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Light in correlated disordered media

Kevin Vynck*, Romain Pierrat, Rémi Carminati†, Luis S. Froufe-Pérez, Frank Scheffold‡, Riccardo Sapienza, Silvia Vignolini, and Juan José Sáenz

Kevin Vynck*

  • Université de Bordeaux, Institut d’Optique Graduate School, CNRS, Laboratoire Photonique Numérique et Nanosciences (LP2N), F-33400 Talence, France and Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière (iLM), F-69622 Villeurbanne, France

Romain Pierrat

  • Institut Langevin, ESPCI Paris, Université PSL, CNRS, F-75005 Paris, France

Rémi Carminati†

  • Institut Langevin, ESPCI Paris, Université PSL, CNRS, F-75005 Paris, France and Institut d’Optique Graduate School, Université Paris–Saclay, F-91127 Palaiseau, France

Luis S. Froufe-Pérez and Frank Scheffold‡

  • Physics Department, University of Fribourg, CH-1700 Fribourg, Switzerland

Riccardo Sapienza

  • Imperial College London, Blackett Laboratory, London SW7 2AZ, United Kingdom

Silvia Vignolini

  • Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom

Juan José Sáenz

  • Donostia International Physics Center (DIPC), 20018 Donostia–San Sebastian, Spain and Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain

  • *kevin.vynck@univ-lyon1.fr
  • †remi.carminati@espci.psl.eu
  • ‡frank.scheffold@unifr.ch
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Rev. Mod. Phys. 95, 045003 – Published 15 November, 2023

DOI: https://doi.org/10.1103/RevModPhys.95.045003

Abstract

The optics of correlated disordered media is a conceptually rich research topic emerging at the interface between the physics of waves in complex media and nanophotonics. Inspired by photonic structures in nature and enabled by advances in nanofabrication processes, recent investigations have unveiled how the design of structural correlations down to the subwavelength scale could be exploited to control the scattering, transport, and localization of light in matter. From optical transparency to superdiffusive light transport to photonic gaps, the optics of correlated disordered media challenges our physical intuition and offers new perspectives for applications. This review examines the theoretical foundations, state-of-the-art experimental techniques, and major achievements in the study of light interaction with correlated disorder, covering a wide range of systems: from short-range correlated photonic liquids to Lévy glasses containing fractal heterogeneities to hyperuniform disordered photonic materials. The mechanisms underlying light scattering and transport phenomena are elucidated on the basis of rigorous theoretical arguments. Ongoing research on mesoscopic phenomena such as transport phase transitions and speckle statistics and the current development of disorder engineering for applications such as light-energy management and visual appearance design are overviewed. Finally, special efforts are made to identify the main theoretical and experimental challenges to address in the near future.

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References (628)

