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The single-channel regime of transport through random media.

Peña A, Girschik A, Libisch F, Rotter S, Chabanov AA - Nat Commun (2014)

Bottom Line: Although the detailed structure of a disordered sample can generally not be fully specified, these transmission eigenchannels can nonetheless be successfully controlled and used for focusing and imaging light through random media.In this single-channel regime, the disordered sample can be treated as an effective 1D system with a renormalized localization length, coupled through all the external modes to its surroundings.Using statistical criteria of the single-channel regime and pulsed excitations of the disordered samples allows us to identify long-lived localized modes and short-lived necklace states at long and short time delays, respectively.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, Texas 78249, USA.

ABSTRACT
The propagation of light through samples with random inhomogeneities can be described by way of transmission eigenchannels, which connect incoming and outgoing external propagating modes. Although the detailed structure of a disordered sample can generally not be fully specified, these transmission eigenchannels can nonetheless be successfully controlled and used for focusing and imaging light through random media. Here we demonstrate that in deeply localized quasi-1D systems, the single dominant transmission eigenchannel is formed by an individual Anderson-localized mode or by a 'necklace state'. In this single-channel regime, the disordered sample can be treated as an effective 1D system with a renormalized localization length, coupled through all the external modes to its surroundings. Using statistical criteria of the single-channel regime and pulsed excitations of the disordered samples allows us to identify long-lived localized modes and short-lived necklace states at long and short time delays, respectively.

No MeSH data available.


Related in: MedlinePlus

Statistics of the single-channel regime of transport.(a) Probability density distributions P(InT) (squares) and P(In sab) (circles) from the numerical data for a planar waveguide of L/ξ=5.25. The solid lines plotted through the data are the predictions from equations (2) and (4), respectively, with . Inset:  versus L/W in the planar waveguides of eight different lengths (squares). The solid line is the best linear fit to the data that yields the localization length ξ=1.52W. The broken line is  for the planar waveguide of L=8W, furnishing the renormalized localization length ξ′=1.74 W. (b) Experimental results and prediction for P(In sab) in the quasi-1D system of L/ξ=2.52 (sample D). Here L/ξ′=1.25 is obtained from fitting the bulk of the measured distribution (circles) with P(In sab) from equation (4) (solid line).
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f2: Statistics of the single-channel regime of transport.(a) Probability density distributions P(InT) (squares) and P(In sab) (circles) from the numerical data for a planar waveguide of L/ξ=5.25. The solid lines plotted through the data are the predictions from equations (2) and (4), respectively, with . Inset: versus L/W in the planar waveguides of eight different lengths (squares). The solid line is the best linear fit to the data that yields the localization length ξ=1.52W. The broken line is for the planar waveguide of L=8W, furnishing the renormalized localization length ξ′=1.74 W. (b) Experimental results and prediction for P(In sab) in the quasi-1D system of L/ξ=2.52 (sample D). Here L/ξ′=1.25 is obtained from fitting the bulk of the measured distribution (circles) with P(In sab) from equation (4) (solid line).

Mentions: The fact that in the deeply localized limit transport is mediated by a single transmission eigenchannel has remarkable consequences for the statistical properties of the single-channel regime. The key insight in this respect is that transmission through a single channel can be mapped onto a strictly 1D system where only one transmission channel exists by default. Such a mapping allows us to predict for the single-channel regime the statistical properties that are already known for 1D systems253940. Consider, for example, the probability density distributions P(sa) and P(sab) in the single-channel regime (equation (4) in Methods), which are entirely determined through P(T)—a distribution that is known analytically in one dimension for arbitrary sample length L123940. To perform this mapping to one dimension, it is tempting to choose the effective 1D system such that it has the same system length L and localization length ξ as in our quasi-1D localized systems. However, for increasing system length L, the quasi-1D systems first go through a diffusive regime (with an Ohmic reduction of the transmission) before localization sets41. By contrast, in true 1D systems such a diffusive regime is entirely absent: only a single channel participates in transport even in samples of vanishing length. Consequently, one would obtain a different value of the average transmission and thus different statistics of transport in one dimension as compared to quasi-1D. Although the mapping between these two situations can only be performed in the localized regime, the presence of a diffusive regime in quasi-1D gives rise to a renormalization of the localization length in 1D. The corresponding effective localization length ξ′ is chosen such that the transmission in 1D is the same as in quasi-1D, , for a given L, which yields a larger ξ′ as compared with the true localization length ξ. Note that ξ′ is L-dependent and approaches ξ for increasing system length L→∞ (see the inset of Fig. 2a). To explicitly test the above renormalization, we compare both our numerical and experimental results with predictions for the probability density of the transmittance in 1D from ref. 42,


The single-channel regime of transport through random media.

