Polarizabilities third-order

There are higher multipole polarizabilities tiiat describe higher-order multipole moments induced by non-imifonn fields. For example, the quadnipole polarizability is a fourth-rank tensor C that characterizes the lowest-order quadnipole moment induced by an applied field gradient. There are also mixed polarizabilities such as the third-rank dipole-quadnipole polarizability tensor A that describes the lowest-order response of the dipole moment to a field gradient and of the quadnipole moment to a dipolar field. All polarizabilities of order higher tlian dipole depend on the choice of origin. Experimental values are basically restricted to the dipole polarizability and hyperpolarizability [21, 24 and 21]. Ab initio calculations are an imponant source of both dipole and higher polarizabilities [20] some recent examples include [26, 22] ... 

If we neglect pure dephasing, the general tensor element of the third order hyperpolarizability relates to those of the first order polarizability tensor according to... 

Flere, the linear polarizability, a (oip 2), corresponds to the doorway stage of the 4WM process while to the window stage. We also see the (complex) Raman resonant energy denominator exposed. Of the tliree energy denominator factors required at third order, the remaining two appear, one each, m the two Imear polarizability tensor elements. 

Frequency-dependent polarizability a and second hyperpolarizability y corresponding to various third-order nonlinear optical processes have been... 

Five large basis sets have been employed in the present study of benzene basis set 1, which has been taken from Sadlej s tables [37], is a ( ()s6pAdl6sAp) contracted to 5s >p2dl >s2p and contains 210 CGTOs. It has been previously adopted by us in a near Hartree-Fock calculation of electric dipole polarizability of benzene molecule [38]. According to our experience, Sadlej s basis sets [37] provide accurate estimates of first-, second-, and third-order electric properties of large molecules [39]. 

Nonintuitive Light Propagation Effects In Third-Order Experiments. One of the first tasks for a chemist desiring to quantify second- and third-order optical nonlinear polarizability is to gain an appreciation of the quantitative manifestations of macroscopic optical nonlinearity. As will be shown this has been a problem as well for established workers in the field. We will present pictures which hopefully will make these situations more physically obvious. 

New THG Methods For Molecular Liquid Characterization. An area which is essential for understanding general third-order nonlinear polarizability is characterization of the purely electronic contributions (48). Several methods have been employed for this... 

In this expression, the Einstein convention of summation over repeated indices has been followed p0 is the permanent dipole moment, while al7, fiijk, and yiJkl are the tensorial elements of the linear polarizability, and the second- and third-order hyperpolarizabilities of the molecule, respectively. 

The process of THG is driven by third-order optical nonlinearity, which defines the nonlinear optical polarizability at the frequency 3[Pg.128]

We have considered scalar, vector, and matrix molecular properties. A scalar is a zero-dimensional array a vector is a one-dimensional array a matrix is a two-dimensional array. In general, an 5-dimensional array is called a tensor of rank (or order) s a tensor of order s has ns components, where n is the number of dimensions of the coordinate system (usually 3). Thus the dipole moment is a first-order tensor with 31 = 3 components the polarizability is a second-order tensor with 32 = 9 components. The molecular first hyperpolarizability (which we will not define) is a third-order tensor. 

Thus, the linear polarizability a (responsible for the value of the refractive index n) can be treated as an electric field amplitude-dependent quantity, i.e., aeff = a + (3-yEo)/4. Remembering that the light intensity is proportional to the square of the field amplitude, this means that the third-order nonlinearity leads to the linear dependence of the refractive index on the light intensity and that, for example, the phase of the propagating beam is modified at high light intensities due to this dependence. 

It should be noted that polarizabilities of various orders can be defined in an alternative way in the SI system of units to that discussed previously. A quantity having the dimension of volume a = a/47re0 can be considered to be an SI analogue of the cgs polarizability. Analogously, y = -y/47re0 (or y = y/eo) can be used as the third-order hyperpolarizability in the SI system, with y having the units of m5 V 3. The presence or absence of the factor of An in the definition of the hyperpolarizability is, unfortunately, not always obvious in literature data. 

The structure/property relationships that govern third-order NLO polarization are not well understood. Like second-order effects, third-order effects seem to scale with the linear polarizability. As a result, most research to date has been on highly polarizable molecules and materials such as polyacetylene, polythiophene and various semiconductors. To optimize third- order NLO response, a quartic, anharmonic term must be introduced into the electronic potential of the material. However, an understanding of the relationship between chemical structure and quartic anharmonicity must also be developed. Tutorials by P. Prasad and D. Eaton discuss some of the issues relating to third-order NLO materials. 

The search of third-order materials should not just be limited to conjugated structures. But only with an improved microscopic understanding of optical nonlinearities, can the scope, in any useful way, be broadened to include other classes of molecular materials. Incorporation of polarizable heavy atoms may be a viable route to increase Y. A suitable example is iodoform (CHI ) which has no ir-electron but has a value (3J ) comparable to" that of bithiophene... 

To conclude this article, it is hoped that the discussion of relevant issues and opportunities for chemists presented here will sufficiently stimulate the interest of the chemical community. Their active participation is vital for building our understanding of optical nonlinearities in molecular systems as well as for the development of useful nonlinear optical materials. It is the time now to search for new avenues other than conjugation effects to enhance third-order optical nonlinearities. Therefore, we should broaden the scope of molecular materials to incorporate inorganic and organometallic structures, especially those involving highly polarizable atoms. 

Out of the large range of possible nonlinear optical effects, chemists are likely to encounter only a limited number of measurement techniques. These include both second- and third-order NLO characterization methods. A brief listing of the different types of measurements, the nonlinear susceptibility involved and the related molecular nonlinear polarizabilities is given here. 

In the limit of the oriented gas model with a one-dimensional dipolar molecule and a two state model for the polarizability (30). the second order susceptibility X33(2) of a polymer film poled with field E is given by Equation 4 where N/V is the number density of dye molecules, the fs are the appropriate local field factors, i is the dipole moment, p is the molecular second order hyperpolarizability, and L3 is the third-order Langevin function describing the electric field induced polar order at poling temperature Tp - Tg. 

The data in Table 1 reveal systematic variations in the measured third order susceptibilities of these phthalocyanines with the metal. There is a monotonic variation of y in the series Co, Ni, Cu, Zn. The nonlinear susceptibility decreases as the d orbitals of the metal become filled. There is also a qualitative correlation between a large hyperpolarizibility and the presence of a weak, near IR transition. However, the variation of the figure of merit, x(3)/ , shows that the correlation between y and the absorption coefficient is not linear. No clear trend is seen in the triad Ni, Pd, Pt although PtPcCP4 does have a larger hyperpolarizibility as might be expected for a larger, more polarizable metal ion. 

In summary, it appears that poly silanes and polygermanes have large third order nonlinear susceptibilities, particularly for materials containing only a saturated sigma bonded polymer backbone. This is consistent with their large polarizabilities and the extensive sigma delocalization along the backbone. In some instances, the... 

As expected, the third order susceptibilities vary significantly with polymer orientation. It seems unlikely however that this feature alone will ever increase the values by more than an order of magnitude and further significant improvements will probably require more highly polarizable substituents, the introduction of... 

In the studies discussed thus far, the potential has been maintained at the PZC in order to minimize the additional dc electric field contribution to the polarizability which can arise through the third order polarizability x(3) [24, 126] where... 

---