Susceptibility second-order nonlinear optical

The first and third order terms in odd powers of the applied electric field are present for all materials. In the second order term, a polarization is induced proportional to the square of the applied electric field, and the. nonlinear second order optical susceptibility must, therefore, vanish in crystals that possess a center of symmetry. In addition to the noncentrosymmetric structure, efficient second harmonic generation requires crystals to possess propagation directions where the crystal birefringence cancels the natural dispersion leading to phase matching. 

Teng, C.C. and Garito A.F., Dispersion of the nonlinear second-order optical susceptibility of organic systems. Phys. Rev. B (1983) 28 6766-6773. 

For obtaining the information on fabrication of noncentrosymmetric LB films with highly efficient second-order optical nonlinearity, six azobenzene-linked amphiphiles were synthesized as a model compound, and their molecular hyperpolarizabilities (3, monolayer-formation at the air-water interface, and molecular orientation and second-order susceptibilities of the azobenzene-linked amphiphiles LB films were evaluated. The molecular structures of the azobenzene-linked amphiphiles are shown in Fig.2. 

Second order, polyazomethine possesses both donor and acceptor groups at the molecular level, which when aligned gives a poled polymer. Tatsuura et al. fabricated an as-deposited poled polymer film by applying anin-situ electric field during CVD and reported on the second order nonlinear optical properties of the obtained film. The polymer film refractive index was reported to be about 1.68 at 632.8 nm. Second order NLO susceptability, p, was found to be... 

Wave mixing of two electric fields can give rise to second-order effects of nonlinear optics [4]. One of these is the harmonic generation that converts the fundamental wavelength of a laser into its half (see Section 12.2.2). But, if electric fields at different frequencies are used, the response of a medium with sufficient second-order dielectric susceptibility can be frequency shifted to the sum and the difference of the two laser frequencies [4]. In particular, sum frequency generation (SFG) is often used to study surfaces and has found applications to examine catalytic combustion [9,36]... 

The importance of the hyperpolarizability and susceptibility values relates to the fact that, provided these values are sufficiently large, a material exposed to a high-intensity laser beam exhibits nonlinear optical (NLO) properties. Remarkably, the optical properties of the material are altered by the light itself, although neither physical nor chemical alterations remain after the light is switched off. The quahty of nonlinear optical effects is cmciaUy determined by symmetry parameters. With respect to the electric field dependence of the vector P given by Eq. (3-4), second- and third-order NLO processes may be discriminated, depending on whether or determines the process. The discrimination between second- and third-order effects stems from the fact that second-order NLO processes are forbidden in centrosymmetric materials, a restriction that does not hold for third-order NLO processes. In the case of centrosymmetric materials, x is equal to zero, and the nonhnear dependence of the vector P is solely determined by Consequently, third-order NLO processes can occur with all materials, whereas second-order optical nonlinearity requires non-centrosymmetric materials. 

The functionalities of the second-order nonlinear optical susceptibility, generally called second-order optical nonlinearity, are second harmonic (SH) generation, optical rectification and generation of addition and subtraction of two incident radiation beams. On the other hand, those of the third-order nonlinear optical susceptibility, which is called third-order optical nonlinearity, are the optical Kerr effect, nonlinear absorption, third harmonic generation and so on. 

Given the interest and importance of chiral molecules, there has been considerable activity in investigating die corresponding chiral surfaces [, and 70]. From the point of view of perfomiing surface and interface spectroscopy with nonlinear optics, we must first examhie the nonlinear response of tlie bulk liquid. Clearly, a chiral liquid lacks inversion synnnetry. As such, it may be expected to have a strong (dipole-allowed) second-order nonlinear response. This is indeed true in the general case of SFG [71]. For SHG, however, the pemiutation synnnetry for the last two indices of the nonlinear susceptibility tensor combined with the... 

The n-electron excitations are viewed as occuring on molecular sites weakly coupled to their neigbors and providing sources of nonlinear optical response through the on-site microscopic second order nonlinear electronic susceptibility... 

A specific set of experiments which must be mentioned, being directly associated with the main topic of this paper, is the work of Bergman, et. al. (22) dealing with the second-order nonlinear optical properties of polyvinylidene fluoride (PVF2). Nonvanishing the second-order nonlinear electric dipole susceptibility, is expected in PVF2 since it exhibits other properties requiring noncentrosymmetric microscopic structure. These properties appear... 

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 ... 

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