Anderson localization as position-dependent diffusion in disordered waveguides

Payne, Ben; Yamilov, Alexey; Skipetrov, S. E.

doi:10.1103/physrevb.82.024205

Cited by 35 publications

(42 citation statements)

References 34 publications

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“…This result is physically plausible, and consistent with scaling theory for macroscopic transport quantities such as, e.g., the conductance. It was tested against numerical simulations [10] and observed in an experiment [11].…”

Section: Introductionmentioning

confidence: 99%

Position-dependent radiative transfer as a tool for studying Anderson localization: Delay time, time-reversal and coherent backscattering

Tiggelen

Skipetrov

Page

2017

Eur. Phys. J. Spec. Top.

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Abstract. Previous work has established that the localized regime of wave transport in open media is characterized by a position-dependent diffusion coefficient. In this work we study how the concept of positiondependent diffusion affects the delay time, the transverse confinement, the coherent backscattering, and the time reversal of waves. Definitions of energy transport velocity of localized waves are proposed. We start with a phenomenological model of radiative transfer and then present a novel perturbational approach based on the self-consistent theory of localization. The latter allows us to obtain results relevant for realistic experiments in disordered quasi-1D wave guides and 3D slabs.

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Section: Introductionmentioning

confidence: 99%

Position-dependent radiative transfer as a tool for studying Anderson localization: Delay time, time-reversal and coherent backscattering

Tiggelen

Skipetrov

Page

2017

Eur. Phys. J. Spec. Top.

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“…In disordered media, both the direction and phase of the propagating waves are randomized in a complex manner, making any attempt to control light propagation particularly challenging. Disordered media are currently investigated in several contexts, ranging from the study of collective multiple scattering phenomena [5,6] to cavity quantum electrodynamics and random lasing [7,8], to the possibility to provide efficient solutions in renewable energy [9], imaging [10], and spectroscopy-based applications [11]. Transport in such systems can be described in terms of photonic modes, or quasi-modes, which exhibit characteristic spatial profiles and spectra [12,13].…”

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confidence: 99%

Engineering of light confinement in strongly scattering disordered media

et al. 2014

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The ability to mold the flow of light at the wavelength scale has been largely investigated in photonic-crystal-based devices, a class of materials in which the propagation of light is driven by interferences between multiply Bragg scattered waves and whose energy dispersion is described by a photonic band diagram [1]. Light propagation in such structures is defined by Bloch modes, which can be engineered by varying the structural parameters of the material [2][3][4]. In disordered media, both the direction and phase of the propagating waves are randomized in a complex manner, making any attempt to control light propagation particularly challenging. Disordered media are currently investigated in several contexts, ranging from the study of collective multiple scattering phenomena [5,6] to cavity quantum electrodynamics and random lasing [7,8], to the possibility to provide efficient solutions in renewable energy [9], imaging [10], and spectroscopy-based applications [11]. Transport in such systems can be described in terms of photonic modes, or quasi-modes, which exhibit characteristic spatial profiles and spectra [12,13]. In diffusive systems, these modes are spatially and spectrally overlapping while in the regime of Anderson localization, they become spatially and spectrally-isolated [14]. Unlike Bloch modes in periodic systems, the precise formation of photonic modes in a single realization of the disorder is unpredictable.Control over light transport can be obtained by shaping the incident wave to excite only a specific part of the modes available in a given system [15][16][17][18]. For fully exploiting the potential of disordered systems, however, a mode control is needed. It was shown 3 theoretically that isolated modes could be selectively tuned and possibly coupled to each other by a local fine modification of the dielectric structure [19,20].In this Article, we demonstrate experimentally the ability to fully control the spectral properties of an individual photonic mode in a two-dimensional disordered photonic structure [21], in a wavelength range that is relevant for photonic research driven applications. A statistical analysis of individual spatially-isolated random photonic modes is performed by multi-dimensional near-field imaging, leading to a detailed determination of intensity fluctuations, decay lengths and mode volumes. We then demonstrate that individual modes can be fine-tuned either by near-field tip perturbation or by local sub-micrometer-scale oxidation of the semiconductor slab [22]. The resonant frequency of a selected mode is gradually shifted until it is in perfect spectral superposition with the frequency of other two modes, located a few micrometers apart and spatially overlapping with the tuned mode. On spectral resonance, we observe frequency crossing and anti-crossing behaviours, respectively, the latter indicating mode interaction. This provides the experimental proof-of- (e) and (f), respectively). The main difference between the two spectra normalized to the average intensity i...

