Second-order nonlinear polarizabilities

Optical second harmonic generation (SHG), which stems from the conversion of two photons of frequency to to a single photon of frequency 2(o, is an inherently surface-sensitive technique. Whereas no optical second harmonic wave is generated in the centrosymmetric bulk of a liquid, molecules participating in the asymmetry of the interface between two liquids (noncentrosymmetric environ-ment) contribute to SHG. Since the square root of SHG signal intensity, is proportional to the number N (per unit area), the molecular orientation (I) and the second order nonlinear polarizability of the SHG active species at the interface... 

The discontinuity of the interface leads to two contributions to the second order nonlinear polarizability, the electric dipole effect due to the structural discontinuity and the quadrupole type contribution arising from the large electric field gradient at the surface. Under the electric dipole approximation, the nonlinear susceptibility of the centrosymmetric bulk medium 2 is zero. If the higher order magnetic dipole... 

The TPA cross section (7>) is proportional to the second-order nonlinear polarizability y. This is derived by consideration of interactions of light with matter causing a change in the dipole moment that is the induced dipole moment /iirld. Induced polarization Pind is proportional to /(ind and the field strength E of the incident light, Eq. (7) [50, 73] ... 

The surface SHG allows us to measure directly an averaged molecular orientation. The basic principle is as follows. The second-order surface nonlinear susceptibility 2) g layer is related to the second-order nonlinear polarizability "o ) Qf he molecules by... 

The most well-known and extensively studied noncentrosymmetric liquid crystalline phase is the smectic—C phase. The helically modulated smectic C system, with a spatially varying spontaneous polarization, is locally characterized by a C2 symmetry the average polarization of the bulk is still vanishing. By unwinding such a helical stmeture, the system behaves as a crystal with C2 point symmetry. Such unwound SmC phases possess sizable second-order nonlinear polarizabilities,with (2) ranging from 8 X 10 m/V for DOBAMBC to about 0.2 X 10 mA for o-nitroalkoxyphenyl-biphenyl-carboxylate. ... 

The determination of the number of the SHG active complex cations from the corresponding SHG intensity and thus the surface charge density, a°, is not possible because the values of the molecular second-order nonlinear electrical polarizability, a , and molecular orientation, T), of the SHG active complex cation and its distribution at the membrane surface are not known [see Eq. (3)]. Although the formation of an SHG active monolayer seems not to be the only possible explanation, we used the following method to estimate the surface charge density from the SHG results since the square root of the SHG intensity, is proportional to the number of SHG active cation com-... 

A novel second-order nonlinear optical medium which should offer considerable fabrication flexibility has been described. The physics of alignment of the highly nonlinearly polarizable moiety was discussed. However, observation of complex dynamical and thermal behavior indicates that an important role is played by the polymer liquid crystalline host. Additional properties of modified members of this family of lc polymers were consequently investigated. The explanations of guest alignment stabilization and thermal dependence of the alignability remain unresolved issues. 

The proportionality constants a and (> are the linear polarizability and the second-order polarizability (or first hyperpolarizability), and x(1) and x<2) are the first- and second-order susceptibility. The quadratic terms (> and x<2) are related by x(2) = (V/(P) and are responsible for second-order nonlinear optical (NLO) effects such as frequency doubling (or second-harmonic generation), frequency mixing, and the electro-optic effect (or Pockels effect). These effects are schematically illustrated in Figure 9.3. In the remainder of this chapter, we will primarily focus on the process of second-harmonic generation (SHG). 

In order to describe second-order nonlinear optical effects, it is not sufficient to treat (> and x<2) as a scalar quantity. Instead the second-order polarizability and susceptibility must be treated as a third-rank tensors 3p and Xp with 27 components and the dipole moment, polarization, and electric field as vectors. As such, the relations between the dipole moment (polarization) vector and the electric field vector can be defined as ... 

For second-order nonlinear polarization, the problem becomes more complex. As can be seen in Figure 13 the anharmonic polarization shows the largest deviation from the linear polarization with large distortion values. Therefore, if the material is not polarizable (i.e., if the electrons can only be perturbed a small distance from their equilibrium positions), then the anharmonicity will not be manifested. For large second-order nonlinearities we need a material that offers both a large linear... 

Lindsay, G. A. and Singer, K. D. (eds) (1995). Polymers for Second-Order Nonlinear Optics. ACS Symposium Series. American Chemical Society, Washington, DC Liptay, W. (1969). Angew. Chem. 81, 195 Angew. Chem. Int. Ed. Engl. 8, 177 Liptay, W. (1974). Excited States, Vol. 1. Dipole Moments and Polarizabilities of Molecules in Excited Electronic States (ed. E. C. Lim). Academic Press, New York, p. 129... 

On the assumption of total symmetry of the tensor of third-order nonlinear polarizability c(— co coi, cog, cog), its non-zero and independent elements are the same as those of Table 12. Direct theoretical calculations of c = c(0 0,0,0) have been performed for the atoms of inert gases and some simple molecules. Values of the tensor elements = c(— cu cu, 0,0) have been determined for numerous molecules from static Kerr effect studies and values of c = c(— cd ot>,coi — col) from measurements of optical birefringence induced by laser li t. Measurements of second-harmonic generation by gases in the presence of a static electric field yield the tensor elements c " = c( — 2co co, to, 0), which can also be obtained from second-harmonic scattering in centro-symmetric liquids. The elements of the tensor c = c(— 3co co, co, co)... 

MOLECULAR SECOND-ORDER NONLINEAR OPTICAL POLARIZABILITIES OF PHOTOCHROMIC MOLECULES... 

It is relevant to cite here two more examples of the application of molecular calculations to spiropyran derivatives. First, in a study of the relationship between photochromism and second-order nonlinear optical (NLO) properties in spiropyran- and spirooxazine-doped polymer films, dipole moments, polarizabilities, and hyperpolarizabilities were estimated by the MNDO method.46 Second, the relative stabilities of the radical anions as well as their spin density distributions for a spiroindolinic series were calculated by an ab initio method in a combined electron paramagnetic resonance (EPR)/electrochemistry study.47... 

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