  1. Abrahams, E., 2010, 50 years of Anderson Localization, Vol. 24 (World Scientific, Singapore).
  2. Abrahams, E., P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, 1979, “Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions,” Phys. Rev. Lett. 42, 673.
  3. Acquista, C., 1976, “Light scattering by tenuous particles: A generalization of the Rayleigh-Gans-Rocard approach,” Appl. Opt. 15, 2932–2936.
  4. Aeby, S., G. J. Aubry, L. S. Froufe-Pérez, and F. Scheffold, 2022, “Fabrication of hyperuniform dielectric networks via heat-induced shrinkage reveals a bandgap at telecom wavelengths,” Adv. Opt. Mater. 10, 2200232.
  5. Aeby, S., G. J. Aubry, N. Muller, and F. Scheffold, 2021, “Scattering from controlled defects in woodpile photonic crystals,” Adv. Opt. Mater. 9, 2001699.
  6. Akkermans, E., and G. Montambaux, 2007, Mesoscopic Physics of Electrons and Photons (Cambridge University Press, Cambridge, England).
  7. Akkermans, E., P. E. Wolf, and R. Maynard, 1986, “Coherent Backscattering of Light by Disordered Media: Analysis of the Peak Line Shape,” Phys. Rev. Lett. 56, 1471.
  8. Akkermans, E., P. E. Wolf, R. Maynard, and G. Maret, 1988, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98.
  9. Alerstam, E., T. Svensson, and S. Andersson-Engels, 2008, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13, 060504.
  10. Allain, C., and M. Cloitre, 1991, “Characterizing the lacunarity of random and deterministic fractal sets,” Phys. Rev. A 44, 3552.
  11. Altissimo, M., 2010, “E-beam lithography for micro-/nanofabrication,” Biomicrofluidics 4, 026503.
  12. Altshuler, B. L’vovich, P. A. Lee, and R. A. Webb, 2012, Eds., Mesoscopic Phenomena in Solids (Elsevier, New York).
  13. Anderson, J. A., C. D. Lorenz, and A. Travesset, 2008, “General purpose molecular dynamics simulations fully implemented on graphics processing units,” J. Comput. Phys. 227, 5342–5359.
  14. Anderson, P. W., 1958, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492.
  15. Anderson, P. W., 1985, “The question of classical localization: A theory of white paint?,” Philos. Mag. B 52, 505–509.
  16. Andkjær, J., V. E. Johansen, K. S. Friis, and O. Sigmund, 2014, “Inverse design of nanostructured surfaces for color effects,” J. Opt. Soc. Am. B 31, 164–174.
  17. Apostol, A., and A. Dogariu, 2003, “Spatial Correlations in the Near Field of Random Media,” Phys. Rev. Lett. 91, 093901.
  18. Apostol, A., and A. Dogariu, 2004, “First-and second-order statistics of optical near fields,” Opt. Lett. 29, 235–237.
  19. Apresyan, L. A., and Y. A. Kravtsov, 1996, Radiation Transfer: Statistical and Wave Aspects (Gordon and Breach, Amsterdam).
  20. Araújo, M. O., T. Passerat de Silans, and R. Kaiser, 2021, “Lévy flights of photons with infinite mean free path,” Phys. Rev. E 103, L010101.
  21. Ardakani, A. G., and M. G. Nezhadhaghighi, 2015, “Controlling Anderson localization in disordered heterostructures with Lévy-type distribution,” J. Opt. 17, 105601.
  22. Asatryan, A. A., P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martijn de Sterke, 1999, “Effects of disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E 60, 6118.
  23. Astratov, V. N., A. M. Adawi, S. Fricker, M. S. Skolnick, D. M. Whittaker, and P. N. Pusey, 2002, “Interplay of order and disorder in the optical properties of opal photonic crystals,” Phys. Rev. B 66, 165215.
  24. Astratov, V. N., V. N. Bogomolov, A. A. Kaplyanskii, A. V. Prokofiev, L. A. Samoilovich, S. M. Samoilovich, and Yu. A. Vlasov, 1995, “Optical spectroscopy of opal matrices with CdS embedded in its pores: Quantum confinement and photonic band gap effects,” Nuovo Cimento Soc. Ital. Fis. 17D, 1349–1354.
  25. Aubry, G. J., L. S. Froufe-Pérez, U. Kuhl, O. Legrand, F. Scheffold, and F. Mortessagne, 2020, “Experimental Tuning of Transport Regimes in Hyperuniform Disordered Photonic Materials,” Phys. Rev. Lett. 125, 127402.
  26. Aubry, G. J., L. Schertel, M. Chen, H. Weyer, C. M. Aegerter, S. Polarz, H. Cölfen, and G. Maret, 2017, “Resonant transport and near-field effects in photonic glasses,” Phys. Rev. A 96, 043871.
  27. Audic, S., and H. Frisch, 1993, “Monte-Carlo simulation of a radiative transfer problem in a random medium: Application to a binary mixture,” J. Quant. Spectrosc. Radiat. Transfer 50, 127–147.
  28. Auzinger, T., W. Heidrich, and B. Bickel, 2018, “Computational design of nanostructural color for additive manufacturing,” ACM Trans. Graph. 37, 1–16.
  29. Bahadur, J., A. P. Radlinski, Y. B. Melnichenko, M. Mastalerz, and A. Schimmelmann, 2015, “Small-angle and ultrasmall-angle neutron scattering (SANS/USANS) study of New Albany shale: A treatise on microporosity,” Energy Fuels 29, 567–576.
  30. Barabanenkov, Y. N., and V. M. Finkel’berg, 1968, “Radiation transport equation for correlated scatterers,” Sov. Phys. JETP 26, 587–591, http://jetp.ras.ru/cgi-bin/e/index/e/26/3/p587?a=list.
  31. Barabanenkov, Y. N., L. Zurk, and M. Y. Barabanenkov, 1995, “Poynting’s theorem and electromagnetic wave multiple scattering in dense media near resonance: Modified radiative transfer equation,” J. Electromagn. Waves Appl. 9, 1393–1420.
  32. Barabanenkov, Yu. N., and V. D. Ozrin, 1995, “Diffusion asymptotics of the Bethe-Salpeter equation for electromagnetic waves in discrete random media,” Phys. Lett. A 206, 116–122.
  33. Barkema, G. T., and N. Mousseau, 2000, “High-quality continuous random networks,” Phys. Rev. B 62, 4985.
  34. Barthelemy, P., J. Bertolotti, K. Vynck, S. Lepri, and D. S. Wiersma, 2010, “Role of quenching on superdiffusive transport in two-dimensional random media,” Phys. Rev. E 82, 011101.
  35. Barthelemy, P., J. Bertolotti, and D. S. Wiersma, 2008, “A Lévy flight for light,” Nature (London) 453, 495.
  36. Bartumeus, F., M. G. E. da Luz, G. M. Viswanathan, and J. Catalan, 2005, “Animal search strategies: A quantitative random-walk analysis,” Ecology 86, 3078–3087.
  37. Batten, R. D., F. H. Stillinger, and S. Torquato, 2008, “Classical disordered ground states: Super-ideal gases and stealth and equi-luminous materials,” J. Appl. Phys. 104, 033504.
  38. Baudouin, Q., R. Pierrat, A. Eloy, E. J. Nunes-Pereira, P.-A. Cuniasse, N. Mercadier, and R. Kaiser, 2014, “Signatures of Lévy flights with annealed disorder,” Phys. Rev. E 90, 052114.
  39. Baum, C. E., 1976, “The singularity expansion method,” in Transient Electromagnetic Fields, Topics in Applied Physics Vol. 10, edited by L. B. Felsen (Springer, New York), pp. 129–179.
  40. Baus, M., and J.-L. Colot, 1987, “Thermodynamics and structure of a fluid of hard rods, disks, spheres, or hyperspheres from rescaled virial expansions,” Phys. Rev. A 36, 3912.
