized CILS spectra, pressure dependent depolarization ratios, and second virial Kerr coefficients. 

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... 

With the initial introduction of the Z-scan technique, Gaussian beams were used for all measurements. However, Gaussian beams are not always readily available. In 1993 Zhao and Pallfy-Muhoray [17] substituted a beam with a top-hat spatial profile for the Gaussian beam to perform Z-scan measurements of the optical Kerr coefficients of materials. A beam with a top-hat spatial profile can be obtained by using an aperture to take a small portion of an expanded beam of a laser with... 

The effect of correlated molecular motions can be observed even in the isotropic phase of nematic liquid crystals near the phase transition temperature. This phenomenon was first studied by Wong and Shen and Frost and Lalanne. They found both a pretransitional increase of the Kerr coefficient and a critical slowing-down in the relaxation process. 

Frequency dependence of the steady Kerr coefficient for poly(y-benzyl glutamate) rods in m-cresol. From Mori et al. (1982). 

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. 

For applications where the ionic strength is as high as 6 M, the ion activity coefficients can be calculated using expressions developed by Bromley (4 ). These expressions retain the first term of equation 9 and additional terms are added, to improve the fit. The expressions are much more complex than equation 9 and require the molalities of the dissolved species to calculate the ion activity coefficients. If all of the molalities of dissolved species are used to calculate the ion activity coefficients, then the expressions are quite unwieldy. However, for the applications discussed in this paper many of the dissolved species are of low concentration and only the major dissolved species need be considered in the calculation of ion activity coefficients. For lime or limestone applications with a high chloride coal and a tight water balance, calcium chloride is the dominant dissolved specie. For this situation Kerr (5) has presented these expressions for the calculation of ion activity coefficients. 

Stemmier, K., D. J. Kinnison, and J. Alistair Kerr, Room Temperature Rate Coefficients for the Reactions of OH Radicals with Some Monomethylene Glycol Monoalkyl Ethers, J. Phys. Chem., 100, 2114-2116 (1996). 

Estimated from the value of the 2PA coefficient reported in the original paper and obtained in a Kerr ellipsometry experiment with photon energies 1.96 eV and 1.55 eV for the pump and probe beams, respectively. 710 nm is the equivalent excitation wavelength for a degenerate experiment. 

Today generator matrices F are known for many properties,10 among them the population of different conformers, the relative stability of macromolecular diastereoisomers, the mean-square end-to-end distance, the radius of gyration, the molecular dipole moment, the molecular optical anisotropy (and, with it, the stress-optical coefficient, the Kerr effect, depolarized light scattering, and the... 

Historically, the earliest nonlinear optical (NLO) effect discovered was the electro-optic effect. The linear electro-optic (EO) coefficient rij defines the Pockels effect, discovered in 1906, while the quadratic EO coefficient sijki relates to the Kerr effect, discovered even earlier (1875). True, all-optical NLO effects were not discovered until the advent of the laser. 

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