Hyperpolarizability imaginary part

Only little has been reported on second-order hyperpolarizabilities yin two-di-mensionally conjugated molecules. Planar systems as e.g. phthalocyanines have been studied for two photon absorption which is proportional to the imaginary part of the nonlinearity y. For planar molecules with a three-fold symmetry, the importance of charge transfer from the periphery to the center of the molecule in order to realize large nonlinearities ywas reported [65]. Off-resonant DFWM experiments revealed promising third-order nonlinearities in two-dimensional phenylethynyl substituted benzene derivatives [66]. Recently, the advantage of two-dimensional conjugation to increase the values of the first-order hyperpolarizability p has also been pointed out [67-69]. 

In general, and for the nonlinear hyperpolarizabilities to be derived below, one introduces r, for the transition between states w) and ). In effect the imaginary term iT o/2 takes the place of ie in Eq. (42). The linear absorption spectrum, which corresponds to the imaginary part of Eq. (45), will be built from smeared out Dirac delta functions of Lorentzian shape, i.e. the frequency-integrated absorption will remain constant regardless of the value of the lifetime broadening. The real part of the polarizability is related to the refractive index n of the sample... 

The aim of the present contribution is to review computational techniques based on the SOS formalism. We shall focus on electronic contributions to fu-st- (jS) and second-order (y) hyperpolarizabilities. With the exception of the imaginary part of y, the non-resonant properties shall be discussed. Some attention will be given to the so-called few-states models, as being very useful "by-product of the SOS formalism. 

In the present contribution the discussion of the NLO response is restricted to off-resonant case. The only exception is the purely resonant quantity, namely imaginary part of second-order hyperpolarizability in the resonant regime (Im-y(-tt> tu, —w, w)). This quantity describes the process of simultaneous absorption of two quanta. The two-photon absorption (TPA) process is much better understood than the three-photon absorption. The basic quantity associated with the two-photon absorption process is the two-photon absorption tensor (S ). In the most general case referring to two different photons (different polarizations and different energies is given by [75, 81] ... 

Alternatively, the TPA cross section can also be shown to be proportional to the imaginary part of the averaged second-order hyperpolarizability . defined at the absorption frequency of )(8jy oc u>, -a), to)). It has been shown... 

However, the effect of the second contribution in Eq. (103), corresponding to the imaginary parts of the hyperpolarizabilities and due to damping effects, will be to obviate complete cancellation of the harmonic signal at this time—only by a... 

The real and imaginary parts of third-order non-linear optical susceptibilities of 10 M solutions of Fe2(CO)6 (/t3-E3P) CpCr(GO)2 (E = S or Se) and the well-known precursor clusters Fe3(CO)9(/i3-E)2 in toluene were measured using Z-scan and ARINS techniques, respectively. The mixed metal clusters display nearly three times the second molar hyperpolarizability values of the corresponding Fes precursors. The results suggest a rich potential of mixed metal, mixed non-metal class of clusters as materials exhibiting large non-linearity. 

The imaginary part of the third-order hyperpolarizability (y) was measured for a series of platinum poly-ynes in both solution and thin-film form, and for a group of related platinum-organic species. 

Transition metal poly-ynes have large third-order optical susceptibilities (X ) which consist of contributions from the real and imaginary parts of the third-order hyperpolarizabilities (y and y", respectively). In previous studies, various optical measurements were used to determine the nonlinear hyper-polarizabilities of the polymers.Most recently, an extensive study of the structural dependence of the hyperpolarizabilities of the platinum and palladium... 

Although the contribution in Eq. 2.172 dominates in the vicinity of a resonance, the CARS signal also has contributions from the nonresonant part of the second hyperpolarizability tensor, both electronic and vibrational, and we will denote these contributions as jg. Denoting furthermore the real and imaginary parts of the tensor in Eq. 2.172 as and y(, respectively we can write our final expression for the CARS signal as... 

We measured the third harmonic generation (THG) of la-e using polystyrene matrices and variable laser wavelengths [136]. In order to understand the influence of the chain length on nonlinear optical properties, it is better to discuss the second hyperpolarizability y, which is a molecular parameter, than the macroscopic susceptibility which is a bulk quantity. For the determination of j/jesj, the imaginary part of the total third-order susceptibility j/res j of the films (thickness 50 and 212 nm) was taken. The result is depicted in Fig. 11.13 [136] in a double logarithmic plot of jy gs] versus the length L of the OPE chains I is a linear function of the number n of repeat units. (See Section 11.1.)... 

Formally, at a microscopic level, the two-photon absorption process can be described by the imaginary part of second hyperpolarizability, y(-co co, -ro, ro), charaeterizing the interaction of the molecule with an optical field of high intensity at a frequency co. As it was already mentioned in the introduction, the most frequently used parameter quantifying the two-photon absorption of the atomic or molecular system is the 2PA cross-section ( 2pa)> usually presented in the GM units (1 GM = 10-50 cm s photon ). Referring to the semi-classical approximation for the degenerate 2PA process, C2PA can be defined as fol-... 

Figure 9. Variation of the real (m) and imaginary (o) parts of the two photon hyperpolarizability (yr) with two-photon energy (2aJt) for the yellow solution. The error bars represent 90% confidence limits. All data are taken in a 1111 geometry (all beams polarized ). The solid lines are theoretical fts to the data according to Equation 3. (Reproduced with permission from Ref. 24. Copyright 1979, American Institute of...

---