  41. Bedeaux, D., and P. Mazur, 1973, “On the critical behaviour of the dielectric constant for a nonpolar fluid,” Physica (Amsterdam) 67, 23–54.
  42. Bedeaux, D., M. M. Wind, and M. A. van Dijk, 1987, “The effective dielectric constant of a dispersion of clustering spheres,” Z. Phys. B 68, 343–354.
  43. Beenakker, C. W. J., C. W. Groth, and A. R. Akhmerov, 2009, “Nonalgebraic length dependence of transmission through a chain of barriers with a Lévy spacing distribution,” Phys. Rev. B 79, 024204.
  44. Behrens, D. J., 1949, “The effect of holes in a reacting material on the passage of neutrons,” Proc. Phys. Soc. London Sect. A 62, 607.
  45. Bellando, L., A. Gero, E. Akkermans, and R. Kaiser, 2014, “Cooperative effects and disorder: A scaling analysis of the spectrum of the effective atomic Hamiltonian,” Phys. Rev. A 90, 063822.
  46. Ben-Avraham, D., and S. Havlin, 2000, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, Cambridge, England).
  47. Benedek, G. B., 1971, “Theory of transparency of the eye,” Appl. Opt. 10, 459–473.
  48. Benzaouia, M., G. Tokić, O. D. Miller, D. K. P. Yue, and S. G. Johnson, 2019, “From Solar Cells to Ocean Buoys: Wide-Bandwidth Limits to Absorption by Metaparticle Arrays,” Phys. Rev. Appl. 11, 034033.
  49. Bergman, M. J., C. García-Astrain, N. Fuchs, K. Manne, P. Yazhgur, L. S. Froufe-Pérez, L. M. Liz-Marzán, and F. Scheffold, 2022, “Macroporous silica foams fabricated via soft colloid templating,” Small Methods 6, 2101491.
  50. Berry, R. S., J. Jellinek, and G. Natanson, 1984, “Melting of clusters and melting,” Phys. Rev. A 30, 919.
  51. Bertolotti, J., K. Vynck, L. Pattelli, P. Barthelemy, S. Lepri, and D. S. Wiersma, 2010, “Engineering disorder in superdiffusive Lévy glasses,” Adv. Funct. Mater. 20, 965–968.
  52. Bertolotti, J., K. Vynck, and D. S. Wiersma, 2010, “Multiple Scattering of Light in Superdiffusive Media,” Phys. Rev. Lett. 105, 163902.
  53. Bertrand, M., A. Devilez, J.-P. Hugonin, P. Lalanne, and K. Vynck, 2020, “Global polarizability matrix method for efficient modeling of light scattering by dense ensembles of non-spherical particles in stratified media,” J. Opt. Soc. Am. A 37, 70–83.
  54. Bibette, J., T. G. Mason, H. Gang, D. A. Weitz, and P. Poulin, 1993, “Structure of adhesive emulsions,” Langmuir 9, 3352–3356.
  55. Bicout, D., and C. Brosseau, 1992, “Multiply scattered waves through a spatially random medium: Entropy production and depolarization,” J. Phys. I (France) 2, 2047–2063.
  56. Bigourdan, F., R. Pierrat, and R. Carminati, 2019, “Enhanced absorption of waves in stealth hyperuniform disordered media,” Opt. Express 27, 8666–8682.
  57. Birowosuto, M. D., S. E. Skipetrov, W. L. Vos, and A. P. Mosk, 2010, “Observation of Spatial Fluctuations of the Local Density of States in Random Photonic Media,” Phys. Rev. Lett. 105, 013904.
  58. Bitterli, B., S. Ravichandran, T. Müller, M. Wrenninge, J. Novák, S. Marschner, and W. Jarosz, 2018, “A radiative transfer framework for non-exponential media,” Dartmouth College Computer Science Technical Report No. TR2018-841.
  59. Bohren, C. F., 2009, “Do extended effective-medium formulas scale properly?,” J. Nanophoton. 3, 039501.
  60. Bohren, C. F., and D. R. Huffman, 2008, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, New York).
  61. Boissé, P., 1990, “Radiative transfer inside clumpy media—The penetration of UV photons inside molecular clouds,” Astron. Astrophys. 228, 483–502, https://ui.adsabs.harvard.edu/abs/1990A%26A...228..483B/abstract.
  62. Borovoi, A., 2002, “On the extinction of radiation by a homogeneous but spatially correlated random medium: Comment,” J. Opt. Soc. Am. A 19, 2517–2520.
  63. Bossard, J. A., L. Lin, and D. H. Werner, 2016, “Evolving random fractal cantor superlattices for the infrared using a genetic algorithm,” J. R. Soc. Interface 13, 20150975.
  64. Böttcher, C. J. F., O. C. van Belle, P. Bordewijk, and A. Rip, 1978, Theory of Electric Polarization, Vol. 2 (Elsevier, New York).
  65. Bozzola, A., M. Liscidini, and L. C. Andreani, 2014, “Broadband light trapping with disordered photonic structures in thin-film silicon solar cells,” Prog. Photovoltaics 22, 1237–1245.
  66. Briant, C. L., and J. J. Burton, 1975, “Molecular dynamics study of the structure and thermodynamic properties of argon microclusters,” J. Chem. Phys. 63, 2045–2058.
  67. Brooks, B. R., et al., 2009, “charmm: The biomolecular simulation program,” J. Comput. Chem. 30, 1545–1614.
  68. Brown, J. C., P. N. Pusey, J. W. Goodwin, and R. H. Ottewill, 1975, “Light scattering study of dynamic and time-averaged correlations in dispersions of charged particles,” J. Phys. A 8, 664.
  69. Bruggeman, D. A. G., 1935, “Berechnung verschiedener physikalischer konstanten von heterogenen substanzen. I. Dielektrizitätskonstanten und leitfähigkeiten der mischkörper aus isotropen substanzen,” Ann. Phys. (Berlin) 416, 636–664.
  70. Buonsante, P., R. Burioni, and A. Vezzani, 2011, “Transport and scaling in quenched two-and three-dimensional Lévy quasicrystals,” Phys. Rev. E 84, 021105.
  71. Burg, S. L., et al., 2019, “Liquid-liquid phase separation morphologies in ultra-white beetle scales and a synthetic equivalent,” Commun. Chem. 2, 100.
  72. Burioni, R., L. Caniparoli, and A. Vezzani, 2010, “Lévy walks and scaling in quenched disordered media,” Phys. Rev. E 81, 060101.
  73. Burioni, R., S. di Santo, S. Lepri, and A. Vezzani, 2012, “Scattering lengths and universality in superdiffusive Lévy materials,” Phys. Rev. E 86, 031125.
  74. Burioni, R., E. Ubaldi, and A. Vezzani, 2014, “Superdiffusion and transport in two-dimensional systems with Lévy-like quenched disorder,” Phys. Rev. E 89, 022135.
  75. Burresi, M., L. Cortese, L. Pattelli, M. Kolle, P. Vukusic, D. S. Wiersma, U. Steiner, and S. Vignolini, 2014, “Bright-white beetle scales optimise multiple scattering of light,” Sci. Rep. 4, 6075.
  76. Burresi, M., V. Radhalakshmi, R. Savo, J. Bertolotti, K. Vynck, and D. S. Wiersma, 2012, “Weak Localization of Light in Superdiffusive Random Systems,” Phys. Rev. Lett. 108, 110604.
  77. Busch, K., and C. M. Soukoulis, 1995, “Transport Properties of Random Media: A New Effective Medium Theory,” Phys. Rev. Lett. 75, 3442.
  78. Caixeiro, S., M. Gaio, B. Marelli, F. G. Omenetto, and R. Sapienza, 2016, “Silk-based biocompatible random lasing,” Adv. Opt. Mater. 4, 998–1003.
  79. Canaguier-Durand, A., R. Pierrat, and R. Carminati, 2019, “Cross density of states and mode connectivity: Probing wave localization in complex media,” Phys. Rev. A 99, 013835.
  80. Cao, H., 2005, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497.
