Third-order nonlinear optical calculation

There have been very few measurements made on the physical properties of Tg derivatives, their relative greater difficulty of preparation when compared with the Tg analogs has meant little interest in their properties. However, TglOSiMeslg has been found to show photoluminescence in the blue region of the spectrum, third-order nonlinear optical properties for TgMeg have been modeled, and electronic properties for and TgMeg have been calculated. 

The third-order nonlinear optical susceptibility x was obtained by comparing the measured signals for the sample with that of carbon disulfide as reference under the same experimental condition. The measured x value is 6.2 x 10 esu for the subphthalocyanine at a concentration 1.25 x 10 M. Considering an isotropic media under the Lorenz-Lorentz approximation, the second hyperpolarizability value was found to be 3.0 x 10 esu. Furthermore, A pirc corresponding to the pure subphthalocyanine 17 was calculated to be 6.9 x 10 esu, about four times higher... 

The coefficients W determine the probabilities of third-order nonlinear optical processes in an unbounded crystal. An analogous expression can be derived for the coefficients determining the probabilities of fourth-order nonlinear optical processes. As already mentioned the derivation for multilevel molecules is rather complicated and has not yet been obtained. However, the simplicity of the final result, that is the simplicity of the nonlinear Hamiltonian, determines the simplicity of the calculations of nonlinear processes. Note also that a similar polariton approach can be applied for consideration of nonlinear processes in low-dimensional nanostructures (chains, quantum wells). For such structures just resonances of the pumping radiation with polaritons of low-dimensional structure and not with excitons will determine the resonances in the absorption of light as well as resonances in nonlinear processes. 

The nonlinear optical (NLO) susceptibilities of bioengineered aromatic polymers synthesized by enzyme-catalyzed reactions are given in Tables 2, 3, and 4. Homopolymers and copolymers are synthesized by enzyme-catalyzed reactions from aromatic monomers such as phenols and aromatic amines and their alkyl-substituted derivatives. The third-order nonlinear optical measurements are carried out in solutions at a concentration of 1 mg/mL of the solvent. Unless otherwise indicated, most of the polymers are solubilized in a solvent mixture of dimethyl formamide and methanol (DMF-MeOH) or dimethyl sulfoxide and methanol (DMSO-MeOH), both in a 4 1 ratio. These solvent mixtures are selected on the basis of their optical properties at 532 nm (where all the NLO measurements reported here are carried out), such as low noise and optical absorption, and solubility of the bioengineered polymers in the solvent system selected. To reduce light scattering, the polymer solutions are filtered to remove undissolved materials, the polymer concentrations are corrected for the final x calculations, and x values are extrapolated to the pure sample based on the concentrations of NLO materials in the solvent used. Other details of the experimental setup and calculations used to determine third-order nonlinear susceptibilities were given earlier and described in earlier publications [5,6,9,17-19]. 

The aim of the current work is three-fold, namely (i) the synthesis of the mono-and bis- triphenylamine adducts of C6o us well as the dumbell TPhA-bridged-(C6o)2 hybrid, (ii) the evaluation of the third-order nonlinear optical properties of the TPhA-modified C6o-based hybrid materials, and (iii) the theoretical calculations aiming at better understanding of the structure-property relations for the investigated push-pull hybrid materials. 

This review covers the theoretical background and some of the practical aspects of nonlinear optics, including a description of the origins of third-order nonlinearities, systems of units that are encountered, experimental techniques that have been used or may be used to probe the third-order NLO properties of organometallic complexes, and computational methods that have or could be used to calculate third-order NLO properties. Subsequent sections collect comprehensive data of organometallic complexes in tables categorized by complex type and discussions of the results of third-order NLO measurements and calculations performed on organometallic... 

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)... 

Primary excitons We conclude this section with a few remarks on the essential states responsible for the nonlinear optical susceptibilities. As described in Chapter 8, there are at most four states in a particular excitation pathway in the sum-over-states calculation of the third-order nonlinear susceptibility, Only a few excitation pathways (and hence states) contribute to this sum. The pathway must contain strong dipole moments to the ground state. In the weak coupling limit these are the and n B states, namely the... 

