Influence of internal reflection on diffusive transport in strongly scattering media

Reflection and Transmission of Waves near the Localization Threshold

“…The last two equations are the radiative boundary conditions at both sides of the slab, featuring the "extrapolation lengths" z e ͑0͞L͒ ϵ 3z 0 D͑0͞L͒͞y E [28]. Berkovits and Kaveh [25] emphasized that flux conservation requires them to contain the diffusion constant D, including interference.…”

“…The middle column shows the relation D͑0͒ ϳ 1͞z 0 . I c ͑u͒ ഠ C͑z ᐉ, z 0 ᐉ, q k 2k sinu͞2͒, used by Lagendijk et al [28]. The line shape exhibits a logarithmic rounding I c ͑u͒ ϳ 1 1 z e ͑0͒j c q 2 k log͑q k j c ͒ when q k j ø 1, rather than the familiar cusp I c ͑u͒ ϳ 1 2 z e jq k j [31].…”

Observation of Anomalous Transport of Strongly Multiple Scattered Light in Thin Disordered Slabs

“…To describe the fact that the diffusive intensity is actually nonzero at a boundary an extrapolation length [6,9] z 0 Ӎ ᐉ is introduced defining the effective slab thickness L eff L 1 2z 0 to be used in diffusion theory. To account for the influence of internal reflection due to the refractive index mismatch at the boundaries [10], the extrapolation length has to be modified according to [11] …”

“…The extrapolation length can also be incorporated in diffusion theory by modifying the boundary conditions of the diffusion equation [6,10,11]. For the stationary case and for isotropic scattering, solutions of the Milne equation show [9] that the value of z 0 for an semi-infinite medium becomes smaller by only a few percent for slab thicknesses 2 # L͞ᐉ # 16.…”

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.…”