Electric fields nonlinear optics

In the analysis of linear and nonlinear optical spectroscopies, the electric fields and optical gates are commonly represented by their amplitudes. Similarly, the material system is represented by an amplitude as well, the wave function. However, optical signals are given by products of such amplitudes. 

The tensors and 7 constitute the molecular origin of the second-and third-order nonlinear optical phenomena such as electro-optic Pock-els effect (EOPE), optical rectification (OR), third harmonic generation (THG), electric field induced second harmonic generation (EFI-SHG), intensity dependent refractive index (IDRI), optical Kerr effect (OKE), electric field induced optical rectification (EFI-OR). To save space we do not indicate the full expressions for and 7 related to the different second and third order processes but we introduce the notations —(Ajy,ui,cj2) and 7(—a , o i,W2,W3), where the frequency relations to be used for the various non-linear optical processes which can be obtained in the case of both static and oscillating monochromatic fields are reported in Table 1.7. 

A number of optical effects arise out of both the first and second hyperpolarizibilities. However, only some among them have been systematically studied for practical applications. In this chapter, we will discuss the electric field-induced optical birefringence in second-order NLO materials and the light-induced optical nonlinearities including optical Kerr effect and two-photon absorption (TPA) in third-order NLO materials. Molecular design for... 

A diagrannnatic approach that can unify the theory underlymg these many spectroscopies is presented. The most complete theoretical treatment is achieved by applying statistical quantum mechanics in the fonn of the time evolution of the light/matter density operator. (It is recoimnended that anyone interested in advanced study of this topic should familiarize themselves with density operator fonnalism [8, 9, 10, H and f2]. Most books on nonlinear optics [13,14, f5,16 and 17] and nonlinear optical spectroscopy [18,19] treat this in much detail.) Once the density operator is known at any time and position within a material, its matrix in the eigenstate basis set of the constituents (usually molecules) can be detennined. The ensemble averaged electrical polarization, P, is then obtained—tlie centrepiece of all spectroscopies based on the electric component of the EM field. 

In order to illustrate some of the basic aspects of the nonlinear optical response of materials, we first discuss the anliannonic oscillator model. This treatment may be viewed as the extension of the classical Lorentz model of the response of an atom or molecule to include nonlinear effects. In such models, the medium is treated as a collection of electrons bound about ion cores. Under the influence of the electric field associated with an optical wave, the ion cores move in the direction of the applied field, while the electrons are displaced in the opposite direction. These motions induce an oscillating dipole moment, which then couples back to the radiation fields. Since the ions are significantly more massive than the electrons, their motion is of secondary importance for optical frequencies and is neglected. 

When light is incident on a material, the optical electric field E results in a polarization P of the material. The polarization can be expressed as the sum of the linear polarization and a nonlinear polarization P ... 

Polarization which can be induced in nonconducting materials by means of an externally appHed electric field is one of the most important parameters in the theory of insulators, which are called dielectrics when their polarizabiUty is under consideration (1). Experimental investigations have shown that these materials can be divided into linear and nonlinear dielectrics in accordance with their behavior in a realizable range of the electric field. The electric polarization PI of linear dielectrics depends linearly on the electric field E, whereas that of nonlinear dielectrics is a nonlinear function of the electric field (2). The polarization values which can be measured in linear (normal) dielectrics upon appHcation of experimentally attainable electric fields are usually small. However, a certain group of nonlinear dielectrics exhibit polarization values which are several orders of magnitude larger than those observed in normal dielectrics (3). Consequentiy, a number of useful physical properties related to the polarization of the materials, such as elastic, thermal, optical, electromechanical, etc, are observed in these groups of nonlinear dielectrics (4). 

Certain glass-ceramic materials also exhibit potentially useful electro-optic effects. These include glasses with microcrystaUites of Cd-sulfoselenides, which show a strong nonlinear response to an electric field (9), as well as glass-ceramics based on ferroelectric perovskite crystals such as niobates, titanates, or zkconates (10—12). Such crystals permit electric control of scattering and other optical properties. 

Nonlinear Optical Devices. A transparent, optically active, sol—gel-derived organic—inorganic glass has been synthesized (68). This hybrid consists of a 2,4-dinitroaminophenylpropyl-triethoxysilane covalently bound to a siUcon alkoxide-derived siUca network. This hybrid exhibits a strong electric field-induced second harmonic signal and showed no signs of crystallization. 

Further subclassification of nonlinear optical materials can be explained by the foUowiag two equations of microscopic, ie, atomic or molecular, polarization,, and macroscopic polarization, P, as power series ia the appHed electric field, E (disregarding quadmpolar terms which are unimportant for device appHcations) ... 

The linear polarizability, a, describes the first-order response of the dipole moment with respect to external electric fields. The polarizability of a solute can be related to the dielectric constant of the solution through Debye s equation and molar refractivity through the Clausius-Mosotti equation [1], Together with the dipole moment, a dominates the intermolecular forces such as the van der Waals interactions, while its variations upon vibration determine the Raman activities. Although a corresponds to the linear response of the dipole moment, it is the first quantity of interest in nonlinear optics (NLO) and particularly for the deduction of stracture-property relationships and for the design of new... 

The first theoretical attempts in the field of time-resolved X-ray diffraction were entirely empirical. More precise theoretical work appeared only in the late 1990s and is due to Wilson et al. [13-16]. However, this theoretical work still remained preliminary. A really satisfactory approach must be statistical. In fact, macroscopic transport coefficients like diffusion constant or chemical rate constant break down at ultrashort time scales. Even the notion of a molecule becomes ambiguous at which interatomic distance can the atoms A and B of a molecule A-B be considered to be free Another element of consideration is that the electric field of the laser pump is strong, and that its interaction with matter is nonlinear. What is needed is thus a statistical theory reminiscent of those from time-resolved optical spectroscopy. A theory of this sort was elaborated by Bratos and co-workers and was published over the last few years [17-19]. 

In the previous Maxwelhan description of X-ray diffraction, the electron number density n(r, t) was considered to be a known function of r,t. In reality, this density is modulated by the laser excitation and is not known a priori. However, it can be determined using methods of statistical mechanics of nonlinear optical processes, similar to those used in time-resolved optical spectroscopy [4]. The laser-generated electric field can be expressed as E(r, t) = Eoo(0 exp(/(qQr ot)), where flo is the optical frequency and q the corresponding wavevector. The calculation can be sketched as follows. 

In the field of polymer chemistry the regio- and stereoselectivity of the Diels-Alder reaction is used for the concerted synthesis of structurally homogeneous double-stranded ladder polymers [39], which are useful materials with nonlinear optical properties and high electrical conductivity. It has turned out that the repeated Diels-Alder method is superior to an alternative two-step process, in which first an open chain precursor is formed followed by polymer ring closure as structural defects can occur [40]. 

Meyers F, Marder SR, Pierce BM, Bredas JL (1994) Electric field modulated nonlinear optical properties of donor-acceptor polyenes sum-over-states investigation of the relationship between molecular polarizabilities (a, p, and y ) and bond length alternation. J Am Chem Soc 116 10703-10714... 

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