Transmission Eigenvalues and the Bare Conductance in the Crossover to Anderson Localization

Shi, Z.B.; Genack, Azriel Z.

doi:10.1103/physrevlett.108.043901

Cited by 98 publications

(121 citation statements)

References 31 publications

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“…In ap pli cations that require power to be transmitted through a scattering medium, one may inject light into open channels to make use of their higher transmission. Indeed, in the microwave regime, researchers have identified open channels with transmission close to unity 46 . The excitation of such channels, which is an experimental challenge yet to be accomplished, could lead to a tenfold increase in the transmission of a disordered waveguide.…”

Section: Using Spatial Degrees Of Freedom To Control Lightmentioning

confidence: 99%

Controlling waves in space and time for imaging and focusing in complex media

et al. 2012

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Section: Using Spatial Degrees Of Freedom To Control Lightmentioning

confidence: 99%

Controlling waves in space and time for imaging and focusing in complex media

et al. 2012

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“…The potential applications range from photovoltaics [7,8] In recent years there have been numerous theoretical and experimental studies on transmission eigenchannels [5,[13][14][15][16][17]. While they can be deduced from the measured transmission matrix [18][19][20][21], it is difficult to directly probe their spatial profiles inside three-dimensional (3D) random media. So far, the open and closed channels are observed only with acoustic wave inside a two-dimensional (2D) disordered waveguide [22], but controlling the energy density distribution has not been realized due to lack of an efficient wavefront modulator for acoustic wave or microwave.…”

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Control of Energy Density inside a Disordered Medium by Coupling to Open or Closed Channels

et al. 2016

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We demonstrate experimentally an efficient control of light intensity distribution inside a random scattering system. The adaptive wavefront shaping technique is applied to a silicon waveguide containing scattering nanostructures, and the on-chip coupling scheme enables access to all input spatial modes. By selectively coupling the incident light to open or closed channels of the disordered system, we not only vary the total energy stored inside the system by 7.4 times, but also change the energy density distribution from an exponential decay to a linear decay and to a profile peaked near the center. This work provides an on-chip platform for controlling light-matter interactions in turbid media.PACS numbers: 42.25. Bs, 42.25.Dd, It has long been known that in disordered media there are many fascinating counter-intuitive effects resulting from interferences of multiply scattered waves [1,2]. One of them is the creation of transmission eigenchannels which can be broadly classified as open and closed [3,4]. Existence of high-transmission (open) channels allows an optimally prepared coherent input beam transmitting through a lossless diffusive medium with order unity efficiency. Opposite to that, waves injected to lowtransmission (closed) channels can barely penetrate the medium and are mostly reflected instead. In general, the penetration depth and energy density distribution of multiply scattered waves inside a disordered medium are determined by the spatial profiles of the transmission eigenchannels that are excited by the incident light. The distinct spatial profiles of open and closed channels suggest that selective coupling of incident light to these channels enables an effective control of total transmission and energy distribution inside the random medium [5,6]. Since the energy density determines the light-matter interactions inside a scattering system, manipulating its spatial distribution opens the door to tailoring optical excitations as well as linear and nonlinear optical processes such as absorption, emission, amplification, and frequency mixing inside turbid media. The potential applications range from photovoltaics [7,8] In recent years there have been numerous theoretical and experimental studies on transmission eigenchannels [5,[13][14][15][16][17]. While they can be deduced from the measured transmission matrix [18][19][20][21], it is difficult to directly probe their spatial profiles inside three-dimensional (3D) random media. So far, the open and closed channels are observed only with acoustic wave inside a two-dimensional (2D) disordered waveguide [22], but controlling the energy density distribution has not been realized due to lack of an efficient wavefront modulator for acoustic wave or microwave. The advantage for optical wave is the availability of spatial light modulator (SLM) with many degrees of freedom, however, the commonly used samples in the optics experiment have an open slab geometry, making it impossible to control all input modes due to finite numerical aperture of the imaging...

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“…The measurement of the TM in random ensembles makes it possible to explore the statistics of conductance and of intensity and total transmission in a single system (39). Optical measurements of the TM have been exploited recently to focus light transmitted through strongly scattering media (19).…”

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Microwave conductance in random waveguides in the cross-over to Anderson localization and single-parameter scaling

Shi

Wang

Genack

2014

Proc. Natl. Acad. Sci. U.S.A.

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The nature of transport of electrons and classical waves in disordered systems depends upon the proximity to the Anderson localization transition between freely diffusing and localized waves. The suppression of average transport and the enhancement of relative fluctuations in conductance in one-dimensional samples with lengths greatly exceeding the localization length, L > > ξ, are related in the single-parameter scaling (SPS) theory of localization. However, the difficulty of producing an ensemble of statistically equivalent samples in which the electron wave function is temporally coherent has so-far precluded the experimental demonstration of SPS. Here we demonstrate SPS in random multichannel systems for the transmittance T of microwave radiation, which is the analog of the dimensionless conductance. We show that for L ∼ 4 ξ, a single eigenvalue of the transmission matrix (TM) dominates transmission, and the distribution of the ln T is Gaussian with a variance equal to the average of −ln T , as conjectured by SPS. For samples in the cross-over to localization, L ∼ ξ, we find a one-sided distribution for ln T . This anomalous distribution is explained in terms of a charge model for the eigenvalues of the TM τ in which the Coulomb interaction between charges mimics the repulsion between the eigenvalues of TM. We show in the localization limit that the joint distribution of T and the effective number of transmission eigenvalues determines the probability distributions of intensity and total transmission for a single-incident channel.T he suppression of transport of coherent quantum or classical waves in disordered media known as Anderson localization (1-3) has been observed for electrons in solids (4), atoms in laser speckle patterns (5), and electromagnetic and acoustic waves in random dielectric and metallic structures (6-9). The variance of relative fluctuations of conductance or of transmission of classical waves increases as hTi falls (7, 10-13), where h. . .i indicates averaging over an ensemble of samples. Large variations in conductance relative to its average value occur for localized waves because the wave can be on-or off-resonance with modes of the medium with centers of localization that are at different positions within the sample (14-16). In addition, modes of the medium may occasionally overlap to enhance coupling through the sample (17). Such fluctuations make it impossible to predict transport in an individual disordered sample. However, fluctuations of the field within disordered samples may be exploited to sharpen focusing in random systems (18,19) and lower the threshold for lasing (20,21). A full account of transport in a random system would begin with the measurement of the probability distributions of conductance in ensembles of random samples with different physical dimensions in the cross-over to Anderson localization.The importance of fluctuations in electronics was first recognized in calculations of conductance mediated by localized states (3). The first observations of the impact o...

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Transmission Eigenvalues and the Bare Conductance in the Crossover to Anderson Localization

Cited by 98 publications

References 31 publications

Controlling waves in space and time for imaging and focusing in complex media

Controlling waves in space and time for imaging and focusing in complex media

Control of Energy Density inside a Disordered Medium by Coupling to Open or Closed Channels

Microwave conductance in random waveguides in the cross-over to Anderson localization and single-parameter scaling

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