Recently there has been a great deal of interest in nonlinear phenomena, both from a fundamental point of view, and for the development of new nonlinear optical and optoelectronic devices. Even in the optical case, the nonlinearity is usually engendered by a solid or molecular medium whose properties are typically determined by nonlinear response of an interacting many-electron system. To be able to predict these response properties we need an efficient description of exchange and correlation phenomena in many-electron systems which are not necessarily near to equilibrium. The objective of this chapter is to develop the basic formalism of time-dependent nonlinear response within density functional theory, i.e., the calculation of the higher-order terms of the functional Taylor expansion Eq. (143). In the following this will be done explicitly for the second- and third-order terms... 

Kobko et al.200 have used a third order response function formalism with TDHF and TDDFT to assess different levels of theory for calculations of excited state structure and nonlinear optical responses in donor-donor and donor-acceptor Ji-conjugated molecules. They make suggestions for numerically efficient approximations. 

This coherence size directly controls the size-scaling behavior of nonlinear optical response. The calculated first- (a), third- (y) and fifth-order (r) static polarizabilities of polyacetylene chains with up to 200... 

As will be outlined in more detail below, the much higher complexity of the d3mamics at conical intersections calls for a new strategy for the calculation of absorption and emission signals, which differs from the established formalism of nonlinear optics, based on higher-order (t3 ically third-order) perturbation theory in the laser-matter interaction. Independently of... 

To summarize, the EOM-PMA considerably facilitates the computation of various optical signals and 2D spectra. With shght alterations, the EOM-PMA can also be applied to compute nonlinear responses in the infrared (IR). The three-pulse EOM-PMA can be extended to calculate the A-pulse-induced nonhnear polarization [51], which opens the way for the interpretation of fifth-order spectroscopies, such as heterodyned 3D IR [52], transient 2D IR [53, 54], polarizability response spectroscopy [55], resonant-pump third-order Raman-probe spectroscopy [56], femtosecond stimulated Raman scattering [57], four-six-wave-mixing interference spectroscopy [58], or (higher than fifth order) multiple quantum coherence spectroscopy [59]. 

The EFISH method (Singer and Garito, 1981) permitted for the first time the establishment of a correlation between molecular structure of organic chromophores and the first hyperpolarizability p. In this method an electric field is applied to a solution of the nonlinear optical materials, resulting in an alignment of the dipoles. A direct determination of P with the EFISH method is not possible the third-order polarization y is measured, the dipole moment p. must be known, and with these values the hyperpolarizability p can be calculated. The EFISH technique is not readily applied to salts as the solutions conduct electricity. 

Organic compounds with delocalized 7r-electron systems are leading candidates for nonlinear optical (NLO) materials, and interest in these materials has grown tremendously in the past decade [108-118]. Reliable structure-property relationships—where property here refers to first-order (linear) polarizability a, second-order polarizability and third-order polarizability y—are required for the rational design of optimized materials for photonic devices such as electro-optic modulators and all-optical switches. Here also, quantum-chemical calculations can contribute a great deal to the establishment of such relationships. In this section, we illustrate their usefulness in the description of the NLO response of donor-acceptor substituted polymethines, which are representative of an important class of organic NLO chromophores. We also show how much the nonlinear optical response depends on the interconnection between the geometric and electronic structures, as was the case of the properties discussed in the previous sections [ 119]. 

Many efforts also currently focus on the gain of a better understanding of the optical nonlinearities in conjugated systems [36-40]. The fast and intense nonlinear responses of organic compounds make them very exciting candidates for the field of photonics, i.e. for an all-optical treatment of information. We discuss in the last section the calculated frequency dispersion of the third-order optical nonlinearities in ohgothiophenes. We also describe the nature of the essential states contributing to the nonlinear response and analyze the chain-size evolution of the calculated hyperpolarizabilities. 

---