Quadratic NLO properties

On account of their particularly extensive delocalized 7r-systems, MPs have received comparatively more attention for their cubic, as opposed to quadratic, NLO properties. From the viewpoint of practical applications, such complexes (and also metallophthalocyanines and other closely related compounds) are of major interest for OL due to their tendency to exhibit RSA behavior. These materials are particularly well suited in this regard because they often exhibit strongly absorbing, long-lived triplet excited states as well as reasonably wide transparency windows over the visible region of interest between the intense B- and Q-bands. 

Several reports have also considered the quadratic NLO properties of DT complexes.458-461 Chen et al. have used NIR absorption data and SC A//12 values to estimate f30 according to the TSM for various Ni11 or Pt11 mixed a-diimine/DT complexes,458,459 and also for several asymmetrically substituted bis(DT)s (e.g., (175) and (176)).460 Dipole analyses indicate that the NIR transition in (175) is primarily LLCT in nature, whereas that of (176) has only limited CT character.460 The complex (177) has a red-shifted LLCT absorption and a considerably larger fa value than (175).461 The // 2 for the NIR band of (177) is also somewhat larger than that of (175), but the two complexes have very similar A//12 values.461... 

The observation of SHG from a molecule deprived of vectorial features, opens new perspectives in molecular engineering towards quadratic NLO properties. Non-dipolar non-centrosymmetric molecular moieties could serve as building block for novel types of NLO materials in which the organization is not influenced by dipole-dipole interactions. 

The quadratic NLO properties of aliphatic polyesters and p-NA systems have also been investigated [84]. Both polyesters, as well as p-NA, belong to the centrosymmetric space groups hence, they individually are not SHG active. When p-NA is mixed with polyesters, the composites attain a non-... 

Numerous compounds of the types (L)AuC=CR and Q+[Au(C=C-R)2] were investigated for their properties as NLO materials. Some of the examples were found to have the largest cubic optical non-linearity for monomeric organometallics.103 Examples are given in Scheme 18. For all of these compounds, the quadratic/cubic hyperpolarizability (linear optical and quadratic NLO response) have been determined. The studies were complemented by cyclovoltammetric measurements.58,59,103,112-117... 

The ab initio calculation of NLO properties has been a topic of research for about three decades. In particular, response theory has been used in combination with a number of electronic structure methods to derive so-called response functions [41 8], The latter describe the response of a molecular system for the specific perturbation operators and associated frequencies that characterize a particular experiment. For example, molecular hyperpolarizabilities can be calculated from the quadratic and cubic response functions using electric dipole operators. From the frequency-dependent response functions one can also determine expressions for various transition properties (e.g. for multi-photon absorption processes) and properties of excited states [42]. 

Quadratic terms in die property expansions are considered to be first-order in electrical anharmonicity, cubic terms are taken to be second-order, etc. Similarly, cubic terms in the vibrational potential are considered to be first-order in mechanical anharmonicity, quartic terms are second-order, and so forth. The notation (n, m) is used hereafter for the order of electrical (n) and mechanical (m) anharmonicity whereas the total order (n -I- m) is denoted by I, II,. Although our definition of orders is reasonable other choices are possible. Two key questions are (1) How important are anharmonicity contributions to vibrational NLO properties and (2) What is the convergence behavior of the double perturbation series in electrical and mechanical anharmonicity Both questions will be addressed later. Here we note that compact expressions, complete through order II in electrical plus mechanical anharmonicity, have been presented [19]. The formulas of order I contain either cubic force constants or second derivatives of the electrical properties with respect to the normal coordinates. Depending upon the level of calculation at least one order of numerical differentiation is ordinarily required to determine these anharmonicity parameters. For electrical properties, the additional normal coordinate derivative may be replaced by an electric field derivative using relations such as d p./dQidQj = —d E/dldAj.ACd, = —dk,/rjF where F is the field and k j is... 

Particularly notable reports from McDonagh et al. describe the molecular quadratic and cubic NLO properties of the 3-fold symmetric octupolar Ru" complexes 43 and 44 [104, 105]. According to the results of 1064nm HRS experiments, moving from the dipolar complex 45 to its octupolar analogue 44 produces... 

The NLO properties of organometallic and coordination complexes are also rich (21, 184, 279-296). Metal-alkyne complexes were first reported 1960 (297) and have recently attracted significant interest because of their potential in materials applications (2, 298). Studies of these types (299) have resulted in the development of structure-NLO response relationships for quadratic optical nonlinearities (p-value), which increase with valence electron count and ease of oxidation of metal. The amplitude is also tunable by ancillary ligand modification and substitution. Select small alkynyl complexes have been shown to exhibit p values at 1064 nm > 2600 x 10 ° esu (299). 

Polymers show interesting properties and can be used in optics and optoelectronics3.4.5. Specially oriented polymers can exhibit optical nonlinear properties and can be used for optical processing purposes. For quadratic NLO polymers the potential applications are mainly fi uency doubling leading to a blue source for optical recording and an electrooptical modulator for optical communications. 

The second-order NLO properties are of interest for a variety of NLO processes [1-3]. One of the most relevant is the SHG, originated by the mixing of three waves two incident waves with frequency co interact with the molecule or the bulk material with NLO properties, defined by a given value of the quadratic hyperpolarizability, fi, or of the second-order electrical susceptibility, respectively, to produce a new electrical wave, named SH, of frequency 2co. Another important second-order NLO process is the electrooptic Pockels effect which requires the presence of an external d.c. electric field, E(0), in addition to the optical E co) electrical field. This effect produces a change in the refractive index of a material proportional to the applied electric field, and can be exploited in devices such as optical switches and modulators [1-3]. 

Recently, the second-order NLO properties of new lanthanide complexes of the type [Ln(N03)3-L] (Ln = La, Gd, Dy, Yb, Y 19), where L is a rather rigid ter-pyridine-like ligand, have been determined by HRS, working with a nonresonant incident wavelength of 1.907 pm. The value of the quadratic hyperpolarizability Si,9i(HRS) increases by increasing the number of/-electrons, from 186 to 288 x 10 ° esu [95]. The dependence of the second-order NLO response on the nature of the lanthanide metal center suggests that/-electrons may contribute to the second-order NLO response [95]. 

The zeroth-order approximation in the BK perturbation treatment of pure vibrational NLO is the double harmonic model. As far as electrical properties are concerned this approximation includes just the terms in the instantaneous property expression that are linear in the normal coordinates (there is no vibrational contribution from the constant term). To these are added the quadratic terms in the pure vibrational (or mechanical) potential which constitute the usual harmonic approximation. Then, in zeroth-order roughly half of the square brackets vanish leaving ... 

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