Microscopic nonlinearities

A number of approaches have been described in the literature for calculating the microscopic nonlinear response and are reviewed in detail elsewhere (1). In this section, these methods are briefly mentioned and a simplified version of time dependent perturbation theory is used to illustrate the intuitive aspects of the microscopic nonlinear polarization. 

In the weak coupling limit, as is the case for most molecular systems, each molecule can be treated as an independent source of nonrlinear optical effects. Then the macroscopic susceptibilities X are derived from the microscopic nonlinearities 3 and Y by simple orientationally-averaged site sums using appropriate local field correction factors which relate the applied field to the local field at the molecular site. Therefore (1,3)... 

In Equation 6, n (a>.) is the intensity independent refractive index at frequency u).,.0 Tlie sum in Equation 5 is over all the sites (n) the bracket, < >, represents an orientational averaging over angles 0 and . Unlike for the second-order effect, this orientational average for the third-order coefficient is nonzero even for an isotropic medium because it is a fourth rank tensor. Therefore, the first step to enhance third order optical nonlinearities in organic bulk systems is to use molecular structures with large Y. For this reason, a sound theoretical understanding of microscopic nonlinearities is of paramount importance. 

The measurement of x of solutions can be used to determine the microscopic nonlinearities Y of a solute, provided Y of the solvent is known. This measurement also provides information on the sign of y and (hence x of the molecules if one knows the sign of Y for the solvent (5,7) Under favorable conditions one can also use solution measurements to determine if Y is a complex quantity. The method utilizes two basic assumptions (i) the nonlinearities of the solute and the solvent molecules are additive, and (ii) Lorentz approximation can be used for the local field correction. Under these two assumptions one can write the x of the solution to be... 

The microscopic nonlinearity y for some molecular structures measured In the liquid phase... 

Figure 1. The optical scattering leading to a single microscopic nonlinear optical event.

II Conjugation alone cannot be relied upon to significantly enhance the optical nonlinearities. The conformational effects and the role of the substituents so that understanding of the molecular structure-property relation can be improved have been studied (89JPC7916). In the case of the thiophene oligomers, a rapid increase in the y value (large microscopic nonlinearity) as a function of N is found. 

This result implies that the energy equipartition relationship of Eq. (2.S) applies as well as the general definitions of Chapter I. Note that for Af m the variable turns out to be coupled weakly to the thermal bath. This condition generates that time-scale separation which is indispensable for recovering an exponential time decay. To recover the standard Brownian motion we have therefore to assiune that the Brownian particle be given a macroscopic size. In the linear case, when M = w we have no chance of recovering the properties of the standard Brownian motion. In the next two sections we shall show that microscopic nonlinearity, on the contrary, may allow that the Markov characters of the standard Brownian motion be recovered with increasing temperature. 

However, recalculating the value of y using the method described in the paper for the field factors, gives the value in brackets. The unbracketed value, for the overall microscopic nonlinearity, converts to 2859 au. In the case of associating liquids the authors argue that equation (7) can be used in modified form with the inclusion of a factor, g, which they deduce from the Kirkwood-Frohlich modification of the Onsager theory,... 

In organic materials, it is convenient to define microscopic nonlinear coefficients that relate the molecular dipole moment with the electric field applied to the molecule. Including the possibility of a permanent molecular dipole moment, /jlq, the molecular dipole moment is related to the electric field components in the frequency domain by ... 

As implied by the trace expression for the macroscopic optical polarization, the macroscopic electrical susceptibility tensor at any order can be written in terms of an ensemble average over the microscopic nonlinear polarizability tensors of the individual constituents. 

Actually, it has been shown that the highest second order susceptibility coefficients (macroscopic nonlinearity), for a given chromophore (microscopic nonlinearity), can be reached in the (polar) crystal classes 1, 2, m and mm2, while other polar crystal classes are less favourable [21]. 

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