  81. Cao, H., and Y. Eliezer, 2022, “Harnessing disorder for photonic device applications,” Appl. Phys. Rev. 9, 011309.
  82. Carminati, R., 2010, “Subwavelength spatial correlations in near-field speckle patterns,” Phys. Rev. A 81, 053804.
  83. Carminati, R., A. Cazé, D. Cao, F. Peragut, V. Krachmalnicoff, R. Pierrat, and Y. De Wilde, 2015, “Electromagnetic density of states in complex plasmonic systems,” Surf. Sci. Rep. 70, 1–41.
  84. Carminati, R., and J. C. Schotland, 2021, Principles of Scattering and Transport of Light (Cambridge University Press, Cambridge, England).
  85. Casasanta, G., and R. Garra, 2018, “Towards a generalized Beer-Lambert law,” Fractal Fract. 2, 8.
  86. Cazé, A., R. Pierrat, and R. Carminati, 2010, “Near-field interactions and nonuniversality in speckle patterns produced by a point source in a disordered medium,” Phys. Rev. A 82, 043823.
  87. Cazé, A., R. Pierrat, and R. Carminati, 2013, “Spatial Coherence in Complex Photonic and Plasmonic Systems,” Phys. Rev. Lett. 110, 063903.
  88. Chabanov, A. A., M. Stoytchev, and A. Z. Genack, 2000, “Statistical signatures of photon localization,” Nature (London) 404, 850–853.
  89. Chan, C. L. C., M. M. Bay, G. Jacucci, R. Vadrucci, C. A. Williams, G. T. van de Kerkhof, R. M. Parker, K. Vynck, B. Frka-Petesic, and S. Vignolini, 2019, “Visual appearance of chiral nematic cellulose-based photonic films: Angular and polarization independent color response with a twist,” Adv. Mater. 31, 1905151.
  90. Chan, C. T., Q. L. Yu, and K. M. Ho, 1995, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16635.
  91. Chan, Y. S., C. T. Chan, and Z. Y. Liu, 1998, “Photonic Band Gaps in Two Dimensional Photonic Quasicrystals,” Phys. Rev. Lett. 80, 956.
  92. Chandler, C. J., B. D. Wilts, J. Brodie, and S. Vignolini, 2017, “Structural color in marine algae,” Adv. Opt. Mater. 5, 1600646.
  93. Chandrasekhar, S., 1960, Radiative Transfer (Dover, New York).
  94. Chang, Y., Y. Ogawa, G. Jacucci, O. D. Onelli, H.-Y. Tseng, and S. Vignolini, 2020, “Hereditary character of photonics structure in Pachyrhynchus sarcitis weevils: Color changes via one generation hybridization,” Adv. Opt. Mater. 8, 2000432.
  95. Chehadi, Z., M. Bouabdellaoui, M. Modaresialam, T. Bottein, M. Salvalaglio, M. Bollani, D. Grosso, and M. Abbarchi, 2021, “Scalable disordered hyperuniform architectures via nanoimprint lithography of metal oxides,” ACS Appl. Mater. Interfaces 13, 37761–37774.
  96. Chen, Y., F. Sgrignuoli, Y. Zhu, T. Shubitidze, and L. Dal Negro, 2023, “Enhanced wave localization in multifractal scattering media,” Phys. Rev. B 107, 054201.
  97. Cherroret, N., D. Delande, and B. A. van Tiggelen, 2016, “Induced dipole-dipole interactions in light diffusion from point dipoles,” Phys. Rev. A 94, 012702.
  98. Ching, E. S. C., P. T. Leung, A. Maassen van den Brink, W. M. Suen, S. S. Tong, and K. Young, 1998, “Quasinormal-mode expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545.
  99. Chung, K., et al., 2012, “Flexible, angle-independent, structural color reflectors inspired by morpho butterfly wings,” Adv. Mater. 24, 2375–2379.
  100. Cobus, L. A., G. Maret, and A. Aubry, 2022, “Crossover from renormalized to conventional diffusion near the three-dimensional Anderson localization transition for light,” Phys. Rev. B 106, 014208.
  101. Conley, G. M., M. Burresi, F. Pratesi, K. Vynck, and D. S. Wiersma, 2014, “Light Transport and Localization in Two-Dimensional Correlated Disorder,” Phys. Rev. Lett. 112, 143901.
  102. Conti, C., and A. Fratalocchi, 2008, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4, 794.
  103. Contini, D., F. Martelli, and G. Zaccanti, 1997, “Photon migration through a turbid slab described by a model based on diffusion approximation. I. theory,” Appl. Opt. 36, 4587–4599.
  104. Cortese, L., L. Pattelli, F. Utel, S. Vignolini, M. Burresi, and D. S. Wiersma, 2015, “Anisotropic light transport in white beetle scales,” Adv. Opt. Mater. 3, 1337–1341.
  105. Cruzan, O. R., 1962, “Translational addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40.
  106. Dalichaouch, R., J. P. Armstrong, S. Schultz, P. M. Platzman, and S. L. McCall, 1991, “Microwave localization by two-dimensional random scattering,” Nature (London) 354, 53–55.
  107. Dal Negro, L., 2022, Waves in Complex Media (Cambridge University Press, Cambridge, England).
  108. Davis, A., and A. Marshak, 1997, “Lévy kinetics in slab geometry: Scaling of transmission probability,” in Fractal Frontiers, edited by T. G. Dewey and M. M. Novak (World Scientific, Singapore), pp. 63–72.
  109. Davis, A. B., and A. Marshak, 2004, “Photon propagation in heterogeneous optical media with spatial correlations: Enhanced mean-free-paths and wider-than-exponential free-path distributions,” J. Quant. Spectrosc. Radiat. Transfer 84, 3–34.
  110. Davis, A. B., and M. Mineev-Weinstein, 2008, “Radiation transport through random media represented as measurable functions: Positive versus negative spatial correlations,” in Proceedings of the International Conference on Mathematics Computational Methods and Reactor Physics (M&C 2009), Saratoga Springs, NY, 2009 (Los Alamos National Laboratory, Technical Report No. LA-UR-08-07249).
  111. de Boer, J., 1949, “Molecular distribution and equation of state of gases,” Rep. Prog. Phys. 12, 305.
  112. Defienne, H., M. Barbieri, I. A. Walmsley, B. J. Smith, and S. Gigan, 2016, “Two-photon quantum walk in a multimode fiber,” Sci. Adv. 2, e1501054.
  113. Demirörs, A. F., et al., 2022, “Three-dimensional printing of photonic colloidal glasses into objects with isotropic structural color,” Nat. Commun. 13, 4397.
  114. Denk, W., J. H. Strickler, and W. W. Webb, 1990, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76.
  115. d’Eon, E., 2018, “A reciprocal formulation of nonexponential radiative transfer. 1: Sketch and motivation,” J. Comput. Theor. Transp. 47, 84–115.
  116. d’Eon, E., 2022, “A hitchhiker’s guide to multiple scattering,” http://www.eugenedeon.com/project/hitchhikers/ (accessed December 21, 2022).
  117. Deparis, O., N. Khuzayim, A. Parker, and J. P. Vigneron, 2009, “Assessment of the antireflection property of moth wings by three-dimensional transfer-matrix optical simulations,” Phys. Rev. E 79, 041910.
  118. De Raedt, H., A. D. Lagendijk, and P. de Vries, 1989, “Transverse Localization of Light,” Phys. Rev. Lett. 62, 47.
  119. de Sousa, N., J. J. Sáenz, Antonio García-Martín, Luis S. Froufe-Pérez, and M. I. Marqués, 2014, “Effect of long-range spatial correlations on the lifetime statistics of an emitter in a two-dimensional disordered lattice,” Phys. Rev. A 89, 063830.
