- Letter
- Open Access
Non-self-similar light transport in scattering media
Phys. Rev. Research 6, L032026 – Published 31 July, 2024
DOI: https://doi.org/10.1103/PhysRevResearch.6.L032026
Abstract
Transport processes underpin a wide variety of phenomena, ranging from chemistry, to physics and ecology. Despite their pervasiveness, however, several distinctive features of these processes are still elusive, making it difficult to recognize and classify the associated transport regimes. Using light scattering as a probe to explore different propagation regimes, we report on the experimental observation of non-self-similar light transport through turbid membranes. Our results show that a breakdown of self-similarity can arise for light waves even in the presence of isotropic and homogeneous disorder, and can be tuned by varying the turbidity of the system. By introducing the concept of self-similarity for light propagation, we provide a unified framework for the classification of light transport regimes—overcoming the dichotomy between normal and anomalous diffusion—and show that non-self-similar propagation is a common and experimentally accessible phenomenon. This insight can help to understand and model other scenarios where light transport is dominated by rare propagation events, such as in nonlinear and active media, but also in other fields of research beyond optics.
Physics Subject Headings (PhySH)
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References (49)
- D. S. Wiersma, Disordered photonics, Nat. Photon. 7, 188 (2013).
- J. Bertolotti, K. Vynck, L. Pattelli, P. Barthelemy, S. Lepri, and D. S. Wiersma, Engineering disorder in superdiffusive Lévy glasses, Adv. Funct. Mater. 20, 965 (2010).
- L. Shi, Y. Zhang, B. Dong, T. Zhan, X. Liu, and J. Zi, Amorphous photonic crystals with only short-range order, Adv. Mater. 25, 5314 (2013).
- L. S. Froufe-Pérez, M. Engel, J. J. Sáenz, and F. Scheffold, Band gap formation and Anderson localization in disordered photonic materials with structural correlations, Proc. Natl. Acad. Sci. USA 114, 9570 (2017).
- L. D. Negro and S. Inampudi, Fractional transport of photons in deterministic aperiodic structures, Sci. Rep. 7, 2259 (2017).
- S. R. Sellers, W. Man, S. Sahba, and M. Florescu, Local self-uniformity in photonic networks, Nat. Commun. 8, 14439 (2017).
- S.-Y. Jeon, H. Kwon, and K. Hur, Intrinsic photonic wave localization in a three-dimensional icosahedral quasicrystal, Nat. Phys. 13, 363 (2017).
- G. J. Aubry, L. S. Froufe-Pérez, U. Kuhl, O. Legrand, F. Scheffold, and F. Mortessagne, Experimental tuning of transport regimes in hyperuniform disordered photonic materials, Phys. Rev. Lett. 125, 127402 (2020).
- A. Patsyk, U. Sivan, M. Segev, and M. A. Bandres, Observation of branched flow of light, Nature (London) 583, 60 (2020).
- S. Yu, C.-W. Qiu, Y. Chong, S. Torquato, and N. Park, Engineered disorder in photonics, Nat. Rev. Mater. 6, 226 (2021).
- K. Vynck, R. Pierrat, R. Carminati, L. S. Froufe-Pérez, F. Scheffold, R. Sapienza, S. Vignolini, and J. J. Sáenz, Light in correlated disordered media, Rev. Mod. Phys. 95, 045003 (2023).
- S. Rotter and S. Gigan, Light fields in complex media: Mesoscopic scattering meets wave control, Rev. Mod. Phys. 89, 015005 (2017).
- J. Böhm, A. Brandstötter, P. Ambichl, S. Rotter, and U. Kuhl, In situ realization of particlelike scattering states in a microwave cavity, Phys. Rev. A 97, 021801(R) (2018).
- H. Yılmaz, C. W. Hsu, A. Yamilov, and H. Cao, Transverse localization of transmission eigenchannels, Nat. Photon. 13, 352 (2019).
- P. Barthelemy, J. Bertolotti, K. Vynck, S. Lepri, and D. S. Wiersma, Role of quenching on superdiffusive transport in two-dimensional random media, Phys. Rev. E 82, 011101 (2010).
- P. Buonsante, R. Burioni, and A. Vezzani, Transport and scaling in quenched two-and three-dimensional Lévy quasicrystals, Phys. Rev. E 84, 021105 (2011).
- R. Savo, M. Burresi, T. Svensson, K. Vynck, and D. S. Wiersma, Walk dimension for light in complex disordered media, Phys. Rev. A 90, 023839 (2014).
- T. Svensson, K. Vynck, E. Adolfsson, A. Farina, A. Pifferi, and D. S. Wiersma, Light diffusion in quenched disorder: Role of step correlations, Phys. Rev. E 89, 022141 (2014).
- M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University Press, Cambridge, UK, 2006).
- A. Doicu and M. I. Mishchenko, Overview of methods for deriving the radiative transfer theory from the Maxwell equations. I: Approach based on the far-field Foldy equations, J. Quant. Spectrosc. Radiat. Transfer 220, 123 (2018).
- M. Leonetti and C. López, Measurement of transport mean-free path of light in thin systems, Opt. Lett. 36, 2824 (2011).
