Nonlinear third-order effect

Since semiconductor materials appear to be general candidates for third order effects, it is not surprising that photoconductive charge transfer complexes such as poly(vinyl carbazole)-trinitrofluorenone (PVK-TNF) would exhibit modest DFWM.(142) The observed nonlinearity at 602 nm, a wavelength absorbed by the CT complex, ranges from 0.2 - 2 x 10"11 esu, increasing as the molar fraction of TNF in the complex, PVK TNF, increased. Charge... 

The fundamental component (aE) is linear in E and represents the linear optical properties discussed above. The second (jfiE-E) third ( yE-E-E) and subsequent harmonic terms are nonlinear in E and give rise to NTO effects. The / and values are referred to, respectively, as the first and second hyperpolarisabilities. The second harmonic term gives rise to second harmonic generation (SHG), the third results in frequency tripling effects, and so on. Importantly, since only the time-averaged asymmetrically induced polarisation leads to second-order NLO effects, the molecule and crystal must be non-centrosymmetric, otherwise the effects will cancel one another. Third-order effects, however, may be observed in both centrosymmetric and non-centrosymmetric materials. 

Before we examine how second- and third-order N LO effects are related to nonlinear polarization, we briefly examine an important symmetry restriction on second-order NLO properties. From Eq. (5), we can see that P(E) = P(0) + xmE + x E2 + x i)E3+... and P -E) = P(0) - x 1)E + xp)E2 - x Eh... we can also see from Fig. 11.1 that P(E) + P(-E) if%(2) + 0. In a centra symmetric material, P(E) is necessarily equal to P(-E) and, therefore, P(0), and other even-order terms must be zero. Therefore, for second-order effects to be observed in a molecule or material, the molecule or material must be non-centrosymmetric. However, no such requirement applies to odd-order processes, such as third-order effects [Fig. 11.1 shows P(E) = P(-E) for a material with only linear and cubic susceptibilities non-zero]. 

The mechanism of the third-order three-body induction interactions is somewhat more complicated. It can be shown that one can distinguish three principal categories. The first mechanism is simply the interaction of permanent moments on the monomer C with the moments induced on B by the nonlinear (second-order) effect of the electrostatic potential of the monomer A plus contributions obtained... 

Thus, in both cases, the molecular unit can be tailored to meet a specific requirement. A second crucial step in engineering a molecular structure for nonlinear applications is to optimize the crystal structure. For second-order effects, a noncentrosymmetrical geometry is essential. Anisotropic features, such as parallel conjugated chains, are also useful for third-order effects. An important factor in the optimization process is to shape the material for a specific device so as to enhance the nonlinear efficiency of a given structure. A thin-film geometry is normally preferred because nonlinear interactions, linear filtering, and transmission functions can be integrated into one precise monolithic structure. 

This work provides a relatively comprehensive review of studies involving ruthenium coordination and organometallic complexes as nonlinear optical (NLO) compounds/materials, including both quadratic (second-order) and cubic (third-order) effects, as well as dipolar and octupolar chromophores. Such complexes can display very large molecular NLO responses, as characterised by hyperpolarizabilities, and bulk effects such as second harmonic generation have also been observed in some instances. The great diversity of ruthenium chemistry provides an unparalleled variety of chromophoric structures, and facile Ru" —> Ru" redox processes can allow reversible and very effective switching of both quadratic and cubic NLO effects... 

The importance of the hyperpolarizability and susceptibility values relates to the fact that, provided these values are sufficiently large, a material exposed to a high-intensity laser beam exhibits nonlinear optical (NLO) properties. Remarkably, the optical properties of the material are altered by the light itself, although neither physical nor chemical alterations remain after the light is switched off. The quahty of nonlinear optical effects is cmciaUy determined by symmetry parameters. With respect to the electric field dependence of the vector P given by Eq. (3-4), second- and third-order NLO processes may be discriminated, depending on whether or determines the process. The discrimination between second- and third-order effects stems from the fact that second-order NLO processes are forbidden in centrosymmetric materials, a restriction that does not hold for third-order NLO processes. In the case of centrosymmetric materials, x is equal to zero, and the nonhnear dependence of the vector P is solely determined by Consequently, third-order NLO processes can occur with all materials, whereas second-order optical nonlinearity requires non-centrosymmetric materials. 

Yang, X. and Xie, S. (1995) Expression of third-order effective nonlinear susceptibility for third-harmonic generation in crystals. Applied Optics, 34, 6130. 

AH the properties dealt with up until now involve linear interactions between light and polymer. Interaction of li t with polymers in the nonlinear region involves second- and third-order effects as well as the phenomenon of photo refrac-tivity (56,57). An optical nonlinear optical (NIX)) polymer is one that, in response to an externally applied electric field, can either vary the speed of incoming light or alter its fi uency. Var3dng the speed of light involves a change in the reflective index of the material. An optically nonlinear polymer has two components the polymer itself and an optically nonlinear molecule (chromophore), which is either chemically attached to the polymer or dissolved in it. 

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 ... 

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... 

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. 

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...

For the application of QDs to three-dimensional biological imaging, a large two-photon absorption cross section is required to avoid cell damage by light irradiation. For application to optoelectronics, QDs should have a large nonlinear refractive index as well as fast response. Two-photon absorption and the optical Kerr effect of QDs are third-order nonlinear optical effects, which can be evaluated from the third-order nonlinear susceptibility, or the nonlinear refractive index, y, and the nonlinear absorption coefficient, p. Experimentally, third-order nonlinear optical parameters have been examined by four-wave mixing and Z-scan experiments. 

Kuzyk MG, Dirk CW (1990) Effects of centrosymmetry on the nonresonant electronic third-order nonlinear optical susceptibility. Phys Rev A 41 5098-5109... 

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. 

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