  120. de Sousa, N., J. J. Sáenz, F. Scheffold, A. García-Martín, and L. S. Froufe-Pérez, 2016a, “Fluctuations of the electromagnetic local density of states as a probe for structural phase switching,” Phys. Rev. A 94, 043832.
  121. de Sousa, N., J. J. Sáenz, F. Scheffold, A. García-Martín, and L. S. Froufe-Pérez, 2016b, “Self-diffusion and structural properties of confined fluids in dynamic coexistence,” J. Phys. Condens. Matter 28, 135101.
  122. Deubel, M., G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, 2004, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444.
  123. Dintinger, J., S. Mühlig, C. Rockstuhl, and T. Scharf, 2012, “A bottom-up approach to fabricate optical metamaterials by self-assembled metallic nanoparticles,” Opt. Mater. Express 2, 269–278.
  124. Dogariu, A., and R. Carminati, 2015, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29.
  125. Dogariu, A., J. Uozumi, and T. Asakura, 1992, “Enhancement of the backscattered intensity from fractal aggregates,” Waves Random Media 2, 259–263.
  126. Dogariu, A., J. Uozumi, and T. Asakura, 1996, “Enhancement factor in the light backscattered by fractal aggregated media,” Opt. Rev. 3, 71–82.
  127. Donev, A., F. H. Stillinger, and S. Torquato, 2005, “Unexpected Density Fluctuations in Jammed Disordered Sphere Packings,” Phys. Rev. Lett. 95, 090604.
  128. Dong, B. Q., X. H. Liu, T. R. Zhan, L. P. Jiang, H. W. Yin, F. Liu, and J. Zi, 2010, “Structural coloration and photonic pseudogap in natural random close-packing photonic structures,” Opt. Express 18, 14430–14438.
  129. Donie, Y. J., et al., 2021, “Phase-separated nanophotonic structures by inkjet printing,” ACS Nano 15, 7305–7317.
  130. Doty, P., and R. F. Steiner, 1952, “Macro-ions. I. Light scattering theory and experiments with bovine serum albumin,” J. Chem. Phys. 20, 85–94.
  131. Doyle, W. T., 1989, “Optical properties of a suspension of metal spheres,” Phys. Rev. B 39, 9852.
  132. Draine, B. T., and P. J. Flatau, 1994, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499.
  133. Dufresne, E. R., H. Noh, V. Saranathan, S. G. J. Mochrie, H. Cao, and R. O. Prum, 2009, “Self-assembly of amorphous biophotonic nanostructures by phase separation,” Soft Matter 5, 1792–1795.
  134. Durant, S., O. Calvo-Perez, N. Vukadinovic, and J.-J. Greffet, 2007, “Light scattering by a random distribution of particles embedded in absorbing media: Diagrammatic expansion of the extinction coefficient,” J. Opt. Soc. Am. A 24, 2943–2952.
  135. Duyens, L. N. M., 1956, “The flattering of the absorption spectrum of suspensions, as compared to that of solutions,” Biochim. Biophys. Acta 19, 1–12.
  136. Dyson, F. J., 1949a, “The radiation theories of Tomonaga, Schwinger, and Feynman,” Phys. Rev. 75, 486.
  137. Dyson, F. J., 1949b, “The s matrix in quantum electrodynamics, Phys. Rev. 75, 1736.
  138. Edagawa, K., 2014, “Photonic crystals, amorphous materials, and quasicrystals,” Sci. Technol. Adv. Mater. 15, 034805.
  139. Edagawa, K., S. Kanoko, and M. Notomi, 2008, “Photonic Amorphous Diamond Structure with a 3D Photonic Band Gap,” Phys. Rev. Lett. 100, 013901.
  140. Egel, A., K. M. Czajkowski, D. Theobald, K. Ladutenko, A. S. Kuznetsov, and L. Pattelli, 2021, “smuthi: A python package for the simulation of light scattering by multiple particles near or between planar interfaces,” J. Quant. Spectrosc. Radiat. Transfer 273, 107846.
  141. Egel, A., L. Pattelli, G. Mazzamuto, D. S. Wiersma, and U. Lemmer, 2017, “celes: cuda-accelerated simulation of electromagnetic scattering by large ensembles of spheres,” J. Quant. Spectrosc. Radiat. Transfer 199, 103–110.
  142. Einstein, A., 1910, “Theorie der opaleszenz von homogenen flüssigkeiten und flüssigkeitsgemischen in der nähe des kritischen zustandes,” Ann. Phys. (Berlin) 338, 1275–1298.
  143. Emiliani, V., F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, 2003, “Near-Field Short Range Correlation in Optical Waves Transmitted through Random Media,” Phys. Rev. Lett. 90, 250801.
  144. Escalante, J. M., and S. E. Skipetrov, 2017, “Longitudinal optical fields in light scattering from dielectric spheres and Anderson localization of light,” Ann. Phys. (Berlin) 529, 1700039.
  145. Evers, F., and A. D. Mirlin, 2008, “Anderson transitions,” Rev. Mod. Phys. 80, 1355.
  146. Fahr, S., C. Rockstuhl, and F. Lederer, 2008, “Engineering the randomness for enhanced absorption in solar cells,” Appl. Phys. Lett. 92, 171114.
  147. Fayard, N., A. Caze, R. Pierrat, and R. Carminati, 2015, “Intensity correlations between reflected and transmitted speckle patterns,” Phys. Rev. A 92, 033827.
  148. Fazio, B., et al., 2016, “Strongly enhanced light trapping in a two-dimensional silicon nanowire random fractal array,” Light Sci. Appl. 5, e16062–e16062.
  149. Felderhof, B. U., 1974, “On the propagation and scattering of light in fluids,” Physica (Amsterdam) 76, 486–502.
  150. Fernández del Río, L., H. Arwin, and K. Järrendahl, 2016, “Polarizing properties and structure of the cuticle of scarab beetles from the Chrysina genus,” Phys. Rev. E 94, 012409.
  151. Fernández-Marín, A. A., J. A. Méndez-Bermúdez, J. Carbonell, F. Cervera, J. Sánchez-Dehesa, and V. A. Gopar, 2014, “Beyond Anderson Localization in 1D: Anomalous Localization of Microwaves in Random Waveguides,” Phys. Rev. Lett. 113, 233901.
  152. Fikioris, J. G., and P. C. Waterman, 1964, “Multiple scattering of waves. II. ‘Hole corrections’ in the scalar case,” J. Math. Phys. (N.Y.) 5, 1413–1420.
  153. Finkel’berg, V. M., 1964, “Mean field strength in an inhomogeneous medium,” Sov. Phys. JETP 19, 494–498, http://jetp.ras.ru/cgi-bin/e/index/e/19/2/p494?a=list.
  154. Fischer, J., and M. Wegener, 2011, “Three-dimensional direct laser writing inspired by stimulated-emission-depletion microscopy,” Opt. Mater. Express 1, 614–624.
  155. Florescu, L., and S. John, 2004, “Photon Statistics and Coherence in Light Emission from a Random Laser,” Phys. Rev. Lett. 93, 013602.
  156. Florescu, M., S. Torquato, and P. J. Steinhardt, 2009, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci. U.S.A. 106, 20658–20663.
  157. Florescu, M., S. Torquato, and P. J. Steinhardt, 2010, “Effects of random link removal on the photonic band gaps of honeycomb networks,” Appl. Phys. Lett. 97, 201103.
  158. Foldy, L. L., 1945, “The multiple scattering of waves. I. General theory of isotropic scattering by randomly distributed scatterers,” Phys. Rev. 67, 107.
  159. Forster, J. D., et al., 2010, “Biomimetic isotropic nanostructures for structural coloration,” Adv. Mater. 22, 2939–2944.
  160. Fraden, S., and G. Maret, 1990, “Multiple Light Scattering from Concentrated, Interacting Suspensions,” Phys. Rev. Lett. 65, 512.
