Large Intensity Fluctuations for Wave Propagation in Random Media

Abstract

The intensity pattern generated by a monochromatic point source in a random medium is studied. Thc intensity-intensity correlation function ls calculated and lt ls sh0%n that. the intensity, as a function of coordinate, exhibits large fluctuations (the speckle pattern). The sensitivity of this speckle pattern to small changes in the source frequency is also studied. PACS numbers: 42.20.Ji, 71.55.Jv A wave propagating in a random medium undergoes multiple scattering from the inhomogeneities.The scattered waves interfere with each other and, as a result, a certain intensity pattern is formed. In a random medium, as opposed, e.g. , to a crystal, one would, naively, expect an efficient averaging process and therefore a fairly smooth intensity pattern, with only small intensity fluctuations.Instead, however, one finds a highly irregular pattern, with large intensity changes over short distances. The irregularities are not due to noise. Each microscopic realization of the random medium, i.e. , each sample of the statistical ensemble, displays its own pattern -a "fingerprint" which reflects the specific arrangement of the inhomogeneities (impurities) in that sample. This phenomenon is quite familiar in optics where it is termed "a speckle pattern" and usually refers to an intensity pattern formed on a screen by light reflected from a rough surface. Below, this term is used in a somewhat broader sense and refers to an intensity pattern formed in the bulk of a disordered medium when a wave (electromagnetic, acoustic, or an electron wave) propagates through it.There exists a huge literature on the subject. ' 3 In early work, usually certain assumptions were made directly on the statistics of the scattered light (rather than on the statistical properties of the disordered medium). The "first principles" work, i.e. , that which tries to derive properties of the speckle patterns directly from the wave equation, is mostly limited to smooth inhomogeneities (the wavelength much shorter than the characteristic inhomogeneity size). 2~T he subject of light propagation in random media has been recently given a new boost as a result of a number of experiments. These experiments revealed an enhanced backscattering, in combination with large intensity fluctuations6 and high sensitivity of the speckle pattern to relatively small changes of the source frequency. 7 Similar phenomena exist, and are being extensively studied, in the electron transport in disordered systems. The point is that as long as the sample size is smaller than the inelastic scattering length (the mesoseopic regime), an electron propagates coherently through the entire sample and, thus, takes a "fingerprint" of the specifi, for that sample, impurity arrangement.This manifests itself in various interference phenomena and in extreme sensitivity of the conductance to small changes of various factors. s '2 The purpose of the present work is to calculate some properties of speckle patterns, specifically the intensity correlation function, for a scalar field. Such a fiel...

Light transport regimes in slow light photonic crystal waveguides

“…Compared to the unperturbed case, the random dielectric potential leads to an additional term ⌺, called the self-energy, which takes into account the correlation induced by disorder in the averaging process of the field. For a homogeneous random medium and in the leading approximation, 19 the self-energy is given by ⌺͑k͒ =−i͑ 0 / cl͒. In such media, the dispersion relation is all the more affected that the mean-free path l is small; i.e., that the random fluctuations of the disordered potential are large.…”

“…In the so-called ladder approximation, the determination of the second moment ͗ ͑ 1 , k 1 ͒ ‫ء‬ ͑ 2 , k 2 ͒͘ of the field from the BetheSalpeter equation, shows that the average intensity at a given spatial point is the sum of the Drude-Boltzmann contribution and a contribution known as the ''diffuson'' contribution. 19,21 The former contribution, that has an exponential decay and can be neglected after several mean-free path l, corresponds to the dispersive regime. 2,18 The latter contribution corresponds to the multiple-scattering regime and is associated with the formation of speckles in the spatial frequency spectrum.…”

Long-time asymptotic of temporal-spatial coherence function for light propagation through time dependent disorder

“…[6,7]). When considering FCF slow coordinate r = (r 1 + r 2 )/2 and time t = (t 1 + t 2 )/2 as well as fast ones: ρ = (r 1 − r 2 )/2 and τ = (t 1 − t 2 )/2 are introduced.…”

“…This activity was inspired by experimental evidence for a number of the phenomena (e.g. enhanced back-scattering [1,2], spatial and frequency correlation of back-scattered and transmitted radiation [3,4]; for a review see [5]) as well as by realizing a close similarity of these phenomena to fluctuation phenomena in electron transport in disordered systems (mesoscopics) [6,7]. The latter brought new physical insight and theoretical methods into the field established in optics many years ago [8].…”

Diffusion in Translucent Media

“…The diffusion approach also describes the transport of classical and quantum waves in multiply scattering media [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] . Waves entering a static disordered sample interfere to produce a wavelength-scale speckled pattern of energy or particle density that is a unique fingerprint of the wave interaction with the disordered sample.…”