Third-order nonlinearity

This is a nonlinear third-order system that has no known analytic solution. However, it can be solved readily by numerical techniques. 

Figure 2 The double-sided Feynman diagrams, which have to be considered in (a) a linear absorption experiment and (b) a nonlinear third-order experiment such as photon echo, pump-probe, transient grating. The diagrams are arranged according to the possible time orderings, as discussed in the text and illustrated in Fig. 4.

Recently, other attempts have been reported by Dai et al. (439) using the complexes 31 (Scheme 26). These authors admit that the efficiency of their materials needs to be improved by optimizing the balance between absorption and nonlinearity. Third-order NLO properties of M(dmit)2 and M(mnt)2 complexes with sandwiched organometallic cations [CpFe(r -C6H6)]+ have also been reported very recently (440). 

In esu units (see Chapter 10), the corresponding nonlinear third-order susceptibility... 

Ever since this technique was introduced by Sheik-Bahae a al, it has been extensively used for the study of third-order nonlinearity in solutions. a typical Z-scan measurement setup is shown in Figure 28. For a constant intensity, the sample could be moved along the z-axis to record the position-dependent variation in nonlinear phenomena. This technique is particularly useful in cases where nonlinear refraction is accompanied by TPA. Nonlinear refractive index (n2) is studied with a closed aperture or normalized aperture Z-scan technique. The TPA coefficient can be obtained through an open aperture Z-scan measurement. The effects arising out of both the real and imaginary parts of the nonlinear third-order susceptibility show up. Thus, for the measurement of ri2, two merit factors W and T are defined to account for the one-photon and two-photon absorptions, respectively ... 

Solution of nonlinear third order BV problem by two methods require "odebv" require"odefd" getfenv(odefd).nprint 1 getfenv(odefd).umin l.e 3,l.e 3 ... 

Joo T, Jia Y, Yu J-Y, Lang M J and Fleming G R 1996 Third-order nonlinear time domain probes of solvation dynamics J. Chem. Phys. 104 6089... 

All nonlinear (electric field) spectroscopies are to be found in all temis of equation (B 1.3.1) except for the first. The latter exclusively accounts for the standard linear spectroscopies—one-photon absorption and emission (Class I) and linear dispersion (Class II). For example, the temi at third order contains by far the majority of the modem Raman spectroscopies (table B 1.3.1 and tableBl.3.2). 

Nonlinear refraction phenomena, involving high iatensity femtosecond pulses of light traveling in a rod of Tfsapphire, represent one of the most important commercial exploitations of third-order optical nonlinearity. This is the realization of mode-locking ia femtosecond Tfsapphire lasers (qv). High intensity femtosecond pulses are focused on an output port by the third-order Kerr effect while the lower intensity continuous wave (CW) beam remains unfocused and thus is not effectively coupled out of the laser. 

In an effort to identify materials appropriate for the appHcation of third-order optical nonlinearity, several figures of merit (EOM) have been defined (1—r5,r51—r53). Parallel all-optical (Kerr effect) switching and processing involve the focusing of many images onto a nonlinear slab where the transmissive... 

LB films of CO-tricosenoic acid, CH2=CH—(CH2)2qCOOH, have been studied as electron photoresists (26—28). A resolution better than 50 nm could be achieved. Diacetylenic fatty acids have been polymerized to yield the corresponding poly (diacetylene) derivatives that have interesting third-order nonlinear optical properties (29). 

The cadmium chalcogenide semiconductors (qv) have found numerous appHcations ranging from rectifiers to photoconductive detectors in smoke alarms. Many Cd compounds, eg, sulfide, tungstate, selenide, teUuride, and oxide, are used as phosphors in luminescent screens and scintiUation counters. Glass colored with cadmium sulfoselenides is used as a color filter in spectroscopy and has recently attracted attention as a third-order, nonlinear optical switching material (see Nonlinear optical materials). DiaLkylcadmium compounds are polymerization catalysts for production of poly(vinyl chloride) (PVC), poly(vinyl acetate) (PVA), and poly(methyl methacrylate) (PMMA). Mixed with TiCl, they catalyze the polymerization of ethylene and propylene. 

Optical properties of cyanines can be usefiil for both chiral substituents/environments and also third-order nonlinear optical properties in polymer films. Methine-chain substituted die arbo cyanines have been prepared from a chiral dialdehyde (S)-(+)-2-j -butylmalonaldehyde [127473-57-8] (79), where the chiral properties are introduced via the chiral j -butyl group on the central methine carbon of the pentamethine (die arbo cyanine) chromophore. For a nonchiral oxadicarbocyanine, the dimeric aggregate form of the dye shows circular dichroism when trapped in y-cyclodextrin (80). Attempts to prepare polymers with carbocyanine repeat units (linked by flexible chains) gave oligomers with only two or three repeat units (81). However, these materials... 

The measured relationships between piezoelectric polarization and strain for x-cut quartz and z-cut lithium niobate are found to be well fit by a quadratic relation as shown in Fig. 4.4. In both materials a significant nonlinear piezoelectric effect is indicated. The effect in lithium niobate is particularly notable because the measurements are limited to much smaller strains than those to which quartz can be subjected. The quadratic polynomial fits are used to determine the second- and third-order piezoelectric constants and are summarized in Table 4.1. Elastic constants determined in these investigations were shown in Chap. 2. 

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

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. 

Rao reported measurement of third-order optical non-linearity in the nanosecond and picosecond domains for phosphorus tetratolyl porphyrins bearing two hydroxyl groups in apical position [89]. Strong nonlinear absorption was found at both 532 nm and 600 nm. The high value of nonlinearity for nanosecond pulses is attributed to higher exited singlet and triplet states. Time resolved studies indicate an ultra-fast temporal evolution of the nonlinearity in this compound. 

The physical properties of the expanded radialenes were greatly enhanced upon donor functionalization, leading to the stable derivatives 76-78 with fully planar conjugated rr-chromophores [110]. These compounds exhibit large third-order nonlinear optical coefficients, can be reversibly reduced or oxidized, and... 

Fig. 8. Examples of some of the donor-acceptor substituted TEEs prepared for the exploration of structure-property relationships in the second- and third-order nonlinear optical effects of fully two-dimensionally-conjugated chromophores. For all compounds, the second hyperpolarizability y [10 esu], measured by third harmonic generation experiments in CHCI3 solution at a laser frequency of either A = 1.9 or 2.1 (second value if shown) pm is given in parentheses. n.o. not obtained...

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