Nonlinear optical properties coefficients

The nonlinear optical properties of thin films of the polymers were investigated through measurement of second-harmonic generation, and exhibit second-harmonic coefficients, d33, in the range 4.1-34 pm/V. 

Nonlinear optical properties depend upon the molecular environment as well as the individual molecular prop erties. In particular, at the molecular level, second harmonic generation depends upon the magnitude of p (the quadratic hyperpolarizability), which is the coefficient... 

As the local electric field in the particles is enhanced at the SPR, the metal nonlinear optical response can be amplified as compared to the bulk solid one. Moreover, the intrinsic nonlinear properties of metals may themselves be modified by effects linked with electronic confinement. These interesting features have led an increasing number of people to devote their research to the study of nonlinear optical properties of nanocomposite media for about two decades. Tire third-order nonlinear response known as optical Kerr effect have been particularly investigated, both theoretically and experimentally. It results in the linear variation of both the refraction index and the absorption coefficient as a function of light intensity. These effects are usually measured by techniques employing pulsed lasers. 

The finite field method is the simplest method for obtaining nonlinear optical properties of molecules. This method was first used by Cohen and Roothaan to calculate atomic polarizabilities at the Hartree-Foclc level. The basic idea is to truncate the expansion of the energy (Eq. [6]) and solve for the desired coefficients by numerical differentiation. For example, if the expression is truncated after the quadratic term, the result is E(P) = E[0) — — iot yF,Fy. 

Ferroelectric lithium niobate (LiNbOs) has been of considerable interest because of its nonlinear optical properties. Conversion of infrared into visible radiation in LiNb03 crystals has been observed (Midwinter and Warner, 1967 Arutyunyan and Mkrtchyan, 1975). Electro-optic coefficients of LiNbOs have been determined for a wide range of frequencies ranging from the visible (Smakula and Claspy, 1967) to the millimeter-wave portion of the spectrum (Vinogradov et al., 1970). Other nonlinear optical properties such as photovoltaic effects (Kratzig and Kurz, 1977) and optically induced refractive index changes (Ashkin et al., 1966 Chen, 1969) have also been observed. 

When a high-intensity laser beam impinges on material, its electromagnetic field induces electrical polarization that gives rise to a variety of nonlinear optical properties, because in this case the higher terms in Eq. (3-4) are not negligible. The determination of the coefficients and that serve to characterize the nonlinear properties is complicated by the fact that they are composed of many elements. With a being equal to two and three, and are composed of 3 = 27 and 81 elements, respectively. Fortunately, these tensors possess symmetry properties that can be invoked to reduce the number of independent elements, for instance, when the optical frequencies involved in the nonhnear interaction are far away from resonance (absorption) [15]. 

Nonlinear optical properties. The optical nonlinearity was characterized by two experiments second harmonic generation (SHG) and electro-optic measurements. All of the results are listed in Table n. The second harmonic generation (SHG) for the poled polyimides was conducted to determine the second harmonic generation coefficients (das). PI 1 possessed the highest value of SHG... 

Increased absorption coefficient and nonlinear optical properties... 

Cross-linked polymeric liquid crystals offer a wide variety of unique and in-tere.sting properties. Because of the interaction between the mesogens and the network backbone in liquid crystal elastomers, mechanical deformations can align the director, and these materials are piezoelectric. Industrial applications of liquid crystalline thermosets are driven by additional properties such as toughness, a tunable coefficient of thermal expansion, ferroelectricity, and nonlinear optical properties. Reviews on this topic are given by Barclay and Ober [4] and by Warner and Terentjev [5]. 

Third-order nonlinear optical properties (namely, quadratic electrooptic coefficient) of this polymeric system at different dye concentrations have been measured using a modified Michelson interferometer at 633nm. For this measurement, the polymer film was spin-coated from the filtered solution on an indium-tin-oxide (FTO) coated glass plate where the ITO layer was used as an electrode. A gold layer of 500A thickness was thermally evaporated onto the polymer film to form the second electrode. The experimental set-up of this modified Michelson interferometer is schematically shown in (Figure 7). 

Fig. 3.11 (A) Single-photon interference in a Mach-Zender interferometer with equal arms. BSl and BS2 are beam-splitters with coefficients Ct and for transmission and reflectirai, respectively (ICrl = Cr = 1/2) Ml and M2 are mirrors (100% reflecting) and D and D2 are photoncounting detectors. The dependence of photon wavefunction If on time and the distance along the optical path is not indicated explicitly. If BS2 is removed, or if either path is blocked before BS2, photons are detected at D1 and D2 with equal probability but when BS2 is presem and both paths are open, photons are detected only at Dl. (B) Two-photon quantum interference. Short pulses of light with frequency v are focused into a crystal with nonlinear optical properties (XTL). This...

Perry, J. W., Marder, S. R., Perry, K. J., Sleva, E. T., Yakymyshyn, C., Stewart, K. R., and Boden, E. P., Organic salts with large electro-optic coefficients, in Nonlinear Optical Properties of Organic Materials IV (Proc. SPIE, 1560), Singer, K. D., Ed., SPIE, Bellingham, 1991, 302. 

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... 

Nonlinear Optical Properties 235 Table 3.15 Two-photon absorption coefficients for a variety of materials. 

A novel photocrosslinkable polymeric system has been developed for processing into films having stable second-order nonlinear optical properties. In the present system, polymers bearing photocrosslinkable chromophores, such as polyvinylcinnamate, are reacted with appropriately designed nonlinear optical molecules with the cinnamate or other photocrosslinkable functionalities for photocrosslinking at one, two or more points. The system can be poled and photocrosslinked in the poled state to yield a material with stable optical nonlinearity and large electro-optic coefficients. 

The semiconducting properties of the compounds of the SbSI type (see Table XXVIII) were predicted by Mooser and Pearson in 1958 228). They were first confirmed for SbSI, for which photoconductivity was found in 1960 243). The breakthrough was the observation of fer-roelectricity in this material 117) and other SbSI type compounds 244 see Table XXIX), in addition to phase transitions 184), nonlinear optical behavior 156), piezoelectric behavior 44), and electromechanical 183) and other properties. These photoconductors exhibit abnormally large temperature-coefficients for their band gaps they are strongly piezoelectric. Some are ferroelectric (see Table XXIX). They have anomalous electrooptic and optomechanical properties, namely, elongation or contraction under illumination. As already mentioned, these fields cannot be treated in any detail in this review for those interested in ferroelectricity, review articles 224, 352) are mentioned. The heat capacity of SbSI has been measured from - 180 to -l- 40°C and, from these data, the excess entropy of the ferro-paraelectric transition... 

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... 

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