Electric-Field Autocorrelation Function

Dynamic light scattering measurements were performed with a Malvern photon correlation system eqxiipped with a krypton ion laser KR 165-11 from Spectra Physics (1 =647.1 nm). The intensity time correlation function (TCP) was recorded by a Malvern autocorrelator. The electric field TCP g,(t) normalized to the base line of the intensity TCP, and its first cumulant F = -Slng (t)/3t at time to were calculated as usual ( )by an on-line computer where 80 cheinnels of a total of 96 chemnels were used for the recording of the TCP, and the leist 12 channels, shifted by 164 seusple times, were used for the detection of the beise line. 

The linear response theory [50,51] provides us with an adequate framework in order to study the dynamics of the hydrogen bond because it allows us to account for relaxational mechanisms. If one assumes that the time-dependent electrical field is weak, such that its interaction with the stretching vibration X-H Y may be treated perturbatively to first order, linearly with respect to the electrical field, then the IR spectral density may be obtained by the Fourier transform of the autocorrelation function G(t) of the dipole moment operator of the X-H bond ... 

In this section it will be outlined how the different molar masses contribute to the TDFRS signal. Of especial interest is the possibility of selective excitation and the preparation of different nonequilibrium states, which allows for a tuning of the relative statistical weights in the way a TDFRS experiment is conducted. Especially when compared to PCS, whose electric field autocorrelation function g t) strongly overestimates high molar mass contributions, a much more uniform contribution of the different molar masses to the heterodyne TDFRS diffraction efficiency t) is found. This will allow for the measurement of small... 

The normalized electric field autocorrelation function gift), which can be calculated from the normalized intensity autocorrelation function g2(t) = (1(0) 7(f)) (I(0)/2 according to the Siegert relation [56]... 

The intensity distribution of particle size, G(a), is related to the experimentally observed electric field autocorrelation function, g[Pg.107]

Photon Correlation. Particles suspended in a fluid undergo Brownian motion due to collisions with the liquid molecules. This random motion results in scattering and Doppler broadening of the frequency of the scattered light. Experimentally, it is more accurate to measure the autocorrelation function in the time domain than measuring the power spectrum in the frequency domain. The normalized electric field autocorrelation function g(t) for a suspension of monodisperse particles or droplets is given by ... 

Here B is an optical constant, or is the total polarizability of the particle, and n is the number of components in each particle. The indexes i and j refer to components of the same particle. If the assumption of independent particles was not made, then the indexes could refer to components of any two particles, and the autocorrelation expression could not be written as a simple sum of contributions from individual particles. The spatial vector r(r) refers to the center of mass of the particle. R(r). In the case of a nonspherical particle (arbitrary shape), Eq. (I0) would describe the coupled motion of the center of mass and the relative arrangement of the components of the particle. For spherical particles, translational and rotational motion arc uncoupled and we have a simplified expression for the electric field time correlation function ... 

The derivation of the basic relation (4.147) reveals the conditions under which the proportionality between drift velocity (or flux) and electric field breaks down. It is essential to the derivation that in a collision, an ion does not preserve any part of its extra velocity component arising from the force field. If it did, then the actual drift velocity would be greater than that calculated by Eq. (4.147) because there would be a cumulative carryover of the extra velocity from collision to collision. In other words, every collision must wipe out all traces of the force-derived extra velocity, and the ion must start afresh to acquire the additional velocity. This condition can be satisfied only if the drift velocity, and therefore the field, is small (see the autocorrelation function. Section 4.2.19). 

Equation (8.159) is strictly valid for a Gaussian distribution of electric fields. The electric field autocorrelation function is related to the dynamic structure factor S q, t) [compare it with the static scattering function S q) in Eq. (3.121)] ... 

The intensity I of the light scattered from a dilute macromolecular or supra-molecular solution is a fluctuating quantity due to the Brownian motion of the scattering particles. These fluctuations can be analysed in terms of the normalised autocorrelation function y1 ( t ) of the scattered electrical field Es, which contains information about the structure and the dynamics of the scattering particles [80]. 

It is clear from Eq. (2.4.15) and Section 1.2 that the light-scattering spectrum is determined from autocorrelation functions of the electric field at the detector. Thus the goal of any theory of light scattering is to show how important physical properties of the scattering medium can be extracted from the measured time-correlation functions. 

Fig. 3. Comparison of our numerical computations for the autocorrelation function of a laser-induced wave-packet in cesium in external electric fields with the experimental results.

In light-scattering experiments one measures the spectral density of the electric field autocorrelation function of the scattered light wave, given as... 

Figure 33. BaseUne-subtracted, normalized intensity antocorrelation function g2(t) (a) and the absolute value of the baseline-subtracted, normalized electric-field autocorrelation function, gi(i) (b).

Electric-Field Autocorrelation Function We consider the autocorrelation function of the electric field E,(t) of the light scattered by solutes. As we have seen in Section 2.4, is a complex quantity. We introduce another normalized autocorrelation function gi(r), which is defined as... 

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