Pockels effect, nonlinear optics-static field

Many of the different susceptibilities in Equations (2.165)-(2.167) correspond to important experiments in linear and nonlinear optics. x<(>> describes a possible zero-order (permanent) polarization of the medium j(1)(0 0) is the first-order static susceptibility which is related to the permittivity at zero frequency, e(0), while ft> o>) is the linear optical susceptibility related to the refractive index n" at frequency to. Turning to nonlinear effects, the Pockels susceptibility j(2)(- to, 0) and the Kerr susceptibility X(3 —to to, 0,0) describe the change of the refractive index induced by an externally applied static field. The susceptibility j(2)(—2to to, to) describes frequency doubling usually called second harmonic generation (SHG) and j(3)(-2 to, to, 0) describes the influence of an external field on the SHG process which is of great importance for the characterization of second-order NLO properties in solution in electric field second harmonic generation (EFISHG). 

Summation over repeated indices is implied and is the th-order susceptibility tensor that describes the interaction between the electric fields and the material. The first two terms on the right-hand side of Equation 8.A1 give the spontaneous polarization and linear optics effects. The last two terms lead to various phenomena in nonlinear optics. They include SHG and EO Pockels and Kerr effects. The EO susceptibilities are obtained by combining optical and static fields therefore, the susceptibilities that describe the EO Pockels and Kerr effects are (-co, co, 0) and x% respectively. In a... 

Particular nonlinear optical phenomena arise also when static electric or magnetic fields are applied. The molecular states and selection rules are thereby modified, leading, for instance, to higher-order, nonlinear-optical variants of the linear (Pockels) and quadratic (Kerr) electro-optical effect, or of the linear (Faraday) and quadratic (Cotton-Mouton) magneto-optical effect. 

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, 2o) = co + co + 0) in a quasi-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 -I- 0), or the quadratic electrooptic (Kerr) effect ( = -I- 0 -I- 0). EFISH is discussed in this article, however, for the important role that it has played in the characterization of nonlinear optical materials for other applications. 

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