Nonlinear properties

Nonlinear properties of normal dielectrics can be studied in the elastic regime by the method of shock compression in much the same way nonlinear piezoelectric properties have been studied. In the earlier analysis it was shown that the shape of the current pulse delivered to a short circuit by a shock-compressed piezoelectric disk was influenced by strain-induced changes in permittivity. When a normal dielectric disk is biased by an electric field and is subjected to shock compression, a current pulse is also delivered into an external circuit. In the short-circuit approximation, the amplitude of this current pulse provides a direct measure of the shock-induced change in permittivity of the dielectric. 

The Z-scan technique, first introduced in 1989 [64, 65], is a sensitive single-beam technique to determine the nonlinear absorption and nonlinear refraction of materials independently from their fluorescence properties. The simplicity of separating the real and imaginary parts of the nonlinearity, corresponding to nonlinear refraction and absorption processes, makes the Z-scan the most widely used technique to measure these nonlinear properties however, it does not automatically differentiate the physical processes leading to the nonlinear responses. 

The SHG active compounds found in Tables II-VIII are just a small fraction of the hundreds of substances we have screened by the powder technique. Of the active compounds only another small fraction will provide crystals of size and quality as is required for optical application. A program in crystal growth as thorough as the effort which has gone into synthesis must be instituted in order to take full advantage of these materials. Overall, it will suffice to say that the promising nonlinear properties observed from such a small fraction of all the possible organic compounds bodes very well for future endeavor. 

Braginsky, V. B., Gorodetsky, M. L., and Ilchenko, V. S., 1989, Quality-factor and nonlinear properties of optical whispering-gallery modes, Phys. Lett A 137(7-8) 393-397. 

J. Paul, C. Christopoulos, and D. W. P. Thomas, "Generalized Material Models in TLM -Part 3 Materials With Nonlinear Properties," IEEE Trans. Antennas Propagat. 50, 997-1004 (2002). 

We consider two examples of waveguide junctions (Fig.l) structure A. when both waveguides have the same width and refractive index profile but possess different nonlinear properties (for simplicity, we assume that input waveguide is linear), and structure B. when both waveguides have the same refractive index profile and nonlinearity but their widths are different. 

Thus we have recently proposed a novel approach in this field and have demonstrated essential advantages of the new type of sensors [21, 22], The new sensor concept is based on the unique nonlinear properties of point contacts which provide rich physical information in many research directions [23]. 

In one application (Maitre, 1981), the parallelism of noncoherent optical convolution methods is combined with video techniques in a totally analog application to images. Matsuoka et al (1982) have developed a hybrid optical-video-digital system based on similar principles. Pipeline processors that perform image convolution at high speed are ideal for digital applications. The inherent simplicity of the method adapts it to high-speed implementations by use of other hybrid techniques. It is even possible to devise a transversal filter that has all the desirable nonlinear properties of the method. We describe this filter in the next section. 

Chemla, D. S. Zyss, J. (eds) (1987) Nonlinear Properties of Organic Molecules and Crystals, Academic Press, New York. 

From the general discussion of the use of nonlinear properties to investigate dynamic phenomena it is clear that the field modulation techniques is but one example of a broader class of methods for the study of fast processes. A drawback, particular to electric field modulation, is the prohibitive heat dissipation in conducting systems. However, any forcing parameter imposing a conductance modulation could be used in principle as, for example, in the study of the dynamics of photoconductive phenomena. 

The third-order nonlinear properties are specified in different ways by different authors and several systems of units are used. The conversions between different systems are not always obvious, as the numerical values of the conversion factors may depend on the definitions of particular properties. Table I lists some of the more important conversion factors and units. It should be noted that conversion of n2 values to /3) values can be performed using Eq. (4) in SI units. A frequently utilized conversion is that between n2 values in SI units (cm2 W1) and in cgs units (esu), namely n2 = (C]y3))/n2, where Q is approximately 0.039.7 Calculation of y values can be performed using Eq. (3). Reference 7 provides a discussion of the pitfalls that arise when applying conversion procedures between nonlinear properties defined in different ways. 

It may thus be concluded that application of metal alkoxides for preparation of PZT-based thin films in many aspects may be nowadays considered to be a routine technique widely used in many laboratories. The research work is presently mostly focused on electrical and microstructural aspects of these films rather than on chemical routes of their preparation. Irrespective of the technique for the precursor preparation, when 10% excess of Pb is introduced (to prevent loss of lead due to the PbO volatility) the ferroelectric perovskite PZT films are obtained after annealing at about 700°C, demonstrating nonlinear properties of the level acceptable for most of the desired applications. Their typical microstructure is presented in Fig. 10.3. 

The new concepts of the nonlinear dynamics are a useful tool for the study of structural phase transitions and nonlinear properties. In particular, the comparison of calculated and exper-... 

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