Coherent Backscattering of Light by Disordered Media: Analysis of the Peak Line Shape

Akkermans, Éric; Wolf, P. E.; Maynard, R.

doi:10.1103/physrevlett.56.1471

Cited by 596 publications

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“…The latter manifests in a slight reduction of the transmission probability of an incident wave through a disordered region as compared to the classically expected value, due to constructive interference between backscattered paths and their time-reversed counterparts. This interference phenomenon particularly leads to a cone-shaped enhancement of the backscattering current in the direction reverse to the incident beam, which was indeed observed [16] and theoretically analyzed [17] in light scattering processes from disordered media. Related weak localization effects also arise in electronic mesoscopic physics, leading to characteristic peaks in the magnetoresistance [18,19].…”

mentioning

confidence: 96%

Coherent Backscattering of Bose-Einstein Condensates in Two-Dimensional Disorder Potentials

Hartung

Wellens²,

Müller³

et al. 2008

Phys. Rev. Lett.

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We study quantum transport of an interacting Bose-Einstein condensate in a two-dimensional disorder potential. In the limit of a vanishing atom-atom interaction, a sharp cone in the angle-resolved density of the scattered matter wave is observed, arising from constructive interference between amplitudes propagating along reversed scattering paths. Weak interaction transforms this coherent backscattering peak into a pronounced dip, indicating destructive instead of constructive interference. We reproduce this result, obtained from the numerical integration of the Gross-Pitaevskii equation, by a diagrammatic theory of weak localization in the presence of nonlinearity. DOI: 10.1103/PhysRevLett.101.020603 PACS numbers: 05.60.Gg, 03.75.Kk, 67.85.ÿd, 72.15.Rn The past years have witnessed an increasing number of theoretical and experimental research activities on the behavior of ultracold atoms in magnetic or optical disorder potentials [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. A central aim in this context is the realization and unambiguous identification of strong Anderson localization with Bose-Einstein condensates, which was attempted by several experimental groups [1][2][3] with recent success [4,5], and theoretically studied both from the perspective of the expansion process of the condensate [6,7] as well as from the scattering perspective [8,9]. Complementary studies were focused on localization properties of Bogoliubov quasiparticles [10,11], on dipole oscillations in the presence of disorder [12,13], as well as on the realization of Bose glass phases [14,15].The above-mentioned topics (apart from Ref.[7]) mainly refer to processes that are essentially one dimensional (1D) by nature. Qualitatively new phenomena, however, do arise in two or three spatial dimensions, due to the scenario of weak localization. The latter manifests in a slight reduction of the transmission probability of an incident wave through a disordered region as compared to the classically expected value, due to constructive interference between backscattered paths and their time-reversed counterparts. This interference phenomenon particularly leads to a cone-shaped enhancement of the backscattering current in the direction reverse to the incident beam, which was indeed observed [16] and theoretically analyzed [17] in light scattering processes from disordered media. Related weak localization effects also arise in electronic mesoscopic physics, leading to characteristic peaks in the magnetoresistance [18,19].In this Letter, we investigate the phenomenon of coherent backscattering with atomic Bose-Einstein condensates that propagate in presence of two-dimensional (2D) disorder potentials. An essential ingredient that comes into play here is the interaction between the atoms of the condensate. On the mean-field level, this is accounted for by the nonlinear term in the Gross-Pitaevskii equation describing the time evolution of the condensate wave function. Indeed, nonlinearities do also appear in scattering processes of light, e....

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mentioning

confidence: 96%

Coherent Backscattering of Bose-Einstein Condensates in Two-Dimensional Disorder Potentials

Hartung

Wellens²,

Müller³

et al. 2008

Phys. Rev. Lett.

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“…Equation (6) is based on the model derived by Akkermans et al [1986] using diffusion theory (which is closely related to scalar radiative transfer theory). This model was adopted and slightly modified by Hapke [2002].…”

Section: Hapke Et Al: Wavelength-dependent Lunar Phase Curve E00h15 mentioning

confidence: 99%

The wavelength dependence of the lunar phase curve as seen by the Lunar Reconnaissance Orbiter wide‐angle camera

et al. 2012

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[1] The Lunar Reconnaissance Orbiter wide-angle camera measured the bidirectional reflectances of two areas on the Moon at seven wavelengths between 321 and 689 nm and at phase angles between 0°and 120°. It is not possible to account for the phase curves unless both coherent backscatter and shadow hiding contribute to the opposition effect. For the analyzed highlands area, coherent backscatter contributes nearly 40% in the UV, increasing to over 60% in the red. This conclusion is supported by laboratory measurements of the circular polarization ratios of Apollo regolith samples, which also indicate that the Moon's opposition effect contains a large component of coherent backscatter. The angular width of the lunar opposition effect is almost independent of wavelength, contrary to theories of the coherent backscatter which, for the Moon, predict that the width should be proportional to the square of the wavelength. When added to the large body of other experimental evidence, this lack of wavelength dependence reinforces the argument that our current understanding of the coherent backscatter opposition effect is incomplete or perhaps incorrect. It is shown that phase reddening is caused by the increased contribution of interparticle multiple scattering as the wavelength and albedo increase. Hence, multiple scattering cannot be neglected in lunar photometric analyses. A simplified semiempirical bidirectional reflectance function is proposed for the Moon that contains four free parameters and that is mathematically simple and straightforward to invert. This function should be valid everywhere on the Moon for phase angles less than about 120°, except at large viewing and incidence angles close to the limb, terminator, and poles.Citation: Hapke, B., B. Denevi, H. Sato, S. Braden, and M. Robinson (2012), The wavelength dependence of the lunar phase curve as seen by the Lunar Reconnaissance Orbiter wide-angle camera,

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“…For R = 1 the same solution applies when replacing the sine functions by cosine functions. For numerical purpose it 2eAmfk might be useful to apply the Poisson summation rule tan(kL) = ( E A , ,~)~-1 ' ( 7 ) to this result and transform to an expansion useful for short times: The normalized eigenvectors are given by tan qk = &Amfk , (9) Using an eigenfunction expansion the Green function G(z2, z,; t) is given by…”

Section: Finite Slabmentioning

confidence: 99%

“…The relevant 3D Green function for enhanced backscattering [9,10,25 ] in which k , is the perpendicular momentum transfer. For the present purpose it is sufficient to limit the discussion to increased backscattering for a semiinfinite slab.…”

Section: Enhanced Backscatteringmentioning

confidence: 99%

Influence of internal reflection on diffusive transport in strongly scattering media

1989

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Coherent Backscattering of Light by Disordered Media: Analysis of the Peak Line Shape

Cited by 596 publications

References 10 publications

Coherent Backscattering of Bose-Einstein Condensates in Two-Dimensional Disorder Potentials

Coherent Backscattering of Bose-Einstein Condensates in Two-Dimensional Disorder Potentials

The wavelength dependence of the lunar phase curve as seen by the Lunar Reconnaissance Orbiter wide‐angle camera

Influence of internal reflection on diffusive transport in strongly scattering media

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