Harmonic susceptibilities

More detailed approaches can be carried out on these non-linear systems with in particular the a.c. susceptibility harmonic analysis. The onset of the third harmonic modulus can be used to detect the irreversibility line [515] however a delicate analysis with several parameters such as frequency and intensity of the a.c. field is necessary. 

Electronic appliances that are highly susceptible to such effects are, however, provided as standard practice with harmonic filters in their incoming circuits. 

Electric motors are susceptible to a variety of forcing functions that cause instability or imbalance. The narrow-bands established to monitor the fundamental and other harmonics of actual running speed are useful in identifying mechanical imbalance, but other indices also should be used. 

Most turbines have relatively long bearing spans and highly flexible shafts. These factors, coupled with variations in process flow conditions, make turbine rotors highly susceptible to shaft deflection during normal operation. Typically, turbines operate in either the second or third mode and should have narrowbands at the second (2x) and third (3x) harmonics of shaft speed to monitor for mode shape. 

The first and third order terms in odd powers of the applied electric field are present for all materials. In the second order term, a polarization is induced proportional to the square of the applied electric field, and the. nonlinear second order optical susceptibility must, therefore, vanish in crystals that possess a center of symmetry. In addition to the noncentrosymmetric structure, efficient second harmonic generation requires crystals to possess propagation directions where the crystal birefringence cancels the natural dispersion leading to phase matching. 

The dominance of the tt -electron excitations in MNA is demonstrated by the experimental finding that along the polar, axis the second harmonic susceptibility X 2 ) (-2< > < >, m/V is the same as the... 

For dilute solutions of the molecule dissolved in a suitable solvent, the DC induced second harmonic susceptibility Tt ia a combination of the... 

These effects Q.2) are all driven by the same third-rank frequency dependent nonlinear susceptibility x2(-u>3 w,, u>2).d is sometimes preferred for second-harmonic generation (SHG). 

Optical detection offers the most conventional technique to time-resolve the coherent phonons. It includes four-wave mixing [8], transient reflectivity [9,10] and transmission [7] measurements, as well as second harmonic generation (SHG) [15,32]. Coherent nuclear displacement Q induces a change in the optical properties (e.g., reflectivity R) of the crystal through the refractive index n and the susceptibility y,... 

The proportionality constants a and (> are the linear polarizability and the second-order polarizability (or first hyperpolarizability), and x(1) and x<2) are the first- and second-order susceptibility. The quadratic terms (> and x<2) are related by x(2) = (V/(P) and are responsible for second-order nonlinear optical (NLO) effects such as frequency doubling (or second-harmonic generation), frequency mixing, and the electro-optic effect (or Pockels effect). These effects are schematically illustrated in Figure 9.3. In the remainder of this chapter, we will primarily focus on the process of second-harmonic generation (SHG). 

Nonvanishing Components of Second-Order Susceptibility Tensor for Second-Harmonic Generation in Electric-Dipole Approximation for Achiral and Chiral Isotropic (i.e. isotropic in the plane of the film) Films0... 

The presence of chirality introduces an additional component in the y direction. This component will rotate the polarization of die second-harmonic field with respect to the polarization of the incident radiation. The amount of optical rotation will depend on the relative magnitude of the chiral and achiral susceptibility components. Furthermore, Py changes sign between the enantiomers... 

The coefficients /, g, and h are unique for each second-harmonic signal and depend on the three susceptibility tensors. We normalize the relative values of the tensor components to = 1- The task is then to determine the complex values of the other 14 tensor components (see Table 9.2). A sufficient number of 8 independent measurements is provided by the p- and s--polarized components of the reflected and transmitted second-harmonic signals for the two orientations of the sample shown in Figure 9.17. The change in sample orientation corresponds to a coordinate transformation that reverses the... 

To analyze the second-order susceptibility, the symmetry of the films was first analyzed by measuring the intensities of the second-harmonic light. The sample was irradiated with polarized light from a Nd YAG laser incident at 45°, and the second-harmonic light emanating from the sample was detected while the sample was rotated around its surface normal. No variation in the second-harmonic intensity was observed as the sample was rotated, indicating... 

There are different paths to achieving surface specificity. One can exploit optical susceptibilities and resonances that are nonzero only at the surface or only for the molecular species of interest adsorbed on the surface. Examples include the use of second-order nonlinear mixing processes such as second harmonic generation7-9 for which the nonlinear susceptibility tensor is nonzero only where inversion symmetry is broken. Spectroscopic techniques with very high selectivity for molecular resonances such as surface-enhanced infrared or Raman spectroscopy10-12 may also be used. 

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