Intensity correlation function

Figure C 1.5.10. Nonnalized fluorescence intensity correlation function for a single terrylene molecule in p-terjDhenyl at 2 K. The solid line is tire tlieoretical curve. Regions of deviation from tire long-time value of unity due to photon antibunching (the finite lifetime of tire excited singlet state), Rabi oscillations (absorjDtion-stimulated emission cycles driven by tire laser field) and photon bunching (dark periods caused by intersystem crossing to tire triplet state) are indicated. Reproduced witli pennission from Plakhotnik et al [66], adapted from [118].

With the advent of extremely large aperture telescopes, there is a growing interest in the statistical properties of the field emitted by astronomical sources (Dravins, 2001). The goal is to obtain important physical information concerning the source by looking at the statistical characteristics of the light it emits. This domain was pioneered by two radio astronomers, Hanbury Brown and Twiss (1956) who measured the intensity correlation function + r))... 

What is the relation between the diffusion coefficient of a monodispersed suspension of spherical particles and the decay of the intensity correlation function ... 

In dynamic or quasi-elastic light scattering, a time dependent correlation function (i (0) i (t)) = G2 (t) is measured, where i (0) is the scattering intensity at the beginning of the experiment, and i (t) that at a certain time later. Under the conditions of dilute solution (independent fluctuation of different small volume elements), the intensity correlation function can be expressed in terms of the electric field correlation function gi (t)... 

The functions, and ij/, are called the synchronous and asynchronous 2D intensity correlation functions, respectively. These functions represent the overall similarity and dissimilarity, respectively, between two intensity variations at vi and V2 caused by changing the magnitude of the perturbation. The results are plotted on two orthogonal axes (vi and V2) with the spectral intensity plotted on the third axis normal to the 2D spectral plane. Figures 3-31A and 3-3 IB illustrate schematic contour maps of a synchronous and an asynchronous 2D correlation spectrum, respectively, where + and - signs indicate the directions of the contour peaks relative to the 2D spectral plane. 

Remark. For fixed t the correlation function in Eq. (21) exhibits a (t )a decay. A (f )a 1 decay of an intensity correlation function was reported in experiments of Orrit s group [4] for uncapped NCs (for that case ot = 0.65 0.2). However, the measured correlation function is a time-averaged correlation function [Eq. (12)] obtained from a single trajectory. Here the correlation function is independent of t thus no comparison between theory and experiment can be made yet. 

These correlations between Stokes and anti-Stokes pulses allow for the conditional preparation of the anti-Stokes pulse with intensity fluctuations that are suppressed compared with classical light. In order to quantify the performance of this technique, we measured the second-order intensity correlation function giis MS ) and mean number of photons fi for the anti-Stokes pulse conditioned on the detection of ns photons in the Stokes channel (see Fig. 4). (For classical states of light, (f1] > 1, whereas an ideal Fock state with n photons has anti-Stokes photons grows linearly with ns, while (AS1) drops below unity, indicating the nonclassical character of the anti-Stokes photon states. In the presence of back-ground counts, gks (AN) does not increase monotonically with ns, but instead exhibits a minimum at ns = 2. The Mandel Q parameter [Mandel 1995] can be calculated using = n f((jns (AS) — 1) from these measurements we... 

If the variance of the number of photons is smaller than its mean value, the held is said to exhibit the sub-Poissonian photon statistics. This effect is related to the second-order intensity correlation function... 

The second-order (intensity) correlation function of a held of a complex amplitude E(R. t) is dehned as... 

The central role in definitions of PAB in a single-mode radiation field plays the intensity correlation function [55]... 

Different normalizations of G (f, t + x) can be applied in the analysis of photon-number correlations. Here, we analyze the normalized two-time second-order intensity correlation functions defined as... 

The photon antibunching according to the y th (y = I, II, III) definition occurs if the normalized intensity correlation function gf t, t + x) increases from its initial value at x 0 ... 

