Retrieving Time-Dependent Green’s Functions in Optics with Low-Coherence Interferometry

Badon, Amaury; Lerosey, Geoffroy; Boccara, Albert Claude; Fink, Mathias; Aubry, Alexandre

doi:10.1103/physrevlett.114.023901

Cited by 23 publications

(18 citation statements)

References 41 publications

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“…This property has been recently demonstrated in optics by retrieving the ballistic and multiple scattering components of the Green's function between individual scatterers [19]. Following this experimental proof-of-concept, we here investigate the case of strongly scattering media.…”

Section: (D)]: (I)mentioning

confidence: 99%

“…1(d)]: (i) A virtual light source of size l c located at point r emits a pulse of duration τ c ; (ii) A virtual pointlike receiver located at point r + ∆r records the time-resolved scattered wave-field. This property has been recently demonstrated in optics by retrieving the ballistic and multiple scattering components of the Green's function between individual scatterers [19]. Following this experimental proof-of-concept, we here investigate the case of strongly scattering media.…”

Section: Passive Measurement Of Time-dependent Green's Functionsmentioning

confidence: 99%

“…If the incident light is spatially and temporally incoherent, the time derivative of the correlation function C(r, r + ∆r, t) should converge towards the difference of the causal and anticausal Green's function [19], such that…”

Section: Passive Measurement Of Time-dependent Green's Functionsmentioning

confidence: 99%

“…The interference term is extracted from the four intensity patterns (Eq.1) recorded at α = 0, π/2, 3π/2 and π, as depicted in Fig.1(b) ("four phase method" [26]). It directly yields the correlation C of the scattered wave-field ψ:If the incident light is spatially and temporally incoherent, the time derivative of the correlation function C(r, r + ∆r, t) should converge towards the difference of the causal and anticausal Green's function [19], such thatwhere g(r, r + ∆r, t) is the time-dependent causal Green's function between a point source at r and a point detector r + ∆r. This fundamental result means that a passive correlation measurement mimics the following active experiment [see Fig.…”

mentioning

confidence: 99%

“…This method is based on the following fundamental result: The cross-correlation (or mutual coherence function) of an incoherent wave field measured at two points A and B can yield the time dependent Green's function g BA (t) between these two points [9][10][11][12]. Previously developed in seismology [13][14][15], in acoustics [16,17] and in the microwave regime [18], the Green's function estimation from the cross-correlations of a diffuse wave-field has been recently extended to optics [19]. A proof-of-concept experiment has demonstrated the passive measurement of time-dependent Green's functions between individual scatterers using low coherence interferometry.…”

Section: Introductionmentioning

confidence: 99%

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Spatio-temporal imaging of light transport in highly scattering media under white light illumination

Badon

Lerosey

et al. 2016

Optica

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Imaging the propagation of light in time and space is crucial in optics, notably for the study of complex media. We here demonstrate the passive measurement of time-dependent Green's functions between every point at the surface of a strongly scattering medium by means of low coherence interferometry. The experimental access to this Green's matrix is essential since it contains all the information about the complex trajectories of light within the medium. In particular, the spatio-temporal spreading of the diffusive halo and the coherent backscattering effect can be locally investigated in the vicinity of each point acting as a virtual source. On the one hand, this approach allows a quantitative imaging of the diffusion constant in the scattering medium with a spatial resolution of the order of a few transport mean free paths. On the other hand, our approach is able to reveal and quantify the anisotropy of light diffusion, which can be of great interest for optical characterization purposes. This study opens important perspectives both in optical diffuse tomography with potential applications to biomedical imaging and in fundamental physics for the experimental investigation of Anderson localization. INTRODUCTIONLight is the most common probe for investigating complex media at the mesoscopic scale as it offers both an excellent resolution and is non invasive at moderate energies. Nonetheless, due to the inhomogeneous distribution of refractive index, light suffers multiple scattering while propagating in or through the medium. Unveiling the complexity of light scattering is then necessary to retrieve the features of an object of interest or of the surrounding environment. In an inhomogeneous medium, it is a classical approach to consider a scattering sample as one realization of a random process, and study statistical physical quantities such as the mean intensity [1][2][3]. Under this approach, several physical parameters are relevant to characterize wave propagation in scattering media: the scattering mean-free path l s , the transport mean-free path l t , the diffusion constant D, the absorption length l a . Classical back scattering imaging techniques, such as optical coherence tomography, fail when multiple scattering predominates [4]. However, one can still measure the long-scale spatial variations of the diffusive parameters. The resulting image is not an image of the refractive index n(r) but e.g., of the diffusion constant D(r) with a resolution of the order of the transport mean free path l t , at best. In the literature, diffuse optical tomography is the gold standard technique to reconstruct the spatial distribution of transport parameters at each point of a volume from intensity measurements at the surface [5]. Unfortunately, this inverse problem is intrinsically nonlinear with respect to the optical properties of the medium. This method is thus computationally intensive and limited in terms of spatial resolution [6][7][8] (e.g. 5 mm in human soft tissues).In this paper, we propose a simple and effic...

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Section: (D)]: (I)mentioning

confidence: 99%

Section: Passive Measurement Of Time-dependent Green's Functionsmentioning

confidence: 99%

Section: Passive Measurement Of Time-dependent Green's Functionsmentioning

confidence: 99%

mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spatio-temporal imaging of light transport in highly scattering media under white light illumination

Badon

Lerosey

et al. 2016

Optica

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Fano Resonances in Topological Photonic Systems

Gorlach

Korobkin

et al. 2018

Springer Series in Optical Sciences

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Far-field probing of leaky topological states in all-dielectric metasurfaces

et al. 2018

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Topological phase transitions in condensed matter systems give rise to exotic states of matter such as topological insulators, superconductors, and superfluids. Photonic topological systems open a whole new realm of research and technological opportunities, exhibiting a number of important distinctions from their condensed matter counterparts. Photonic modes can leak into free space, which makes it possible to probe topological photonic phases by spectroscopic means via Fano resonances. Based on this idea, we develop a technique to retrieve the topological properties of all-dielectric metasurfaces from the measured far-field scattering characteristics. Collected angle-resolved spectra provide the momentum-dependent frequencies and lifetimes of the photonic modes that enable the retrieval of the effective Hamiltonian and extraction of the topological invariant. Our results demonstrate how the topological states of open non-Hermitian systems can be explored via far-field measurements, thus paving a way to the design of metasurfaces with unique scattering characteristics controlled via topological effects.

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Retrieving Time-Dependent Green’s Functions in Optics with Low-Coherence Interferometry

Cited by 23 publications

References 41 publications

Spatio-temporal imaging of light transport in highly scattering media under white light illumination

Spatio-temporal imaging of light transport in highly scattering media under white light illumination

Fano Resonances in Topological Photonic Systems

Far-field probing of leaky topological states in all-dielectric metasurfaces

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