Nonlinear materials characterization

Much of the work presented in this chapter represents a synergistic effort from several complementary research fields quantum-chemical theory, chemical synthesis, and nonlinear optical materials characterization. This combination of expertise... 

In this paper it has been attempted to provide an introductory overview of some of the various nonlinear optical characterization techniques that chemists are likely to encounter in studies of bulk materials and molecular structure-property relationships. It has also been attempted to provide a relatively more detailed coverage on one topic to provide some insight into the connection between the macroscopic quantities measured and the nonlinear polarization of molecules. It is hoped that chemists will find this tutorial useful in their efforts to conduct fruitful research on nonlinear optical materials. 

We have presented a review of the salient features of nonlinear integrated optics. It appears that nonlinear organic materials can play an important role in second- and third-order guided-wave devices. This field requires a great deal of material characterization and processing, however, before significant advances are realized. 

On the route to all-optical signal processing the development of materials with large third-order nonlinear optical effects is of decisive importance. For the material characterization and the assessment of its usefulness for applications the absolute value of the third-order nonlinear optical susceptibility y has to be known. Since most measurements are performed relative to a reference material, the establishment of a well accepted value for a standard material is important. 

The most widely employed material characterization techniques in third-order nonlinear optics are third-harmonic generation (THG) [21], degenerate four wave-mixing (DFWM) [22], Z-scan [6], and optical limiting by direct two-photon absorption (TPA) and fluorescence spectroscopy induced by TPA [23]. All of them will be discussed in the following. Further measurement techniques such as electric-field induced second-harmonic generation (EFISH) [24], optical Kerr... 

Similar methods have been used to prepare CdS NCs in optical quality borosilicate glasses." Nonlinear optical characterization of one composite sample with particle sizes ranging from 2.5-5.5nm yielded a range for of 10 -10 esu. Optical gain measurements of a similar material afforded a value of 33 cm at room temperature. At 11 K, maximum gain values reached 200 cm , and like the optical nonlinearities, these values were also dependent on NC concentration. ... 

However, the figure of merit presented in Eq. (78) is not useful in characterizing third-order nonlinear materials because it is not dimensionless and it does not separate between linear and nonlinear absorption. More appropriate dimensionless figures of merit have been proposed by Stegeman [55, 56],... 

While, in principle, the second-order response should have a higher strength than the third-order response, a strong geometrical condition (noncentrosymmetry at the atomic/molecular and at the bulk levels) limits the availability of second-order nonlinear materials. Experimentally, one has to ensure that a noncentrosymmetric configuration is used if one desires to measure the strength of the second-order nonlinear response, characterized by... 

The measurement of third-order nonlinear response, characterized by is simplified because no geometrical condition in the material is required. The intensity-dependent refractive index, a unique feature of the third-order nonlinear response, allows to characterize by smdying the change in the refractive index of the nonlinear material. This effect is exploited in numerous technical applications, and results in different experimental techniques that determine x - However, the absence of a geometrical condition in the material results in an extra complication when measurements are performed, since all materials (cell walls, glass, air,...) contribute to ... 

The Micnaelis-Menten equation and other similar nonlinear expressions characterize immobilized enzyme kinetics. Therefore, for a spherical porous carrier particle with enzyme molecules immobilized on its external as well as internal surfaces, material balance of the substrate will result in the following ... 

Because of their large optical nonlinearities and good mechanical, chemical, thermal, and optical stability, organic nonlinear materials are among the leading practical materials for device applications [2]. A number of experimental techniques have been proposed to obtain information about the dispersion, the sign, and the contributions of both the real and imaginary parts of the nonlinear optical response. In this chapter, we will explore the methods most widely used to characterize the third-order nonlinear coefficient and introduce some of the more recent results. 

The electro-optic phenomenon, as the name implies, involves the interaction of electrical (DC-200 GHz frequency) and optical (2-4 X lO Hz frequency) fields within a material characterized by large hyperpolarizability (molecular second-order optical nonlinearity). Applications of this phenomenon focus on either the transduction of electrical signals into optical signals (e.g., as in the transduction of television signals onto fiber optic transmissions as in the community antenna television (CATV) industry) or the switching of an optical signal (e.g., as effected in local nodes of a local area network, LAN) between different transmission lines. 

The J-integral is proposed as a fracture criterion for materials characterized by nonlinear stress-strain relations and its critical value denoted corresponds to rapid crack propagation. 

SHG is certainly one of the most direct techniques able to characterize NLO properties of second order materials. By using polarized radiation incident on a nonlinear material, being the direction 3 the optical axis of the nonlinear material with reference to Fig. 3.3, it can be shown that SH intensity for the two polarizations (S and P) is given by [23] ... 

Yost, W.T. and Cantrell, J.H., Material characterization using acoustic nonlinearity parameters and harmonic generation engineering materials. Rev. Prog. QNDE, 13B, 1669-1676 (1990). 

A wide variety of techniques have been employed for the characterization of thin film samples of nonlinear polymeric materials. Many of these are similar to techniques described in the previous section for bulk material characterization, and are employed with thin film samples both to assess differences in material properties in the two physical forms and because certain measurements such as absorption or electro-optic effects may be more easily made in thin film samples. Other techniques are specific to thin film samples in which light can be guided, for which parameters can be measured having no bulk equivalent, such as waveguide scatter or nonlinear mode coupling. 

The geometric and material nonlinear phenomena characterizing structures near collapse are very complicated in nature and require, in most cases, highly sophisticated numerical tools for their simulation. A common feature of most nonlinear analysis algorithms is that the load is applied in successive steps and iterations are performed within each step to achieve convergence (Stricklin et al. 1973). 

In using nonlinear mechanical models, in addition to utilizing nonlinear elastic and shear thickening or thinning dashpot elements, a perturbation technique can also be used to incorporate nonlinear behavior. This is accomplished by adding small perturbation terms which are functions of the current level of elastic strain and strain rate to the elastic and viscous coefficients, respectively. This method was originally proposed by Davis (1964) and later applied by Renieri et al. (1976) in material characterization of bulk adhesives. 

We have heretofore had ample discussion of linear optical properties of ZnO and related materials. In this section, the nonlinear processes in ZnO are discussed, a topic that has been investigated in some detail. The research on nonlinear optical properties of semiconductors is motivated by electro-optic devices that can be used in telecommunications and optical computing as efficient harmonic generators, optical mixers, and tunable parametric oscillators, among others. The nonlinear optical properties such as second harmonic generation (SHG), that is, (2(0i, 2(02), and the sum frequency generation (SFG), that is, (materials characterization, particularly surfaces, because the second-order susceptibility coefficient is very sensitive to the change in symmetry (178,179). The crystal should be... 

E. W. Van Stryland and M. Sheik-Bahae in Characterization Tecliniqnes and Tabulations for Oi anic Nonlinear Materials, M. G. Kuzyk and C. W. Dirk, Eds., MarcelDetdcer, Inc., New York, 1998,... 

The polarization P is given in tenns of E by the constitutive relation of the material. For the present discussion, we assume that the polarization P r) depends only on the field E evaluated at the same position r. This is the so-called dipole approximation. In later discussions, however, we will consider, in some specific cases, the contribution of a polarization that has a non-local spatial dependence on the optical field. Once we have augmented the system of equation B 1.5.16. equation B 1.5.17. equation B 1.5.18. equation B 1.5.19 and equation B 1.5.20 with the constitutive relation for the dependence of Pon E, we may solve for the radiation fields. This relation is generally characterized tlirough the use of linear and nonlinear susceptibility tensors, the subject to which we now turn. 

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