  161. Frenkel, D., R. J. Vos, C. G. De Kruif, and A. Vrij, 1986, “Structure factors of polydisperse systems of hard spheres: A comparison of Monte Carlo simulations and Percus-Yevick theory,” J. Chem. Phys. 84, 4625–4630.
  162. Froufe-Pérez, L. S., R. Carminati, and J. J. Sáenz, 2007, “Fluorescence decay rate statistics of a single molecule in a disordered cluster of nanoparticles,” Phys. Rev. A 76, 013835.
  163. Froufe-Pérez, L. S., M. Engel, P. F. Damasceno, N. Muller, J. Haberko, S. C. Glotzer, and F. Scheffold, 2016, “Role of Short-Range Order and Hyperuniformity in the Formation of Band Gaps in Disordered Photonic Materials,” Phys. Rev. Lett. 117, 053902.
  164. Froufe-Pérez, L. S., M. Engel, J. J. Sáenz, and F. Scheffold, 2017, “Band gap formation and Anderson localization in disordered photonic materials with structural correlations,” Proc. Natl. Acad. Sci. U.S.A. 114, 9570–9574.
  165. Froufe-Pérez, L. S., W. Guerin, R. Carminati, and R. Kaiser, 2009, “Threshold of a Random Laser with Cold Atoms,” Phys. Rev. Lett. 102, 173903.
  166. Gaio, M., M. Peruzzo, and R. Sapienza, 2015, “Tuning random lasing in photonic glasses,” Opt. Lett. 40, 1611–1614.
  167. Gaio, M., D. Saxena, J. Bertolotti, D. Pisignano, A. Camposeo, and R. Sapienza, 2019, “A nanophotonic laser on a graph,” Nat. Commun. 10, 226.
  168. Galinski, H., G. Favraud, H. Dong, J. S. Totero Gongora, G. Favaro, M. Döbeli, R. Spolenak, A. Fratalocchi, and F. Capasso, 2017, “Scalable, ultra-resistant structural colors based on network metamaterials,” Light Sci. Appl. 6, e16233.
  169. Galisteo-López, J. F., M. Ibisate, R. Sapienza, L. S. Froufe-Pérez, Á. Blanco, and C. López, 2011, “Self-assembled photonic structures,” Adv. Mater. 23, 30–69.
  170. Gallinet, B., J. Butet, and O. J. F. Martin, 2015, “Numerical methods for nanophotonics: Standard problems and future challenges,” Laser Photonics Rev. 9, 577–603.
  171. Galusha, J. W., M. R. Jorgensen, and M. H. Bartl, 2010, “Diamond-structured titania photonic-bandgap crystals from biological templates,” Adv. Mater. 22, 107–110.
  172. Galusha, J. W., L. R. Richey, J. S. Gardner, J. N. Cha, and M. H. Bartl, 2008, “Discovery of a diamond-based photonic crystal structure in beetle scales,” Phys. Rev. E 77, 050904.
  173. Gansel, J. K., M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, 2009, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515.
  174. García, P. D., R. Sapienza, J. Bertolotti, M. D. Martín, Á. Blanco, A. Altube, L. Vina, D. S. Wiersma, and C López, 2008, “Resonant light transport through Mie modes in photonic glasses,” Phys. Rev. A 78, 023823.
  175. García, P. D., R. Sapienza, Á. Blanco, and C. López, 2007, “Photonic glass: A novel random material for light,” Adv. Mater. 19, 2597–2602.
  176. García, P. D., R. Sapienza, L. S. Froufe-Pérez, and C. López, 2009, “Strong dispersive effects in the light-scattering mean free path in photonic gaps,” Phys. Rev. B 79, 241109.
  177. García, P. D., R. Sapienza, C. Toninelli, C. López, and D. S. Wiersma, 2011, “Photonic crystals with controlled disorder,” Phys. Rev. A 84, 023813.
  178. García, P. D., S. Stobbe, I. Söllner, and P. Lodahl, 2012, “Nonuniversal Intensity Correlations in a Two-Dimensional Anderson-Localizing Random Medium,” Phys. Rev. Lett. 109, 253902.
  179. Gast, A. P., and W. B. Russel, 1998, “Simple ordering in complex fluids,” Phys. Today 51, No. 12, 24–30.
  180. Ge, D., E. Lee, L. Yang, Y. Cho, M. Li, D. S. Gianola, and S. Yang, 2015, “A robust smart window: Reversibly switching from high transparency to angle-independent structural color display,” Adv. Mater. 27, 2489–2495.
  181. Ge, L., Y. D. Chong, and A. D. Stone, 2010, “Steady-state ab initio laser theory: Generalizations and analytic results,” Phys. Rev. A 82, 063824.
  182. Geigenmüller, U., and P. Mazur, 1986, “The effective dielectric constant of a dispersion of spheres,” Physica (Amsterdam) 136A, 316–369.
  183. Ghofraniha, N., I. Viola, F. Di Maria, G. Barbarella, G. Gigli, L. Leuzzi, and C. Conti, 2015, “Experimental evidence of replica symmetry breaking in random lasers,” Nat. Commun. 6, 6058.
  184. Glazov, G. N., and G. A. Titov, 1977, “An integral equation for the average radiation intensity in a stochastically macroinhomogeneous,” Sov. Phys. J. 20, 1204–1208.
  185. Gnedenko, B. V., and A. N. Kolmogorov, 1954, Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, Cambridge, England).
  186. Goerlitzer, E. S. A., R. N. Klupp Taylor, and N. Vogel, 2018, “Bioinspired photonic pigments from colloidal self-assembly,” Adv. Mater. 30, 1706654.
  187. Goetschy, A., and S. E. Skipetrov, 2011, “Euclidean matrix theory of random lasing in a cloud of cold atoms,” Europhys. Lett. 96, 34005.
  188. Gomard, G., R. Peretti, E. Drouard, X. Meng, and C. Seassal, 2013, “Photonic crystals and optical mode engineering for thin film photovoltaics,” Opt. Express 21, A515–A527.
  189. Gomard, G., J. B. Preinfalk, A. Egel, and U. Lemmer, 2016, “Photon management in solution-processed organic light-emitting diodes: A review of light outcoupling micro- and nanostructures,” J. Photon. Energy 6, 030901.
  190. Goodman, J. W., 2007, Speckle Phenomena in Optics: Theory and Applications (Roberts and Co., Greenwood Village, CO).
  191. Goodman, J. W., 2015, Statistical Optics (John Wiley & Sons, New York).
  192. Gorodnichev, E. E., A. I. Kuzovlev, and D. B. Rogozkin, 2014, “Depolarization coefficients of light in multiply scattering media,” Phys. Rev. E 90, 043205.
  193. Gorsky, S., W. A. Britton, Y. Chen, J. Montaner, A. Lenef, M. Raukas, and L. Dal Negro, 2019, “Engineered hyperuniformity for directional light extraction,” APL Photonics 4, 110801.
  194. Gottardo, S., R. Sapienza, P. D. García, A. Blanco, D. S. Wiersma, and C. López, 2008, “Resonance-driven random lasing,” Nat. Photonics 2, 429.
  195. Gower, A. L., I. D. Abrahams, and W. J. Parnell, 2019, “A proof that multiple waves propagate in ensemble-averaged particulate materials,” Proc. R. Soc. A 475, 20190344.
  196. Gower, A. L., and G. Kristensson, 2021, “Effective waves for random three-dimensional particulate materials,” New J. Phys. 23, 063083.
  197. Gower, A. L., W. J. Parnell, and I. D. Abrahams, 2019, “Multiple waves propagate in random particulate materials,” SIAM J. Appl. Math. 79, 2569–2592.
  198. Gower, A. L., M. J. A. Smith, W. J. Parnell, and I. D. Abrahams, 2018, “Reflection from a multi-species material and its transmitted effective wavenumber,” Proc. R. Soc. A 474, 20170864.
  199. Granchi, N., R. Spalding, M. Lodde, M. Petruzzella, F. W. Otten, A. Fiore, F. Intonti, R. Sapienza, M. Florescu, and M. Gurioli, 2022, “Near-field investigation of luminescent hyperuniform disordered materials,” Adv. Opt. Mater. 10, 2102565.