- L. Pattelli, G. Mazzamuto, D. S. Wiersma, and C. Toninelli, Diffusive light transport in semitransparent media, Phys. Rev. A 94, 043846 (2016).
- G. Mazzamuto, L. Pattelli, C. Toninelli, and D. Wiersma, Deducing effective light transport parameters in optically thin systems, New J. Phys. 18, 023036 (2016).
- R. Metzler, J.-H. Jeon, A. G. Cherstvy, and E. Barkai, Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking, Phys. Chem. Chem. Phys. 16, 24128 (2014).
- G. Muñoz-Gil, G. Volpe, M. A. Garcia-March, E. Aghion, A. Argun, C. B. Hong, T. Bland, S. Bo, J. A. Conejero, N. Firbas et al., Objective comparison of methods to decode anomalous diffusion, Nat. Commun. 12, 6253 (2021).
- R. Ferrari, A. Manfroi, and W. Young, Strongly and weakly self-similar diffusion, Physica D 154, 111 (2001).
- P. Castiglione, A. Mazzino, P. Muratore-Ginanneschi, and A. Vulpiani, On strong anomalous diffusion, Physica D 134, 75 (1999).
- K. Andersen, P. Castiglione, A. Mazzino, and A. Vulpiani, Simple stochastic models showing strong anomalous diffusion, Eur. Phys. J. B 18, 447 (2000).
- R. Artuso and G. Cristadoro, Anomalous transport: A deterministic approach, Phys. Rev. Lett. 90, 244101 (2003).
- D. N. Armstead, B. R. Hunt, and E. Ott, Anomalous diffusion in infinite horizon billiards, Phys. Rev. E 67, 021110 (2003).
- A. Rebenshtok, S. Denisov, P. Hänggi, and E. Barkai, Non-normalizable densities in strong anomalous diffusion: Beyond the central limit theorem, Phys. Rev. Lett. 112, 110601 (2014).
- E. Aghion, D. A. Kessler, and E. Barkai, Large fluctuations for spatial diffusion of cold atoms, Phys. Rev. Lett. 118, 260601 (2017).
- X. Wang, Y. Chen, and W. Deng, Strong anomalous diffusion in two-state process with Lévy walk and Brownian motion, Phys. Rev. Res. 2, 013102 (2020).
- J. Vollmer, L. Rondoni, M. Tayyab, C. Giberti, and C. Mejía-Monasterio, Displacement autocorrelation functions for strong anomalous diffusion: A scaling form, universal behavior, and corrections to scaling, Phys. Rev. Res. 3, 013067 (2021).
- P. Rampal, J. Weiss, D. Marsan, and M. Bourgoin, Arctic sea ice velocity field: General circulation and turbulent-like fluctuations, J. Geophys. Res. 114, C10014 (2009).
- N. Gal and D. Weihs, Experimental evidence of strong anomalous diffusion in living cells, Phys. Rev. E 81, 020903(R) (2010).
- D. Krapf, G. Campagnola, K. Nepal, and O. B. Peersen, Strange kinetics of bulk-mediated diffusion on lipid bilayers, Phys. Chem. Chem. Phys. 18, 12633 (2016).
- L. Pattelli, R. Savo, M. Burresi, and D. S. Wiersma, Spatio-temporal visualization of light transport in complex photonic structures, Light: Sci. Appl. 5, e16090 (2016).
- L. A. Cobus, G. Maret, and A. Aubry, Crossover from renormalized to conventional diffusion near the three-dimensional Anderson localization transition for light, Phys. Rev. B 106, 014208 (2022).
- L. Pattelli and G. Mazzamuto, Experimental imaging and Monte Carlo modeling of ultrafast pulse propagation in thin scattering slabs, J Biomed. Opt. 27, 083020 (2022).
- B. Wang, J. Kuo, S. C. Bae, and S. Granick, When Brownian diffusion is not Gaussian, Nat. Mater. 11, 481 (2012).
- D. Goldstein, T. Elhanan, M. Aronovitch, and D. Weihs, Origin of active transport in breast-cancer cells, Soft Matter 9, 7167 (2013).
- A. Gabrielski, G. Badin, and L. Kaleschke, Anomalous dispersion of sea ice in the Fram Strait region, J. Geophys. Res. 120, 1809 (2015).
- A. Vezzani, E. Barkai, and R. Burioni, Rare events in generalized Lévy walks and the big jump principle, Sci. Rep. 10, 2732 (2020).
- N. Levernier, O. Bénichou, and R. Voituriez, Universality classes of hitting probabilities of jump processes, Phys. Rev. Lett. 126, 100602 (2021).
- L. Régnier, M. Dolgushev, S. Redner, and O. Bénichou, Universal exploration dynamics of random walks, Nat. Commun. 14, 618 (2023).
- P. Barthelemy, J. Bertolotti, and D. S. Wiersma, A Lévy flight for light, Nature (London) 453, 495 (2008).
- R. Burioni, L. Caniparoli, and A. Vezzani, Lévy walks and scaling in quenched disordered media, Phys. Rev. E 81, 060101(R) (2010).
- F. Martelli, F. Tommasi, A. Sassaroli, L. Fini, and S. Cavalieri, Verification method of Monte Carlo codes for transport processes with arbitrary accuracy, Sci. Rep. 11, 19486 (2021).