Polarization and spatial coherence of electromagnetic waves in uncorrelated disordered media

Abstract

International audienc

Electromagnetic field correlations in three-dimensional speckles

“…The use of a radiative transfer equation for the full crossspectral density matrix, that would allow a description of 3D coherence and polarization, is still a subject of current research. In the simplified diffusion-approximation model, that amounts to performing a large scale asymptotics of the RTE, a transport equation can be found [63], that leads to the results summarized in section 2.3.7.…”

“…where R is the position vector defining the center of the observation region, the origin of coordinates coincinding with the illuminating point source, and R ± X/2 define the two observation points around position R. Without loss of generality, one can take direction j = k = 1 to coincide with the direction of vector X, and the result reads [63] W jk (R, X) = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 with…”

“…A peturbative calculation of the full cross-spectral density matrix W can be performed in the bulk of an uncorrelated disordered medium, under illumination by a monochromatic electric-dipole point source [63]. The calculation is based on the Bethe-Salpeter equation (33), but all elements W jk (r, r ′ , ω) = E j (r, ω) E * k (r ′ , ω) are calculated, and not only the trace as in section 2.3.4.…”

Speckle fluctuations resolve the interdistance between incoherent point sources in complex media

“…(6) is known to enter the expression of field-field spatial correlations in random fields, such as blackbody radiation or volume speckle patterns [19][20][21][22] and the description of time-reversed fields [12], and is at the core of Green's-function retrieval techniques based on ambient noise correlations [9]. It is proportional to the cross density of states (CDOS), which was introduced in a different context for the description of spatial coherence in complex systems [23].…”

Circular Bessel statistics: derivation and application to wave propagation in random media

“…In 3D systems, scalar theory for a particular vector field component (co-or cross-pol) holds when there is a sufficient number of scattering events so that each orthogonal vector component of the field solution (the scalar) has equivalent information. However, with weaker overall scatter, the temporal response of a random medium depends on polarization [8], leading to the need to consider vector descriptions [9]. While the response of the copolarized light is faster with reducing scatter, the scatter needs to be quite weak for the zero-mean circular Gaussian assumption for this field component to break down [8].…”