  200. Graves, S. M., and T. G. Mason, 2008, “Transmission of visible and ultraviolet light through charge-stabilized nanoemulsions,” J. Phys. Chem. C 112, 12669–12676.
  201. Green, M. A., 2002, “Lambertian light trapping in textured solar cells and light-emitting diodes: Analytical solutions,” Prog. Photovoltaics 10, 235–241.
  202. Greffet, J.-J., and R. Carminati, 1995, “Relationship between the near-field speckle pattern and the statistical properties of a surface,” Ultramicroscopy 61, 43–50.
  203. Greffet, J.-J., and R. Carminati, 1997, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237.
  204. Grimes, C. A., and D. M. Grimes, 1991, “Permeability and permittivity spectra of granular materials,” Phys. Rev. B 43, 10780.
  205. Grishina, D. A., C. A. M. Harteveld, A. Pacureanu, D. Devashish, A. Lagendijk, P. Cloetens, and W. L. Vos, 2019, “X-ray imaging non-destructively identifies functional 3D photonic nanostructures,” ACS Nano 13, 13932–13939.
  206. Grishina, D. A., C. A. M. Harteveld, L. A. Woldering, and W. L. Vos, 2015, “Method for making a single-step etch mask for 3D monolithic nanostructures,” Nanotechnology 26, 505302.
  207. Groth, C. W., A. R. Akhmerov, and C. W. J. Beenakker, 2012, “Transmission probability through a Lévy glass and comparison with a Lévy walk,” Phys. Rev. E 85, 021138.
  208. Guo, Y., A. Jarabo, and S. Zhao, 2021, “Beyond Mie theory: Systematic computation of bulk scattering parameters based on microphysical wave optics,” ACM Trans. Graph. 40, 285.
  209. Haberko, J., L. S. Froufe-Pérez, and F. Scheffold, 2020, “Transition from light diffusion to localization in three-dimensional amorphous dielectric networks near the band edge,” Nat. Commun. 11, 1–9.
  210. Haberko, J., N. Muller, and F. Scheffold, 2013, “Direct laser writing of three-dimensional network structures as templates for disordered photonic materials,” Phys. Rev. A 88, 043822.
  211. Haberko, J., and F. Scheffold, 2013, “Fabrication of mesoscale polymeric templates for three-dimensional disordered photonic materials,” Opt. Express 21, 1057–1065.
  212. Haefner, D., S. Sukhov, and A. Dogariu, 2008, “Stochastic Scattering Polarimetry,” Phys. Rev. Lett. 100, 043901.
  213. Haefner, D., S. Sukhov, and A. Dogariu, 2010, “Scale-dependent anisotropic polarizability in mesoscopic structures,” Phys. Rev. E 81, 016609.
  214. Haines, A. I., C. E. Finlayson, D. R. E. Snoswell, P. Spahn, G. P. Hellmann, and J. J. Baumberg, 2012, “Anisotropic resonant scattering from polymer photonic crystals,” Adv. Mater. 24, OP305–OP308.
  215. Hansen, J.-P., and I. R. McDonald, 1990, Theory of Simple Liquids (Elsevier, New York).
  216. Häntsch, Y., G. Shang, B. Lei, B. Winhard, A. Petrov, M. Eich, E. Holm, G. A. Schneider, and K. P. Furlan, 2021, “Tailoring disorder and quality of photonic glass templates for structural coloration by particle charge interactions,” ACS Appl. Mater. Interfaces 13, 20511–20523.
  217. Häntsch, Y., G. Shang, A. Petrov, M. Eich, and G. A. Schneider, 2019, “YSZ hollow sphere photonic glasses: Tailoring optical properties for highly saturated non-iridescent structural coloration,” Adv. Opt. Mater. 7, 1900428.
  218. Hart, R. W., and R. A. Farrell, 1969, “Light scattering in the cornea,” J. Opt. Soc. Am. 59, 766–774.
  219. He, M., J. P. Gales, É. Ducrot, Z. Gong, G.-R. Yi, S. Sacanna, and D. J. Pine, 2020, “Colloidal diamond,” Nature (London) 585, 524–529.
  220. Ho, K. M., C. T. Chan, and C. M. Soukoulis, 1990, “Existence of a Photonic Gap in Periodic Dielectric Structures,” Phys. Rev. Lett. 65, 3152.
  221. Honeycutt, J. D., and H. C. Andersen, 1987, “Molecular dynamics study of melting and freezing of small Lennard-Jones clusters,” J. Phys. Chem. 91, 4950–4963.
  222. Hosemann, R., 1963, “Crystalline and paracrystalline order in high polymers,” J. Appl. Phys. 34, 25–41.
  223. Hu, H., A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. van Tiggelen, 2008, “Localization of ultrasound in a three-dimensional elastic network,” Nat. Phys. 4, 945.
  224. Huang, J., N. Eradat, M. E. Raikh, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, 2001, “Anomalous Coherent Backscattering of Light from Opal Photonic Crystals,” Phys. Rev. Lett. 86, 4815.
  225. Hunt, T., et al., 2007, “A comprehensive phylogeny of beetles reveals the evolutionary origins of a superradiation,” Science 318, 1913–1916.
  226. Hunter, R. S., and R. W. Harold, 1987, The Measurement of Appearance (John Wiley & Sons, New York).
  227. Hwang, V., A. B. Stephenson, S. Barkley, S. Brandt, M. Xiao, J. Aizenberg, and V. N. Manoharan, 2021, “Designing angle-independent structural colors using Monte Carlo simulations of multiple scattering,” Proc. Natl. Acad. Sci. U.S.A. 118, e2015551118.
  228. Hwang, V., A. B. Stephenson, S. Magkiriadou, J.-G. Park, and V. N. Manoharan, 2020, “Effects of multiple scattering on angle-independent structural color in disordered colloidal materials,” Phys. Rev. E 101, 012614.
  229. Hynne, F., and R. K. Bullough, 1987, “The scattering of light. II. The complex refractive index of a molecular fluid,” Phil. Trans. R. Soc. A 321, 305–360.
  230. Imagawa, S., K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, 2010, “Photonic band-gap formation, light diffusion, and localization in photonic amorphous diamond structures,” Phys. Rev. B 82, 115116.
  231. Ioffe, A. F., and A. R. Regel, 1960, “Non-crystalline, amorphous and liquid electronic semiconductors,” in Progress in Semiconductors, Vol. 4, edited by A. F. Gibson (Heywood, London), pp. 237–291.
  232. Ishii, K., T. Iwai, J. Uozumi, and T. Asakura, 1998, “Optical free-path-length distribution in a fractal aggregate and its effect on enhanced backscattering,” Appl. Opt. 37, 5014–5018.
  233. Ishimaru, A., 1978, Wave Propagation and Scattering in Random Media, Vol. 2 (Academic Press, New York).
  234. Izrailev, F. M., A. A. Krokhin, and N. M. Makarov, 2012, “Anomalous localization in low-dimensional systems with correlated disorder,” Phys. Rep. 512, 125–254.
  235. Jacucci, G., J. Bertolotti, and S. Vignolini, 2019, “Role of anisotropy and refractive index in scattering and whiteness optimization,” Adv. Opt. Mater. 7, 1900980.
  236. Jacucci, G., L. Schertel, Y. Zhang, H. Yang, and S. Vignolini, 2021, “Light management with natural materials: From whiteness to transparency,” Adv. Mater. 33, 2001215.
  237. Jacucci, G., S. Vignolini, and L. Schertel, 2020, “The limitations of extending nature’s color palette in correlated, disordered systems,” Proc. Natl. Acad. Sci. U.S.A. 117, 23345–23349.