Peña A, Girschik A, Libisch F, Rotter S, Chabanov AA - Nat Commun (2014)

Statistics of the single-channel regime of transport.(a) Probability density distributions P(InT) (squares) and P(In sab) (circles) from the numerical data for a planar waveguide of L/ξ=5.25. The solid lines plotted through the data are the predictions from equations (2) and (4), respectively, with . Inset:  versus L/W in the planar waveguides of eight different lengths (squares). The solid line is the best linear fit to the data that yields the localization length ξ=1.52W. The broken line is  for the planar waveguide of L=8W, furnishing the renormalized localization length ξ′=1.74 W. (b) Experimental results and prediction for P(In sab) in the quasi-1D system of L/ξ=2.52 (sample D). Here L/ξ′=1.25 is obtained from fitting the bulk of the measured distribution (circles) with P(In sab) from equation (4) (solid line).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3973072&req=5

f2: Statistics of the single-channel regime of transport.(a) Probability density distributions P(InT) (squares) and P(In sab) (circles) from the numerical data for a planar waveguide of L/ξ=5.25. The solid lines plotted through the data are the predictions from equations (2) and (4), respectively, with . Inset: versus L/W in the planar waveguides of eight different lengths (squares). The solid line is the best linear fit to the data that yields the localization length ξ=1.52W. The broken line is for the planar waveguide of L=8W, furnishing the renormalized localization length ξ′=1.74 W. (b) Experimental results and prediction for P(In sab) in the quasi-1D system of L/ξ=2.52 (sample D). Here L/ξ′=1.25 is obtained from fitting the bulk of the measured distribution (circles) with P(In sab) from equation (4) (solid line).
Mentions: The fact that in the deeply localized limit transport is mediated by a single transmission eigenchannel has remarkable consequences for the statistical properties of the single-channel regime. The key insight in this respect is that transmission through a single channel can be mapped onto a strictly 1D system where only one transmission channel exists by default. Such a mapping allows us to predict for the single-channel regime the statistical properties that are already known for 1D systems253940. Consider, for example, the probability density distributions P(sa) and P(sab) in the single-channel regime (equation (4) in Methods), which are entirely determined through P(T)—a distribution that is known analytically in one dimension for arbitrary sample length L123940. To perform this mapping to one dimension, it is tempting to choose the effective 1D system such that it has the same system length L and localization length ξ as in our quasi-1D localized systems. However, for increasing system length L, the quasi-1D systems first go through a diffusive regime (with an Ohmic reduction of the transmission) before localization sets41. By contrast, in true 1D systems such a diffusive regime is entirely absent: only a single channel participates in transport even in samples of vanishing length. Consequently, one would obtain a different value of the average transmission and thus different statistics of transport in one dimension as compared to quasi-1D. Although the mapping between these two situations can only be performed in the localized regime, the presence of a diffusive regime in quasi-1D gives rise to a renormalization of the localization length in 1D. The corresponding effective localization length ξ′ is chosen such that the transmission in 1D is the same as in quasi-1D, , for a given L, which yields a larger ξ′ as compared with the true localization length ξ. Note that ξ′ is L-dependent and approaches ξ for increasing system length L→∞ (see the inset of Fig. 2a). To explicitly test the above renormalization, we compare both our numerical and experimental results with predictions for the probability density of the transmittance in 1D from ref. 42,

Bottom Line: Although the detailed structure of a disordered sample can generally not be fully specified, these transmission eigenchannels can nonetheless be successfully controlled and used for focusing and imaging light through random media.In this single-channel regime, the disordered sample can be treated as an effective 1D system with a renormalized localization length, coupled through all the external modes to its surroundings.Using statistical criteria of the single-channel regime and pulsed excitations of the disordered samples allows us to identify long-lived localized modes and short-lived necklace states at long and short time delays, respectively.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, Texas 78249, USA.

ABSTRACT
The propagation of light through samples with random inhomogeneities can be described by way of transmission eigenchannels, which connect incoming and outgoing external propagating modes. Although the detailed structure of a disordered sample can generally not be fully specified, these transmission eigenchannels can nonetheless be successfully controlled and used for focusing and imaging light through random media. Here we demonstrate that in deeply localized quasi-1D systems, the single dominant transmission eigenchannel is formed by an individual Anderson-localized mode or by a 'necklace state'. In this single-channel regime, the disordered sample can be treated as an effective 1D system with a renormalized localization length, coupled through all the external modes to its surroundings. Using statistical criteria of the single-channel regime and pulsed excitations of the disordered samples allows us to identify long-lived localized modes and short-lived necklace states at long and short time delays, respectively.

No MeSH data available.


Related in: MedlinePlus