Polarization nonlinear effect

Nonlinear effects are characterized by new components of the -field generated from the acceleration of charges as the nonlinear polarization P [second, third, and higher terms in Equation (4.1)] drives the electric field. When linear absorption... 

We have assumed hitherto that the polarization produced in a solid is proportional to the electric field of the radiation (linear behaviour). The electric fields produced can be very high in laser beams and nonlinear effects therefore become significant. Polarization would then contain multiples of frequencies, as given by... 

Just as linear polarization leads to linear optical effects, such as refractive index and birefringence, nonlinear polarization leads to other and usually more subtle (nonlinear) effects. It is precisely these effects we hope to understand and exploit. In Figure 14, application of a symmetric field (i.e., the electric field associated with the light wave) to the anharmonic potential leads to an asymmetric polarization response. This polarization wave shows diminished maxima in one direction and accentuated... 

The terms beyond odE are not linear in E they are referred to as the nonlinear polarization and give rise to nonlinear optical effects. Also note that at small fields the polarization will more nearly approximate a linear response however, with increasing field strength, nonlinear effects become more important. Since a p, y, there were few observations of NLO effects before the invention of the laser with its associated large electric fields. 

Comments on NLO and Electrooptic Coefficients. Typically, the Pockels effect is observed at relatively low frequencies (up to gigahertz) so that slower nonlinear polarization mechanisms, such as vibrational polarizations, can effectively contribute to the "r" coefficients. The tensor used traditionally by theorists to characterize the second-order nonlinear optical response is xijk Experimentalists use the coefficient dijk to describe second-order NLO effects. Usually the two are simply related by equation 31 (16) ... 

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). 

Nonlinear effects are usually described in terms of polarization P through the material constitutive relation ... 

The principal structural requirement for second order nonlinear effects in assemblies of molecules is the lack of a centre of symmetry, and considerable efforts have been expended in trying to induce potentially useful molecular entities to crystallize in non-centrosymmetric or polar crystals (Curtin and Paul 1981 Liter et al. 1991). As demonstrated below, this is a necessary, but not sufficient condition for obtaining nonlinear effects. True to form, the variety of crystallization experiments has led to a number of polymorphic structures, and to information about the relationship between the properties of these materials and their structures, as well as useful guidelines for attempting to obtain the desired non-centrosymmetric crystal structures. 

One step better for determining accurate nonlinear susceptibilities was made by using high-level ab initio (hyper)polarizabilities [100,101], and this made possible the calculation of nonlinear susceptibilities without recourse to experimental information except for the crystal structure. For the nonpolar benzene crystal, the differences in the x tensor between the submolecule treatment and the point-dipole approximation were small [100]. However, the differences were larger for some components of the tensor of the urea crystal [101], which is polar. The effects of the surroundings, due mostly to the permanent molecular... 

When a molecule is subjected to laser light (that is—very high intensity electric field), its polarizability can change and be driven beyond the normal regime. Therefore, the polarization, which is a function of the applied field and leads to nonlinear effect, can be expressed as. 

The local ohmic behavior is not in contradiction with the fact that Eq. (41) shows a nonlinear variation of 7 with the potential drop A >. At low potentials, fA4> 1, the DBL is practically nonpolarized (i.e. the ionic concentrations take their bulk values throughout the DBL) and the slope of the current-voltage curve is When increasing A, the slope of the current-voltage curve decreases owing to the development of concentration polarization. The effective conductivity varies then with position and this makes the overall system behavior to be nonohmic. 

Coherent nonlinear effects involve interactions that occur before the wave functions that describe the excitations of the medium have time to relax or dephase. They occur primarily when the nonlinear interaction involves one- or two-photon resonances, and the duration of the laser pulse is shorter than the dephasing time of the excited state wave functions, a time that is equivalent to the inverse of the linewidth of the appropriate transition. Coherent nonlinear optical interactions generally involve significant population transfer between the states of the medium involved in the resonance. As a result, the nonlinear polarization cannot be described by the simple perturbation expansion given in Eq. (2), which assumed that the population was in the ground state. Rather, it must be solved for as a dynamic variable along with the optical fields. 

Table 4.1-149 Electro-optical constants of zinc compounds. Under the influence of an electric field, the refractive index changes in accordance to the nonlinearity of the dielectric polarization (Pockels effect). Crystals with hexagonal symmetry have three electro-optical constants rsi, 733, 751 crystals with cubic symmetry have only one electro-optical constant 741...

NonlinGar SuSCeptibilitiGS. Nonlinear optical effects are formally im-derstood through the series expansion of the ith component of the polarization (average dipole moment per unit volume) P of a material in powers of the electric-field in the medium E (typically on the order of 10 V/m or greater for nonlinear effects to appear), as in (13)... 

Consider the problem of a linearity polarized laser incident upon a homeotropically aligned nematic film, as shown in Fig. 1. We shall limit our discussion to the case in which < < 1, for the sake of simplicity as well as for practical considerations (because in general a small reorientation 6 will contribute to a rather large change in the optical refractive index for nonlinear effects to manifest). Since the theoretical results for the (3 0 case have been discussed before,... 

The d tensor is more general, and encompasses all second-order nonlinear effects. The nonlinear components of the polarization are usually written... 

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