Nonlinear optical susceptibility calculation

The nonlinear optical susceptibility can be calculated by assuming a one-dimensional molecule and a non-interacting molecular ensemble at the poling conditions, and is given by... 

Ward, J.F. Calculation of nonlinear optical susceptibilities using diagrammatic perturbation theory. Rev. Mod. Phys. 37, 1-18 (1965)... 

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... 

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... 

The nonlinear optical susceptibilities can be calculated, in principle, on the basis of the density matrix formalism. However, one can often draw some conclusions about the nonlinear optical output from symmetry considerations. The nonlinear susceptibility tensors reflect the structural symmetry of the crystal since they are determined by its electronic or vibrational states. 

Levine, B.F. (1973) Bond-charge calculation of nonlinear optical susceptibilities for various crystal structures. Physical Review B Condensed Matter, 7, 2600. 

WARD J.F., (1985), "Calculation of Nonlinear Optical Susceptibilities Using Diagrammatic Perturbation Theory" Rev. Mod. Phys., 37. I-I8. 

Of particular significance with regard to relating the nonlinear susceptibilities to the microscopic nature of materials is the application of the Phillips-Van Vechten (PV) quantum dielectric theory of solids (Chapter 1, this volume) by Levine " to the calculation of the Miller delta. He has successfully computed the Miller delta and nonlinear optical susceptibility d for a large variety of nonlinear optical materials, including those in whieh d electrons play a role in the bonding. 

Nonlinear optical susceptibilities of materials can now be calculated from bond ionicity, atomic radii, and d-electron contribution to the bonding. 

One result of studying nonlinear optical phenomena is, for instance, the determination of this susceptibility tensor, which supplies information about the anharmonicity of the potential between atoms in a crystal lattice. A simple electrodynamic model which relates the anharmonic motion of the bond charge to the higher-order nonlinear susceptibilities has been proposed by Levine The application of his theory to calculations of the nonlinearities in a-quarz yields excellent agreement with experimental data. 

The calculation of the electric properties of individual molecules as found in an infinitely dilute gas has for long been of great interest to quantum chemists. This curiosity has been spurred in recent decades by the increasing importance of the communications industry in the world and the parallel need for materials having specific properties for electronic, optical, and other devices. In particular, the nonlinear-optical quantities, defined at the microscopic level as hyperpolarizabilities and at the macroscopic level as nonlinear susceptibilities, have played a... 

In tune with the above introductory remarks, we have arranged this review in the following way Section II deals with the oriented gas model that employs simple local field factors to relate the microscopic to the macroscopic nonlinear optical responses. The supermolecule and cluster methods are presented in Section III as a means of incorporating the various types of specific interactions between the entities forming the crystals. The field-induced and permanent mutual (hyper)polarization of the different entities then account for the differences between the macroscopic and local fields as well as for part of the effects of the surroundings. Other methods for their inclusion into the nonlinear susceptibility calculations are reviewed in Section IV. In Section V, the specifics of successive generations of crystal orbital approaches for determining the nonlinear responses of periodic infinite systems are presented. Finally,... 

Another scheme to calculate and interpret macroscopic nonlinear optical responses was formulated by Mukamel and co-workers [112 114] and incorporated intermolecular interactions as well as correlation between matter and the radiation field in a consistent way by using a multipolar Hamiltonian. Contrary to the local field approximation, the macroscopic susceptibilities cannot be expressed as simple functionals of the single-molecule polarizabilities, but retarded intermolecular interactions (polariton effects) can be included. 

In the above discussion, we have only considered the effects due to the CTE-CTE repulsion, which contribute to the resonant nonlinear absorption (as well as to other resonant nonlinearities) by the CTE themselves. Here, however, we want to mention a more general mechanism by which the nonlinear optical properties of media containing CTEs in the excited state can be enhanced. This influence is due to the strong static electric field arising in the vicinity of an excited CTE, If, for example, the CTE (or CT complex) static electric dipole moment is 20 Debye, at a distance of 0.5 nm it creates a field Ecte of order 107 V/cm. Such strong electric fields have to be taken into account in the calculation of the nonlinear susceptibilities, because they change the hyperpolarizabilities a, / , 7, etc. of all molecules close to the CTE. For instance, in the presence of these CTE induced static fields, the microscopic molecular hyperpolarizabilities are modified as follows... 

In nonlinear optics the theoretical framework falls naturally into two parts. First, one must calculate a nonlinear susceptibility (x) which describes the microscopic (i.e., atomic contribution to the polarization induced by the propagation of the laser beam at frequency w,). For the general case, this polarization is written as a power series in the electric field (w,) so that... 

Nonlinear optical measurements provide the most direct probe of the electronic states. Conversely, the nonlinear susceptibilities can be calculated if there exists a theoretical imderstanding of the excited states. We describe the theory of linear and nonlinear optical processes, and recast the so-called essential states model in terms of the primary excitons. 

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]. 

These nonlinear (microscopic) susceptibilities are derived from explicit calculations of the dipolar interaction between a particular atom or molecule with incident optical fields (see Chapter 10). In the presence of other atoms or molecules, and their polarizations, an atom or molecule will experience a net depolarization field in addition to... 

In a non-exhaustive literature search, a brief account is given here on the study of phonon and its vibrations. Corso et al. did an extensive study of density functional perturbation theory for lattice dynamics calculations in a variety of materials including ferroelectrics [93]. They employed a nonlinear approach to mainly evaluate the exchange and correlation energy, which were related to the non-linear optical susceptibility of a material at low frequency [94], The phonon dispersion relation of ferroelectrics was also studied extensively by Ghosez et al. [95, 96] these data were, however, related more with the structure and metal-oxygen bonds rather than domain vibrations or soliton motion. In a very interesting work, a second peak in the Raman spectra was interpreted by Cohen and Ruvalds [97] as evidence for the existence of bound state of the two phonon system and the repulsive anharmonic phonon-phonon interaction which splits the bound state off the phonon continuum was estimated for diamond. 

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