Spatial-Field Correlation: The Building Block of Mesoscopic Fluctuations

Abstract

The absence of self averaging in mesoscopic systems is a consequence of long-range intensity correlation. Microwave measurements suggest and diagrammatic calculations confirm that the correlation function of the normalized intensity with displacement of the source and detector, ∆R and ∆r, respectively, can be expressed as the sum of three terms, with distinctive spatial dependences. Each term involves only the sum or the product of the square of the field correlation function, F ≡ F 2 E . The leading-order term is the product, the next term is proportional to the sum. The third term is proportional to [F (∆R)F (∆r) + [F (∆R) + F (∆r)] + 1].

Numerical study of light correlations in a random medium close to the Anderson localization threshold

“…We averaged over 48 configurations and 60 λ i , similar to the microwave experiments of Ref. [13]. In addition, due to the invariance of correlations in the empty part of the waveguide, we averaged over 10 observation planes.…”

“…[13]. The scatterers were randomly positioned (without overlapping) with a fixed filling fraction f = 0.3.…”

Statistics and control of waves in disordered media

“…In contrast to a conventional focusing lens, in which the size of the focused beam is diffraction limited and so equal to λ /2 divided by the numerical aperture of the lens, the profile of the focused beam through a disordered medium depends only upon the property of the random system itself [56,94,101]. The average intensity at a point b at a distance ∆r from the focal point I f oc (∆r) normalized by the peak intensity for a diffusive sample can be expressed in terms of degree of the long range intensity correlation κ and the square of the amplitude of the field correlation function, F(∆r) = |E(r)E * (r + ∆r)|/ I(r) I(r + ∆r) ,…”

“…But the magnitude of fluctuations of intensity and total transmission normalized by their ensemble average values give a straightforward measure of the degree of localization which is robust against absorption [48]. The magnitudes of relative fluctuations in electronic conductance [11][12][13], classical intensity and total transmission and the degrees of spatial, spectral and temporal correlation of flux increase through the localization transition [40,43,[49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]. Large fluctuations in transmitted intensity were observed in the critical regime of the Anderson localization transition in acoustic measurements in a slab of brazed aluminum beads [64].…”

Incomplete Photonic Band Gap as Inferred from the Speckle Pattern of Scattered Light Waves

“…It is described in statistical terms, with the help of probability distributions and correlation functions. The intensity correlation function, δI(r)δI(r ′ ) , where δI(r) is the deviation from the averaged intensity at point r, contains a short range term [1], C 1 (r, r ′ ), which oscillates on a scale of the wave length and exponentially decays beyond the mean free path, l. It also contains small long-range terms [2][3][4], which become dominant for |r − r ′ | ≫ l. Although the theory of speckle patterns was developed some time ago, it is only recently that the first experimental measurements of the spatial correlator C 1 (r, r ′ ) were reported both for microwaves [5] and optical waves [6,7]. These experiments were carried out for isotropic disordered media; macroscopic isotropy was also assumed in the existing theories.…”