Imaginary susceptibility

Losses caused by multiphoton ionization are usually incorporated as either an equivalent current (see e.g. [30,31]) or an imaginary susceptibility contribution that extracts from the held the energy needed for the free-electron generation. 

Imaginary susceptibility in the infrared, Xi, plotted against the frequency. In the theoretical curve no effect is included for acoustical modes and the relative intensities of the three oxygen local mode peaks are scaled by the appropriate value for Anp-, from Table 11-2. (The absolute scale was chosen to fit the experimental curve.) The experimental curve is from Milcr (1968). 

Referring to samples, 1, 2, and 3 [12], Fig. 7 shows the results obtained for the real, and imaginary, susceptibility components over the frequency range 100 MHz to 6 GHz. It is apparent that a resonant-like profile, indicated by the x component changing sign, at a frequency /res, is characteristic of all the samples, /res is seen to vary from 0.54 GHz for sample 1 to 4.4 GHz for sample 3. As 27i/res = yZ/i = ylK/Mg (where and K are average values of the particle internal field and anisotropy constant, respectively), this result is a signature of the difference in internal field and anisotropy constant of the particles. The susceptibility profiles have the same resonant form as that obtained for sample 4 (see Fig. 8) these profiles are shown to have the form predicted by Eqs. (111), (113), and (116). Furthermore, the actual values of Ha and K can be determined by means of polarized measurements as will be demonstrated now for sample 4. 

Fig. 163. Ni(C404)-2H20. Field dependence of the real susceptibility xL and of the imaginary susceptibility y" where Zm = Zm-ii m [72014],...

If the rate of sweep through the resonance frequeney is small (so-called slow passage), a steady-state solution, in which the derivatives are set to zero, is ob-tained. The result expresses M,., and as funetions of cu. These magnetization components are not actually observed, however, and it is more useful to express the solutions in terms of the susceptibility, a complex quantity related to the magnetization. The solutions for the real (x ) and imaginary (x") components then are... 

For each EA spectrum, the transmission T was measured with the mechanical chopper in place and the electric field off. The differential transmission AT was subsequently measured without the chopper, with the electric field on, and with the lock-in amplifier set to detect signals at twice the electric-field modulation frequency. The 2/ dependency of the EA signal is due to the quadratic nature of EA in materials with definite parity. AT was then normalized to AT/T, which was free of the spectral response function. To a good approximation [18], the EA signal is related to the imaginary part of the optical third-order susceptibility ... 

Figure 10.1 Temperature dependence of imaginary parts of the ac susceptibility (real parts in insets) recorded on powder samples of 1 at different frequencies as indicated, at...

That is, the rate of energy absorption Q is linearly related to the imaginary part of linear susceptibility x( >). 

We consider a model for the pump-probe stimulated emission measurement in which a pumping laser pulse excites molecules in a ground vibronic manifold g to an excited vibronic manifold 11 and a probing pulse applied to the system after the excitation. The probing laser induces stimulated emission in which transitions from the manifold 11 to the ground-state manifold m take place. We assume that there is no overlap between the two optical processes and that they are separated by a time interval x. On the basis of the perturbative density operator method, we can derive an expression for the time-resolved profiles, which are associated with the imaginary part of the transient linear susceptibility, that is,... 

Far from the Laue condition the absorption shows the normal photoelectric absorption, as would be measured (with allowance for density) in a liquid or gas of the same atomic species. Close to the Laue condition, the absorption is quantified by the imaginary parts of the susceptibilities, leading to imaginary components of the wavevectors. These imaginary components are always normal to the crystal surface and hence the planes of constant attenuation are parallel to the surface. The attenuation coefficient (n) normal to the surface is given by (n)=-4 lm(K o) (4.28)... 

Static charge-density susceptibilities have been computed ab initio by Li et al (38). The frequency-dependent susceptibility x(r, r cd) can be calculated within density functional theory, using methods developed by Ando (39 Zang-will and Soven (40 Gross and Kohn (4I and van Gisbergen, Snijders, and Baerends (42). In ab initio work, x(r, r co) can be determined by use of time-dependent perturbation techniques, pseudo-state methods (43-49), quantum Monte Carlo calculations (50-52), or by explicit construction of the linear response function in coupled cluster theory (53). Then the imaginary-frequency susceptibility can be obtained by analytic continuation from the susceptibility at real frequencies, or by a direct replacement co ico, where possible (for example, in pseudo-state expressions). 

Fio. 3. Imaginary (x O and real parts of rf susceptibility as a function of magnetic field strength H. Field modulation and resulting NMR signal are schematically illustrated for the absorption curve (x ). 

In a full dynamics scaling analysis, the imaginary component of the dynamic susceptibility of a spin glass is scaled according to [130]... 

Heterodyne detection is widely used to improve the SNR of optical measurements. The additional advantage of heterodyne detection for CARS measurements is that it allows direct extraction of either real or imaginary parts of the susceptibility tensor (Vinergoni et al. 2004 Evans et al. 2004). Being introduced for CARS spectroscopy about 30 years ago (Eesley et al. 1978), heterodyne detection was for a long... 

The proper phase shift introduced to the signal wave allows direct measurements of the imaginary part of the resonant nonlinear optical susceptibility, i.e ... 

Evans, C. L., Potma, E. O., and Xie, X. S. N. 2004. Coherent anti-Stokes Raman scattering spectral interferometry Determination of the real and imaginary components of nonlinear susceptibility for vibrational microscopy. Opt. Lett. 29(24) 2923-25. 

This phase shift is akin to the phase shift experienced by a damped harmonic oscillator driven in the vicinity of the oscillator s eigenfreqnency Hence, the presence of a vibrational resonance not only changes the amplitnde of the signal field, bnt also its phase. To incorporate this effect, the resonant nonlinear susceptibility is no longer real as it contains imaginary contributions ... 

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