DC Kerr effect

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... 

Y(- , 0,0) dc-Kerr effect dc-K Electro-optical Kerr Effect (EOKE)... 

Che, T. M., Carney, R. V., Khanarian, G., Keosiuan, R. A., and Borzo, M., Electro-optical dc Kerr effects and solid-state deuterium NMR studies of stable gel-derived glass organic polymer composites, J. Non-Cryst. Solids, 102, 280-287 (1988). 

Perpete, Quinet and Champagne have shown that vibrational contributions to the y-hyperpolarizability of various symbioticaUy substituted quadrupolar JT-conjugated molecules are large. Using ab initio calculations at the HF level they calculate the response functions for the dc-Kerr effect, degenerate four wave mixing, hyper-Raman effect and electric field induced SHG. 

Different averaging expressions hold for the dc-Kerr effect and other... 

Electro-optical or dc-Kerr effect (EOKE, dc-Kerr) y" r(- >o,o) ... 

Apart from SHG and THG, Eq. (3) also reveals a second-order DC contribution (optical rectification) and the optical Kerr effect (i.e., the dependence of the term at the original frequency upon the light intensity / CX Eg ). A similar expression can be derived for the macroscopic polarization. Other NLO effects can be described utilizing different frequencies and/or static "(0) or magnetic B(0) fields (see Table 1). 

P( P(-o> w,0) P(0 -fa>,w) Y( - Y(-2(i) (i>,tD,0) Y(-o) (i>,0,0) Second harmonic generation (SHG) Electrooptic Pockels effect Optical rectification Third harmonic generation DC electric-field-induced SHG Intensity-dependent refractive index Optical Kerr effect Coherent anti-Stokes Raman pSHG pEOPE pOR. yTHG. EFISH oj DC-SHG. JlDRI or. yOKE. yCARS... 

In some cases, other second-hyperpolarizability quantities may be required, such as for the Kerr effect, which measures the depolarization of light in the presence of a DC field. The corresponding second hyperpolarizability is given as... 

Combination with Static Fieids. A common technique, useful for optoelectronic devices, is to combine a monochromatic optical field with a DC or quasistatic field. This combination can lead to refractive index and absorption changes (linear or quadratic electrooptic effects and electroabsorption), or to electric-field induced second-harmonic generation (EFISH or DC-SHG, 2 > = > - - third-order process. In EFISH, the DC field orients the molecular dipole moments to enable or enhance the second-harmonic response of the material to the applied laser frequency. The combination of a DC field component with a single optical field is referred to as the linear electrooptic (Pockels) effect co = co + 0), or the quadratic electrooptic (Kerr) effect ( > = > - - 0 -I- 0). These electrooptic effects are discussed extensively in the article Electrooptical Applications (qv). EFISH is... 

Because of the extensive overlap with electro-optics and nonlinear optics, the reader is referred to separate articles on these topics in this encyclopedia. See ElectroopticAL Applications for a discussion of the changes in the optical response of polymers dne to an applied AC or DC electric field from the so-called Pockels or Kerr effects. Also see, for an overview. Nonlinear Optical Properties. 

Figure 11 shows the change in the refractive indices AWj and Ang as a function of an applied dc electric field for a PLZT (9.5/65/35) ceramic. The dc field was cycled from 0 to +1.1 MV.m+ down to -1.1 MV.m i, and back up to 0. Awj remained near zero while Afig decreased quadratically with the dc field, due to the electro-optic Kerr effect, until a minimum of -... 

The majority of existing experimental data on hyperpolarizabflities are derived from ESHG and dc-Kerr measurements (Shelton and Rice 1994). The dc-I rr effect differs from the other nonlinear optical processes as it allows for absolute measmements without the need for a reference measurement. The measured molar Kerr constant is (Shelton and Rice 1994) ... 

The argument Rp implies structure relaxation in the field, and P" means the nuclear relaxation part of P, while the subscript oc oo invokes the so-called infinite optical frequency (lOF) approximation. In principle, this procedure allows one to obtain most of the major dynamic vibrational NR contributions in addition to the purely static ones of Eqs.4.5. 7. The linear term in the electric field expansion of Eq. (4) gives the dc-Pockels effect the quadratic term gives the optical Kerr Effect and the linear term in the expansion of beta yields dc-second harmonic generation (all in the lOF approximation). For laser frequencies in the optical region it has been demonstrated that the latter approximation is normally quite accurate [29-31]. In fact, this approximation is equivalent to neglecting terms of the order with respect to unity (coy is a vibrational frequency). In terms of Bishop and Kirt-man perturbation theory [32-34] all vibrational contributions through first-order in mechanical and/or electrical anharmonicity, and some of second-order, are included in the NR treatment [35]. 

In passive mode-locking, an additional element in the cavity can be a saturable absorber (e.g., an organic dye), which absorbs and thus attenuates low-intensity modes but transmits strong pulses. Kerr lens mode-locking exploits the optical Kerr63 or DC quadratic electro-optic effect here the refractive index is changed by An = (c/v) K E2, where E is the electric field and K is the Kerr constant. 

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