Multiple Light Scattering in Magneto-optically Active Media

Erbacher, Frank; Lenke, Ralf; Maret, Georg

doi:10.1209/0295-5075/21/5/008

Cited by 81 publications

(74 citation statements)

References 12 publications

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“…This implies a dramatic increase of the scattering cross section at resonance, but also a great sensitivity to any external perturbation like a magnetic field. Typically, few Gauss are enough to bring the atom completely off resonance, in sharp contrast with previous studies where Teslas were needed to induce significant effects [3]. Concurrently, a giant Faraday effect is observed in the cold atomic cloud [8].…”

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confidence: 88%

Hanle Effect in Coherent Backscattering

et al. 2002

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We study the shape of the coherent backscattering (CBS) cone obtained when resonant light illuminates a thick cloud of laser-cooled rubidium atoms in presence of a homogenous magnetic field. We observe new magnetic field-dependent anisotropies in the CBS signal. We show that the observed behavior is due to the modification of the atomic radiation pattern by the magnetic field (Hanle effect in the excited state). 32.80.Pj When a multiply scattering medium is illuminated by a laser beam, the scattered intensity results from the interference between the amplitudes associated with the various scattering paths; for a disordered medium, the interference terms are washed out when averaged over many sample configurations, except in a narrow angular range around exact backscattering where the average intensity is enhanced. This phenomenon, known as coherent backscattering (CBS), is due to a two-wave constructive interference (at exact back-scattering) between waves following a given scattering path and the associated reverse path, where exactly the same scatterers are visited in the reversed order [1]. The maximum enhancement is obtained when the amplitudes of the interfering paths are exactly balanced. For a convenient choice of polarization, time-reversal symmetry directly implies the equality of the interfering amplitudes. More generally, the interference phenomenon is very robust and qualitatively insensitive to most characteristics of the sample and illuminating wave.However, applying a magnetic field on the sample breaks the time-reversal invariance. It was predicted [2], then experimentally observed [3] and theoretically studied [4,5] that it results in a decrease of the CBS enhancement as well as some rather complicated behavior of the cone shape. In our current understanding of CBS, two ingredients are essential : the individual scattering event, characterized for example by the radiation pattern of each scatterer (this is the single scattering ingredient), and the propagation in the medium between scattering events (this is the "average effective medium" ingredient). Of course, these two ingredients are not independent since the optical theorem links the propagation in the medium to the individual scattering. In the presence of a magnetic field, both ingredients can be affected. For the propagation, this is well known under the name of Faraday effect (and the Voigt or Cotton-Mouton effect) and can be described by the modification of the complex refractive index by the magnetic field. The magnetic field-induced variation of the radiation pattern is much less studied, because it is very small in usual magnetooptically active materials; it is responsible for the "photonic Hall effect" predicted by van Tiggelen [6] and later observed experimentally [7]. In this paper, we show a novel situation where it is experimentally and theoretically possible to discriminate between the two ingredients and where the modification of the radiation pattern dominates the propagation effects.In our experiment, we analyze coheren...

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confidence: 88%

Hanle Effect in Coherent Backscattering

et al. 2002

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“…In the absence of a magnetic field, the polarization on two time-inverted paths will map, such that interference is possible. 21 This is not necessarily the case for other paths constituting the incoherent background, which leads to a fac- The whole setup is put in a black box to shield stray light. The combination of two circular polarizing foils ͑CP͒, is used to suppress singly scattered light.…”

Section: A Polarization In Multiple Scatteringmentioning

confidence: 99%

A precise method to determine the angular distribution of backscattered light to high angles

Groß

Störzer

Fiebig

et al. 2007

Review of Scientific Instruments

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We present an approach to measure the angular dependence of the diffusely scattered intensity of a multiple scattering sample in backscattering geometry. Increasing scattering strength give rise to an increased width of the coherent backscattering and sets higher demands on the angular detection range. This is of particular interest in the search for the transition to Anderson localization of light. To cover a range of −60°to +85°from direct back-reflection, we introduced a new parallel intensity recording technique. This allows one-shot measurements, with fast alignment and short measuring time, which prevents the influence of illumination variations. Configurational average is achieved by rotating the sample and singly scattered light is suppressed with the use of circularly polarized light up to 97%. This implies that backscattering enhancements of almost two can be achieved. In combination with a standard setup for measuring small angles up to ±3°, a full characterization of the coherent backscattering cone can be achieved. With this setup we are able to accurately determine transport mean free paths as low as 235 nm.

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“…It is convement to work momentanly with the weighted delay time W= φ'Ι and to iccover Ρ(Ι,φ') from P(I,W) at the end The charactenstic function (20) is the Founer transform of P(I, W) The average { ) is over the vectois u and v and over the set of eigenvalues {τ,} The average over one of the vectors, say v, is easily camed out, because it is a Gaussian integiation The lesult is a determmant The Hermitian matnx H is a sum of dyadic products of the vectors u and u, with «, = «,?-,, and hence has only two non-vamshing eigenvalues λ + and λ_ Some stiaightfoiwaid hneai algebra gives wheie we have defined the spectial moments The resultmg detemunant is (22) ( 23) 1 , (24) hence ip -i\ (25) An inveise Founei tiansfoim, followed by a change of vanables from I,W to Ι,φ', gives (27) and (28) The curve for n = m is calculated from Eqs (29) and (30) The same value for γ is used äs m the diffusive regime (Fig 2) X(…”

Section: A Distinct-mode Excitation and Detectionmentioning

confidence: 99%

“…The case β = 2 of broken time-reversal symmetry is less important for optical applications, but has been realized in microwave expenments [24][25][26] Theie is now no difference between n = m and n Φ m The matnces U and V have the same statistical distnbution äs for the case of preserved timereveisal symmetry Hence, by followmg the Steps of See III A, we anive agam at Eq (26), with spectral moments B k äs defined in Eq (23) Theu jomt distnbution has now to be calculated fiom Eq (8) with ß = 2 This calculation is carried out m Appendix B The result is…”

Section: H Broken Time-reversal Symmetrymentioning

confidence: 99%

Localization-induced coherent backscattering effect in wave dynamics

2001

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We investigate the statistics of smgle-mode delay times of waves reflected from a disordered waveguide m the presence of wave locahzation The distribution of delay times is quahtatively different from the distribution in the diffusive regime, and sensitive to coherent backscattering The probability of finding small delay times is enhanced by a factor close to v2 for reflection angles near the angle of incidence This dynamic effect of coherent backscattering disappears m the diffusive regime DOI 10 1103/PhysRevE 63 026605 PACS number(s) 42 25 Dd, 42 25 Hz, 72 15 Rn

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Multiple Light Scattering in Magneto-optically Active Media

Cited by 81 publications

References 12 publications

Hanle Effect in Coherent Backscattering

Hanle Effect in Coherent Backscattering

A precise method to determine the angular distribution of backscattered light to high angles

Localization-induced coherent backscattering effect in wave dynamics

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