Figure 2.5 Relaxation rates F of the intensity correlation functions as a function of q2 obtained via a photon correlation spectroscopy experiment. The sample was a w/o-droplet microemulsion made of D2 0/n-octane-di8/CioE4. On the oil-continuous side of the phase diagram the scattered light intensity is usually low leading to rather large errors of the individual data points. Nevertheless, from the slope of the linear fit the translational diffusion coefficient is obtained. (Figure redrawn with data from Ref. [67].)...

Here, E is the complex conjugated of Es. Experimentally, the intensity correlation function g2(t) is determined,... 

The dynamic behavior of linear charged polyelectrolytes in aqueous solution is not yet understood. The interpretation of dynamic light scattering (DLS) of aqueous solutions of sodium poly(styrene sulfonate) (NaPSS) is particularly complicated. The intensity correlation function shows a bimodal shape with two characteristic decay rates, differing sometimes by two or three orders of magnitude, termed fast and slow modes. The hrst observations in low salt concentration or salt free solution were reported by Lin et al. [31] for aqueous solutions of poly(L-lysine). Their results are described in terms of an extraordinary-ordinary phase transition. An identical behavior was hrst observed by M. Drifford et al. in NaPSS [32], Extensive studies on this bimodal decay on NaPSS in salt-free solution, or solutions where the salt concentration is increased slowly, have been reported [33-36]. The fast mode has been attributed to different origins such as the coupled diffusion of polyions and counterions [34,37,38] or to cooperative fluctuations of polyelectrolyte network [33,39] in the semidilute solutions. 

FIG. 14 Example of the bimodal decay of the intensity correlation function of NaPSS/LaCl3 system NaPSS concentration C = 0.1 M and LaCl3 concentration Cs = 1CT3 M (B-point on Figure 15). The scattering wave vector is q = 2.3 X 1(T3 A-1. 

The evolution of the effective diffusion coefficients following the a-line is shown in Figure 16. A bimodal decay of the intensity correlation function is observed on this line. Two modes (slow and fast) are present, and the amplitude of the slow mode is increasing from A (Cs/C 0.2) to B (Cs/C 10 2). 

The power-law behaviour in the time intensity correlation function (TCP)... 

Electric field correlation function Intensity correlation function Enthalpy... 

Fig. 10 Intensity correlation functions measured at five different sample position at...

The characteristic sample position dependency for the poly(acrylic acid) sample MBAAm-2 is illustrated in Fig. 10. Several measurements of g f) at different sample positions are shown (scattering angle 6 = 90°). After each measurement the sample was rotated in the measuring cell to adjust another position. Each position yields a different intensity correlation function g f) coruiected with a different value for Xp. The resulting field correlation functions represent the fully fluctuating component. They all are described by one curve g " f). 

The additional components for achieving a PFS measurement are polarizing optics for manipulating both the illumination and scattered polarization states a polarizing beam splitter for directing orthogonal states into two detectors, and a means of forming three polarization-sensitive intensity correlation functions. 

Figure 18.16 Intensity-intensity correlation functions for a symmetric PS-PI block copolymer with = 3.4 X 10 Da in benzene at different weight concentrations, (a) G2 q, t) versus w, (b) the Laplace inversion time decay rate distribution GiV) (c) F versus for the three modes. Source Reprinted with permission from Pan C, Maurer W, Liu Z, Lodge TP, Stepanek P, von Meerwall ED, Watanabe H. Macromolecules 1995 28 1643 [87]. Copyright 1995 American Chemical Society.

The intensity correlation function was measured using a 96-channel Malvern single-clipped digital correlator which had been modified such that the last four channels were shifted 320 delay times to allow an accurate determination of the baseline. The measured and computed baselines typically agree to within Differences between these values indicated the presence of dust contamination. Correlation functions with greater deviations in baseline were analyzed only in a qualitative way since they were considered to be unreliable. 

Time Correlation Function. The measured, self-beating intensity correlation function can be expressed as... 

One of the other useful quantities to characterize dynamical processes in SMS is the fluorescence intensity correlation function, also called the second-order correlation function, defined by [73, 74]... 

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