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“…Microwave measurements in quasi-1D samples of the time-dependence of transmission in more deeply localized samples [66] show dramatically reduced decay rates for transmission compared to both diffusion theory and the self-consistent localization theory. Since the slow-down of decay rates is associated with long-lived modes [67][68][69], this indicates that the self-consistent theory is valid near the localization transition but not for deeply localized waves [65,[70][71][72]. The approach to localization can also be seen in the saturation of the spread of a wave with time delay on the output surface of the sample, which is independent of absorption.…”

Section: Introductionmentioning

confidence: 72%

“…For a localized sample, wave interference cannot be neglected in calculating the average profile [116,117]. The intensity profile for localized waves excited by radiation incident from one side of the sample is found to fall more rapidly toward the center of the open medium [70][71][72]. This profile can be found by solving a generalized diffusion equation with a position dependent diffusion coefficient, which reflects the increasing renormalization of transport with depth into the sample due to wave interference [70].…”

Section: Introductionmentioning

confidence: 99%

Statistics and control of waves in disordered media

Shi¹,

Davy²,

Genack³

2015

Opt. Express

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Fundamental concepts in the quasi-one-dimensional geometry of disordered wires and random waveguides in which ideas of scaling and the transmission matrix were first introduced are reviewed. We discuss the use of the transmission matrix to describe the scaling, fluctuations, delay time, density of states, and control of waves propagating through and within disordered systems. Microwave measurements, random matrix theory calculations, and computer simulations are employed to study the statistics of transmission and focusing in single samples and the scaling of the probability distribution of transmission and transmittance in random ensembles. Finally, we explore the disposition of the energy density of transmission eigenchannels inside random media. References and links 1. J. C. Dainty, Laser speckle and related phenomena (Springer-Verlag, Berlin, 1975). 2. I. M. Vellekoop and A. P. Mosk, "Focusing coherent light through opaque strongly scattering media," Opt. Lett. 32, 2309Lett. 32, -2311Lett. 32, (2007. 3. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, "Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media," Phys. Rev. Lett. 104, 100601 (2010). 4. D. S. Fisher and P. A. Lee, "Relation between conductivity and transmission matrix," Phys. Rev. B 23, 6851-6854 (1981). 5. O. N. Dorokhov, "Transmission coefficient and the localization length of an electron in N bond disorder chains," JETP Lett. 36, 318 (1982). 6. O. N. Dorokhov, "On the coexistence of localized and extended electronic states in the metallic phase," Solid State Commun. 51, 381-384 (1984). 7. B. L. Altshuler, P. A. Lee, and R. A. Webb, eds. Mesoscopic phenomena in solids (Elsevier, Amsterdam, 1991). 8. E. Akkermans and G. Montambaux, Mesoscopic physics of electrons and photons (Cambridge University, 2007). 9. E. Abrahams, 50 years of Anderson localization (World Scientific Publishing Co. Pte. Ltd., 2010). 10. P. W. Anderson, "Absence of diffusion in certain random lattices," Phys. Rev. 109, 1492Rev. 109, -1505Rev. 109, (1958. 11. R. A. Webb, S. Washburn, C. P. Umbach, and R. B. Laibowitz, "Observation of h/e Aharonov-Bohm oscillations in normal-metal rings," Phys. Rev. Lett. 54, 2696Lett. 54, -2699Lett. 54, (1985. 12. B. L. Altshuler and D. E. Khmelnitskii, "Fluctuation properties of small conductors," JETP Lett. 42, 359 (1985). 13. P. A. Lee and A. D. Stone, "Universal conductance fluctuations in metals," Phys. Rev. Lett. 55, 1622Lett. 55, (1985. 14. K. M. Watson, "Multiple scattering of electromagnetic waves in an underdense plasma, J. Math. Phys. 10, 688 (1969 Lett. 55, 2692Lett. 55, (1985. 17. P. Wolf and G. Maret, " Weak localization and coherent backscattering of photons in disordered media, Phys.Rev. Lett. 55, 2696Lett. 55, (1985. 18. E. Akkermans, P. E. Wolf, and R. Maynard, "Coherent backscattering of light by disordered media: analysis of the peak line shape, Phys. Rev. Lett. 56, 1 (1986). 19. A. F. Ioffe and A....

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Anderson localization as position-dependent diffusion in disordered waveguides

Cited by 35 publications

References 34 publications

Position-dependent radiative transfer as a tool for studying Anderson localization: Delay time, time-reversal and coherent backscattering

Position-dependent radiative transfer as a tool for studying Anderson localization: Delay time, time-reversal and coherent backscattering

Engineering of light confinement in strongly scattering disordered media

Statistics and control of waves in disordered media

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