Anderson localization of light

Journal name:
Nature Photonics
Volume:
7,
Pages:
197–204
Year published:
DOI:
doi:10.1038/nphoton.2013.30
Received
Accepted
Published online

Abstract

Over the past decade, the Anderson localization of light and a wide variety of associated phenomena have come to the forefront of research. Numerous investigations have been made into the underlying physics of how disorder affects transport in a crystalline lattice incorporating disorder. The physics involved relies on the analogy between the paraxial equation for electromagnetic waves and the Schrödinger equation describing quantum phenomena. Experiments have revealed how wavefunctions evolve during the localization process, and have led to discoveries of new physics that are universal to wave systems incorporating disorder. This Review summarizes the phenomena associated with the transverse localization of light, with an emphasis on the history, new ideas and future exploration of the field.

At a glance

Figures

  1. Transition from ballistic transport to diffusive transport, and eventually to Anderson localization.
    Figure 1: Transition from ballistic transport to diffusive transport, and eventually to Anderson localization.

    a, Transverse localization scheme. A probe beam propagates in a photonic lattice with a controlled level of disorder. Without disorder, the beam exhibits ballistic transport; its width increases linearly with propagation distance (left). Under the influence of disorder, the beam becomes exponentially localized in the transverse plane, maintaining its mean width throughout propagation (right). bd, Ensemble-averaged intensity distribution at the output face of the lattice. The results reveal a gradual transition from ballistic transport (b), where the diffraction pattern reflects the lattice symmetry, to diffusion (c) in the presence of disorder (intensity profile has a Gaussian shape, plotted in logarithmic scale), and, at stronger disorder, to Anderson localization with exponentially decaying tails (d). Figure reproduced with permission from ref. 18, © 2007 NPG.

  2. Hyper-transport of a light beam propagating through fluctuating spatial disorder.
    Figure 2: Hyper-transport of a light beam propagating through fluctuating spatial disorder.

    ad, Ensemble-averaged shape of the beam exiting the medium (cross-sections displayed in a logarithmic scale, with their corresponding width Weff). a, Without disorder, the beam undergoes ballistic transport. b, When disorder is propagation-invariant, the beam displays Anderson localization, which is manifested in its exponential structure. c,d, When disorder evolves during propagation, the beam expands faster than it would in the ballistic transport regime. eh, Corresponding spatial power spectra of the beams displayed in panels ad. i, Simulation results showing the width of the ensemble-averaged power spectrum of the beams, undergoing ballistic transport (homogeneous medium; lower curve), localization (propagation-invariant disorder; middle curve) and hyper-transport (evolving disorder; upper curve). For ballistic transport, the spectral width is conserved. For localization, the spectrum initially expands but once localization is reached the width remains unchanged. In contrast, the spectrum of a beam undergoing hyper-transport expands continuously. Figure reproduced with permission from ref. 48, © 2012 APS.

  3. Simulations of the correlations between the positions of two particles co-localizing in a disordered lattice.
    Figure 3: Simulations of the correlations between the positions of two particles co-localizing in a disordered lattice.

    a, Particles are launched in adjacent sites, labelled 0 and 1. b,c, Correlation map for detecting two bosons (b) and fermions (c) at locations r and q. Note the checkered pattern for fermions. d, Probability distribution for the distance between two co-localizing bosons (blue) and fermions (red). eh, Simulations as in ad, but for two particles launched at sites −1 and +1. Figure reproduced with permission from ref. 60, © 2010 APS.

  4. Experimental measurements of quantum correlations in a 1D photonic lattice.
    Figure 4: Experimental measurements of quantum correlations in a 1D photonic lattice.

    a, Intensity–intensity correlations measured for light launched into site 0. b, Intensity correlation as a function of distance between the waveguides. The oscillatory correlation echoes the quantum distribution for indistinguishable bosons. Figure reproduced with permission from ref. 62, © 2011 APS.

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Affiliations

  1. Physics Department, Technion – Israel Institute of Technology, Haifa 32000, Israel

    • Mordechai Segev
  2. Solid State Institute, Technion – Israel Institute of Technology, Haifa 32000, Israel

    • Mordechai Segev
  3. Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel

    • Yaron Silberberg
  4. CREOL/College of Optics, University of Central Florida, Orlando, Florida 32816, USA

    • Demetrios N. Christodoulides

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