Origins of Nonlinear Optical Effects

When electromagnetic radiation interacts with matter it causes the electron density in the material to oscillate at the same frequency as the incident light. Since the interaction of light and matter is a time-resolved process involving many photons, it should not be a surprise that the oscillation produced by 

5j( ) is the linear polarisability tensor at frequency and describes the linear variation of the induced dipole with the electric held. The resulting oscillation in the polarisation (oscillating dipole) is, in effect, a moving charge, and will therefore emit radiation of the same frequency as the oscillation. This gives rise to linear optical effects such as birefringence and refraction. 

The fundamental component (oE) is linear in E and represents the linear optical properties discussed above. The second (yjSE E) third (- yE E E) and subsequent harmonic terms are nonlinear in E and give rise to NLO effects. The 5 and /values are referred to, respectively, as the first and second hyperpolarisabilities. The second harmonic term gives rise to second harmonic generation (SHG), the third results in frequency tripling effects, and so on. Importantly, since only the time-averaged asymmetrically induced polarisation leads to second-order NLO effects, the molecule and crystal must be non-centrosymmetric, otherwise the effects will cancel one another. Third-order effects, however, may be observed in both centrosymmetric and non-centrosymmetric materials. 

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In the introduction to this chapter we gave an intuitive explanation of the origin of nonlinear optical effects and stressed the key role played by high power lasers and coherent light beams. These two concepts are defined here. We will describe one specific characteristic of laser light, namely the absorption saturation, and finally we will discuss susceptibility and frequency conversion of light. 

At a fundamental wavelength of 1064 nm, large and anisotropic optical nonlinearity was also observed. The values of X (3) and are 4.5 x 1010 esu and 1.0 x 10 10 esu, respectively. The large values are due to the two photon resonance, because the harmonic wavelength of 355 nm is near off-resonance region. From the two-photon fluorescence measurement, we confirmed that a two-photon absorption band, which is origin of the enhancement effect, exist around 532 nm, half of the fundamental wavelength. 

This tutorial deals with nonlinear optical effects associated with the first nonlinear term in expression for the polarization expansion described in the next section. The first nonlinear term is the origin of several interesting and important effects including second-harmonic generation, the linear electrooptic or Pockels effect,... 

The tutorial begins with a description of the basic concepts of nonlinear optics and presents illustrations from simple models to account for the origin of the effects. The microscopic or molecular origin of these effects is then discussed in more detail. Following this, the relationship between molecular responses and the effects observed in bulk materials are presented and finally some of the experimental methods used to characterize these effects are described. 

We have shown the molecular orbital theory origin of structure - function relationships for electronic hyperpolarizability. Yet, much of the common language of nonlinear optics is phrased in terms of anharmonic oscillators. How are the molecular orbital and oscillator models reconciled with one another The potential energy function of a spring maps the distortion energy as a function of its displacement. A connection can indeed be drawn between the molecular orbitals of a molecule and its corresponding effective oscillator . 

In an organic molecule, the nonlinear optical effect originates from nonlinear polarization of the molecules. The polarizability of a molecule is the ability of a charge in the molecule to be displaced under the driving of the electric field. Under an intense optical field, induced polarizability p can be expressed as a polynomial function of local field strength e, [34] ... 

The variation in absorption due to the electric field modulation (Equation 19.16) is a nonlinear optical effect. We now consider the origin of nonlinear behavior in materials. In a classical description [89-91], the electric field interacts with the charges (q) in an atom through the force (qF). which displaces the centre of the electron density away from the nucleus. This results in charge separation and thus in a field-induced dipole pi. For an assembly of atoms, the average summation over all atoms ultimately gives rise to the bulk polarization P vector of the material. P opposes the externally applied field and is given by ... 

The prediction [19] that a low power optical field can induce appreciable director reorientation just above the dc field induced Freedericksz transition has been verified experimentally [20,21] concurrently with experimental and theoretical work on optical reorientation [22-24]. Since then, it has become one of the most intensively studied nonlinear optical effects in liquid crystals [3]. The phenomenon originates from the tendency of the director to align parallel to the electric field of light due to the anisotropic molecular polarizability. The free energy density arising from the interaction of a plane electromagnetic wave and the liquid... 

The linear electro-optical (EO) behavior, i.e., the Pockels effect, constitutes a manifestation of nonlinear optical features of anisotropic and non-centro-symmetric media. Functional architectures based on host polymer matrixes and guest SiC nanoparticles (nc-SiC) as active chromophores were realized. The intrinsic dipole moments of the chromophore combined with the eventual polarization at the interfaces with the host matrix constitute the physical origin of the electro-optical responses. The experiments were carried out in hybrid materials based on SiC nanocrystals and matrixes such as PVK, PMMA, or PC. 

However, its was found possible to infer all four microscopic tensor coefficients from macroscopic crystalline values and this impossibility could be related to the molecular unit anisotropy. It can be shown that the molecular unit anisotropy imposes structural relations between coefficients of macroscopic nonlinearities, in addition to the usual relations resulting from crystal symmetry. Such additional relations appear for crystal point group 2,ra and 3. For the monoclinic point group 2, this relation has been tested in the case of MAP crystals, and excellent agreement has been found, triten taking into account crystal structure data (24), and nonlinear optical measurements on single crystal (19). This approach has been extended to the electrooptic tensor (4) and should lead to similar relations, trtten the electrooptic effect is primarily of electronic origin. 

While the linear absorption and nonlinear optical properties of certain dendrimer nanocomposites have evolved substantially and show strong potential for future applications, the physical processes governing the emission properties in these systems is a subject of recent high interest. It is still not completely understood how emission in metal nanocomposites originates and how this relates to their (CW) optical spectra. As stated above, the emission properties in bulk metals are very weak. However, there are some processes associated with a small particle size (such as local field enhancement [108], surface effects [29], quantum confinement [109]) which could lead in general to the enhancement of the fluorescence efficiency as compared to bulk metal and make the fluorescence signal well detectable [110, 111]. 

The origin of the nonlinearity and hysteresis in the films is most likely due to displacement of domain walls [4], If domain walls move in a medium with a random distribution of pinning center, the response of the material can be described, in the first approximation by Rayleigh relations. We next demostrate how optical interferometry can be sued to verify whether this particular model applies to the investigated pzt thin film. In the case of the converse piezoelectric effect, when the driving field E is varied between — Eo and Eo, the piezoelectric strain x is hysteretic and can be expressed by the following Rayleigh relations ... 

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