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Physical review. B./Physical review. B

Long-range correlation of transmitted light through transmission eigenchannels in disordered media

Peilong Hong, Mingfang Yi, Liwei Zhang, Yi Liang, Guoquan Zhang

Published Jan 6, 2025• 2 citations
Publisher

Abstract

Long-range correlation characterizes the nondiffusive scattering paths of light through disordered media, playing an important role in the coherent control of multiply scattered light. Here, we report the long-range correlation of subsets of coherently interacting scattering paths, known as transmission eigenchannels. We find that the high-transmission eigenchannels exhibit a negative long-range correlation, in contrast to conventional positive long-range correlation. Moreover, when the transmission decreases, a prominent negative-to-positive transition of long-range correlation emerges for these eigenchannels. Finally, we demonstrate that this intriguing negative-to-positive transition originates from the characteristic transmission fluctuations of the eigenchannels. Our study provides valuable insights into the long-range correlation of scattered light in disordered media, constituting an important step toward advanced control of scattered light by manipulating the long-range correlation.

DOI
10.1103/physrevb.111.024202

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Long-range correlation characterizes the nondiffusive scattering paths of light through disordered media, playing an important role in the coherent control of multiply scattered light. Here, we report the long-range correlation of subsets of coherently interacting scattering paths, known as transmission eigenchannels. We find that the high-transmission eigenchannels exhibit a negative long-range correlation, in contrast to conventional positive long-range correlation. Moreover, when the transmission decreases, a prominent negative-to-positive transition of long-range correlation emerges for these eigenchannels. Finally, we demonstrate that this intriguing negative-to-positive transition originates from the characteristic transmission fluctuations of the eigenchannels. Our study provides valuable insights into the long-range correlation of scattered light in disordered media, constituting an important step toward advanced control of scattered light by manipulating the long-range correlation.
We have measured the correlation in frequency-dependent intensity fluctuations in the total transmission through random dielectric samples, using visible light in a (essentially) plane-wave geometry. The correlation function, of which the width at half maximum is proportional to ${\mathit{L}}^{\mathrm{\ensuremath{-}}2}$ (L is the thickness of the sample), decays as (\ensuremath{\Delta}\ensuremath{\omega}${)}^{\mathrm{\ensuremath{-}}1/2}$. This constitutes the experimental proof for the buildup of long-range intensity correlations in the propagation of classical waves by multiple scattering.
Understanding the complex interactions of the quantum light with different media provides valuable insights into potential applications in quantum tomography, microscopy, circuit and network design, and imaging. This thesis investigates quantum light interaction with two types of media: I. Random media entailing multiple scattering (Chapters 2-5), and II. Structured media, specifically designed to control quantum interferences (Chapters 6 and 7). In the first part of the thesis, and through solving the Lippmann-Schwinger equation for collections of small scatterers, a first principle scalar model for multiple scattering in finite-sized random media is developed. This efficient numerical model serves as the basis for investigating the coherent backscattering, a manifestation of weak localization in random media, for several bounded random media and various illuminations. Through employing mode expansion, next, the developed model is adapted to a general class of quantum-optical studies and quantum correlations are successfully derived and analyzed in scattering from finite disordered structures as well as systems of few scatterers. In multiple scattering of two-photon states in weak localization regime, the emergence of coherent two-photon backscattering is presented for the first time in coincidence detection, and it is demonstrated that quantum correlations can be used as a probe of entanglement dimensionality. Multiple scattering of two-photon states results in granular patterns known as speckle patterns. The statistical properties of single- and two-photon speckle patterns in scattering of different states are numerically calculated and the speckle visibilities and relevant parameters are derived. Specifically, the deviation of the probability density functions from negative exponential distributions, traditionally recognized as Rayleigh statistics in classical scattering, is identified, and shown to significantly depend on the presence of entanglement. Lastly, a different numerical implementation (based on COMSOL Multiphysics package) is used to consolidate our findings by incorporating the polarization effects. Coherent backscattering and coherent two-photon backscattering are observed for co-polarized fields in scattering from synthesized disordered media. It is demonstrated that depending on the particle exchange symmetry in polarization entangled excitation, the photons can exhibit statistical tendency to bunch together in the same mode, appear in separate modes (antibunching), or show a mixed response after multiple scattering. These bosonic-, fermionic-, and anyonic-like behaviors are studied in connection with coherent backscattering phenomenon, and it is demonstrated that the degree of enhancement in backscattering depends on the exchange symmetries. The simplicity and effectiveness of the implemented scattering analysis and the significance of the consequent conclusions suggest our approach as a promising platform for ‘numerical experiments’ without the limitations of analytical or semi-analytical models, and a practical tool prior to experiments. In the second part of the thesis, the random media operating as multimode platforms are replaced with engineered surfaces, i.e., metasurfaces, to realize targeted quantum interferences. First, a design roadmap for general lossy, asymmetric, and unbalanced coupling networks is presented, allowing to achieve maximum programmability in two-photon interferences. Next, two switchable metasurface-based coupling networks are designed to control nonclassical two-photon interferences via thermally driven crystallographic phase transitions. Numerical simulations confirm smooth transition between coalescence and anti-coalescence, aiming to address the current need in quantum optics for free-space compact devices creating tunable quantum interferences and acting as fast modulators for the second order quantum correlations. Our proposed compact and rapidly controllable devices pave the way towards new quantum applications as well as improving the current free-space quantum systems.
Structural disorder results in multiple scattering in real photonic crystals, which have been widely used for applications and studied for fundamental interests. The interaction of light with such complex photonic media is expected to show interplay between disorder and order. For a completely disordered medium, the intensity statistics is well-known to obey Rayleigh statistics with a negative exponential distribution function, corresponding to absence of correlations. Intensity statistics is unexplored however for complex media with both order and disorder. We study experimentally the intensity statistics of light reflected from photonic crystals with various degree of disorder. We observe deviations from the Rayleigh distribution and the deviations increase with increasing long-range order.
We analyze the scattering of light from dipolar emitters whose disordered positions exhibit correlations induced by static, long-range dipole-dipole interactions. The quantum-mechanical position correlations are calculated for zero-temperature bosonic atoms or molecules using variational and diffusion quantum Monte Carlo methods. For stationary atoms in dense ensembles in the limit of low light intensity, the simulations yield solutions for the optical responses to all orders of position correlation functions that involve electronic ground and excited states. We calculate how coherent and incoherent scattering, collective linewidths, line shifts, and eigenmodes, and disorder-induced excitation localization are influenced by the static interactions and the density. We find that dominantly repulsive static interactions in strongly confined oblate and prolate traps introduce short-range ordering among the dipoles, which curtails large fluctuations in the light-mediated resonant dipole-dipole interactions. This typically results in an increase in coherent reflection and optical depth, accompanied by reduced incoherent scattering. The presence of static dipolar interactions permits the highly selective excitation of subradiant eigenmodes in dense clouds. This effect becomes even more pronounced in a prolate trap, where the resonances narrow below the natural linewidth. When the static dipolar interactions affect the optical transition frequencies, the ensemble exhibits inhomogeneous broadening due to the nonuniformly experienced static dipolar interactions that suppress cooperative effects, but we argue that, e.g., for Dy atoms such inhomogeneous broadening is negligible. Published by the American Physical Society 2024