Incoherent Branched Flow of Light

Open Access

Incoherent Branched Flow of Light

Anatoly Patsyk, Yonatan Sharabi, Uri Sivan, and Mordechai Segev

Phys. Rev. X 12, 021007 – Published 11 April 2022

Abstract

Waves traveling in weakly disordered media possessing long-range correlations experience a universal phenomenon known as branched flow, where the waves split and form channels (branches) of enhanced intensity that keep dividing as the waves propagate. Branched flow effects have been studied experimentally in various systems, thus far always with coherent waves. We present the first experimental observation of branched flow of spatially incoherent light. We show that the primary effect of branching occurs for both coherent and incoherent light, but each pronounced branch is accompanied by sidelobes arising from interference, which disappear when the waves are incoherent. The position of the first caustic, where the branches reach peak intensity, remains the same as the coherence is reduced, but the branch statistics changes and some branches blur or disappear.

Received 15 November 2021
Accepted 9 February 2022

DOI:https://doi.org/10.1103/PhysRevX.12.021007

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Lasers Light-matter interaction Optical coherence Photonics

Atomic, Molecular & Optical

Authors & Affiliations

Anatoly Patsyk^1,3, Yonatan Sharabi^1,3, Uri Sivan^1,3, and Mordechai Segev ^1,2,3

¹Physics Department, Technion-Israel Institute of Technology, Haifa 3200003, Israel
²Electrical Engineering Department, Technion-Israel Institute of Technology, Haifa 3200003, Israel
³Solid State Institute and the Russell Berrie Nanotechnology Institute, Technion, Haifa 3200003, Israel

Popular Summary

Branched flow is a striking wave phenomenon, in which waves split into branching channels reminiscent of lightning and river deltas. It occurs when waves propagate through a weakly disordered potential with a correlation length longer than the wavelength. First observed in a 2D electron gas, it can occur in many types of waves including microwaves in resonators and laser light in thin soap membranes. Until now, however, all branched flow experiments have been with coherent waves. Here, we present the first experimental study of branched flow with waves lacking spatial coherence.

In our experiment, we shine laser light, whose spatial coherence we control with a rotating diffuser, into a thin film of liquid soap. The light propagating within the soap film experiences scattering from thickness variations that act as a 2D medium with a random (yet correlated) variation in the effective index of refraction. We find that branched flow with incoherent light is qualitatively different than with coherent light, displaying fewer branches and exhibiting a narrower intensity distribution, where the very-high- and very-low-intensity peaks are rare.

Our study elucidates the effect of coherence and interference on branched flow, allowing for the design of future experiments with partially coherent waves.

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Vol. 12, Iss. 2 — April - June 2022

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Images

Figure 1
(a) Experimental setup showing the main components, the path the light beam follows, and the imaging system. (b) Effective refractive index landscape of a soap film reconstructed using DNN from an image of the halogen light reflected from the film. (c) BF generated by a coherent plane wave. (d) BF generated by a localized source coupled to the film (the fiber tip seen on the left).
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Figure 2
Examples of branched flow patterns formed by (a) coherent plane wave, (b) coherent speckled beam generated by passing a coherent plane wave through a static diffuser, (c) partially-spatially-incoherent beam, generated by passing a coherent plane wave through the same diffuser while rotating.
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Figure 3
(a),(b) BF intensity patterns observed in the same region of the soap film for a coherent plane wave (a) and an incoherent wave (b). The two images demonstrate the smearing effect of incoherence smoothening the intensity pattern and concealing the coherent features. (c),(d) Intensity cross section taken along the full (c) and dashed (d) red lines in (a) and (b) (blue and red plots, respectively). The cross sections highlight the stark contrast between the two BF patterns. (e) Enlargement of the region marked in (c), highlighting the difference in the region surrounding each BF channel.
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Figure 4
(a)–(c) Intensity patterns produced by a single scatterer in (a) ray optics simulation and (b),(c) wave propagation simulations of an incident coherent and partially-spatially-incoherent beam in the paraxial approximation, respectively. (a) shows the ray structure of the scattered light forming caustics. (b) shows the main caustic lobes accompanied by weaker sidelobes and interference pattern. (c) shows two branches with no sidelobes and interference pattern. The main lobes are common to all three cases. (d),(e) Simulation of coherent and incoherent BF in a specific realization of refractive index landscape reconstructed from the experiment.
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Figure 5
(a) Probability distribution of coherent and incoherent BF intensity as observed in experiments and in simulations. The intensity distribution of BF is narrower for spatially incoherent light, and the probability to observe very high or low intensities is smaller than for the coherent waves. (b) The same data as in (a) on a $P [Log (I)] - Log (I / I_{mean})$ scale. The coherent distribution is broad, while the incoherent one is concentrated around the mean. (c) Scintillation index along the propagation direction calculated from experimental data. The similar peak position discloses that branching starts at the same distance for coherent and spatially incoherent light. The measured values in (c) are reduced (compared to the true values) by additional background light, which is inevitable when coupling a multimode (or incoherent) beam into a thin film. (d) Scintillation index calculated from simulations for coherent, speckled, and incoherent waves. Branching starts at the same distance for all cases, but the intensity fluctuations are markedly different.
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