  238. Janson, S., T. Luczak, and A. Rucinski, 2011, Random Graphs, Vol. 45 (John Wiley & Sons, New York).
  239. Jarabo, A., C. Aliaga, and D. Gutierrez, 2018, “A radiative transfer framework for spatially-correlated materials,” ACM Trans. Graph. 37, 1–13.
  240. Jendrzejewski, F., A. Bernard, K. Mueller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, 2012, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys. 8, 398–403.
  241. Jensen, J. S., and O. Sigmund, 2011, “Topology optimization for nano-photonics,” Laser Photonics Rev. 5, 308–321.
  242. Jeon, D.-J., S. Ji, E. Lee, J. Kang, L. D’Alba, M. D. Shawkey, and J.-S. Yeo, 2022, “How the Eurasian jay expands its color palette by optimizing multiple scattering,” Adv. Opt. Mater. 11, 2202210.
  243. Jiao, Y., and S. Torquato, 2011, “Maximally random jammed packings of platonic solids: Hyperuniform long-range correlations and isostaticity,” Phys. Rev. E 84, 041309.
  244. Jin, C., X.Meng, B. Cheng, Z. Li, and D. Zhang, 2001, “Photonic gap in amorphous photonic materials,” Phys. Rev. B 63, 195107.
  245. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, 2011, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, NJ).
  246. Johansen, V. E., O. D. Onelli, L. M. Steiner, and S. Vignolini, 2017, “Photonics in nature: From order to disorder,” in Functional Surfaces in Biology III, Biologically-Inspired Systems Vol. 10, edited by S. N. Gorb and Elena V. Gorb (Springer, New York), pp. 53–89.
  247. John, S., 1984, “Electromagnetic Absorption in a Disordered Medium near a Photon Mobility Edge,” Phys. Rev. Lett. 53, 2169.
  248. John, S., 1987, “Strong Localization of Photons in Certain Disordered Dielectric Superlattices,” Phys. Rev. Lett. 58, 2486.
  249. Johnson, S. G., and J. D. Joannopoulos, 2001, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190.
  250. Kaplan, P. D., A. D. Dinsmore, A. G. Yodh, and D. J. Pine, 1994, “Diffuse-transmission spectroscopy: A structural probe of opaque colloidal mixtures,” Phys. Rev. E 50, 4827.
  251. Keller, J. B., 1964, “Stochastic equations and wave propagation in random media,” in Stochastic Processes in Mathematical Physics and Engineering, Vol. 16, edited by R. E. Bellmann (American Mathematical Society, Providence), pp. 145–170.
  252. Kim, J., G. Zhang, F. H. Stillinger, and S. Torquato, 2018, “Inversion problems for Fourier transforms of particle distributions,” J. Stat. Mech. 113302.
  253. Kim, J. B., C. Chae, S. H. Han, S. Y. Lee, and S.-H. Kim, 2021, “Direct writing of customized structural-color graphics with colloidal photonic inks,” Sci. Adv. 7, eabj8780.
  254. Kim, S.-H., S. Magkiriadou, D. K. Rhee, D. S. Lee, P. J. Yoo, V. N. Manoharan, and G.-R. Yi, 2017, “Inverse photonic glasses by packing bidisperse hollow microspheres with uniform cores,” ACS Appl. Mater. Interfaces 9, 24155–24160.
  255. Kim, S., S. Yoon, H. Seok, J. Lee, and H. Jeon, 2010, “Band-edge lasers based on randomly mixed photonic crystals,” Opt. Express 18, 7685–7692.
  256. Kinoshita, S., and S. Yoshioka, 2005, “Structural colors in nature: The role of regularity and irregularity in the structure,” ChemPhysChem 6, 1442–1459.
  257. Kirkwood, J. G., 1936, “On the theory of dielectric polarization,” J. Chem. Phys. 4, 592–601.
  258. Kittel, C., 1976, Introduction to Solid State Physics, Vol. 8 (Wiley, New York).
  259. Klages, R., G. Radons, and I. M. Sokolov, 2008, Anomalous Transport: Foundations and Applications (John Wiley & Sons, New York).
  260. Klar, T. A., R. Wollhofen, and J. Jacak, 2014, “Sub-Abbe resolution: From STED microscopy to STED lithography,” Phys. Scr. 014049.
  261. Klatt, M. A., J. Kim, and S. Torquato, 2020, “Cloaking the underlying long-range order of randomly perturbed lattices,” Phys. Rev. E 101, 032118.
  262. Klatt, M. A., P. J. Steinhardt, and S. Torquato, 2019, “Phoamtonic designs yield sizeable 3D photonic band gaps,” Proc. Natl. Acad. Sci. U.S.A. 116, 23480–23486.
  263. Klatt, M. A., P. J. Steinhardt, and S. Torquato, 2022, “Wave propagation and band tails of two-dimensional disordered systems in the thermodynamic limit,” Proc. Natl. Acad. Sci. U.S.A. 119, e2213633119.
  264. Knyazikhin, Y., J. Kranigk, R. B. Myneni, O. Panfyorov, and G. Gravenhorst, 1998, “Influence of small-scale structure on radiative transfer and photosynthesis in vegetation canopies,” J. Geophys. Res. Atmos. 103, 6133–6144.
  265. Koenderink, A. F., A. Lagendijk, and W. L. Vos, 2005, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102.
  266. Koenderink, A. F., M. Megens, G. van Soest, W. L. Vos, and A. Lagendijk, 2000, “Enhanced backscattering from photonic crystals,” Phys. Lett. A 268, 104–111.
  267. Kondov, S. S., W. R. McGehee, J. J. Zirbel, and B. DeMarco, 2011, “Three-dimensional Anderson localization of ultracold matter,” Science 334, 66–68.
  268. Kostinski, A. B., 2001, “On the extinction of radiation by a homogeneous but spatially correlated random medium,” J. Opt. Soc. Am. A 18, 1929–1933.
  269. Kostinski, A. B., 2002, “On the extinction of radiation by a homogeneous but spatially correlated random medium: Reply to comment,” J. Opt. Soc. Am. A 19, 2521–2525.
  270. Kostinski, A. B., and A. R. Jameson, 2000, “On the spatial distribution of cloud particles,” J. Atmos. Sci. 57, 901–915.
  271. Krachmalnicoff, V., E. Castanié, Y. De Wilde, and R. Carminati, 2010, “Fluctuations of the Local Density of States Probe Localized Surface Plasmons on Disordered Metal Films,” Phys. Rev. Lett. 105, 183901.
  272. Krauss, T. F., M. Richard, and S. Brand, 1996, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699.
  273. Kristensson, G., 1980, “Electromagnetic scattering from buried inhomogeneities—A general three-dimensional formalism,” J. Appl. Phys. 51, 3486–3500.
  274. Kristensson, G., 2015, “Coherent scattering by a collection of randomly located obstacles—An alternative integral equation formulation,” J. Quant. Spectrosc. Radiat. Transfer 164, 97–108.
  275. Kumar, S., and C. L. Tien, 1990, “Dependent absorption and extinction of radiation by small particles,” J. Heat Transfer 112, 178–185.
  276. Labastie, P., and R. L. Whetten, 1990, “Statistical Thermodynamics of the Cluster Solid-Liquid Transition,” Phys. Rev. Lett. 65, 1567.
  277. Lagendijk, A., B. van Tiggelen, and D. S. Wiersma, 2009, “Fifty years of Anderson localization,” Phys. Today 62, No. 8, 24–29.
  278. Lagendijk, A., and B. A. van Tiggelen, 1996, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215.
  279. Lakhtakia, A., 1992, “General theory of the Purcell-Pennypacker scattering approach and its extension to bianisotropic scatterers,” Astrophys. J. 394, 494–499.
  280. Lalanne, P., W. Yan, K. Vynck, C. Sauvan, and J.-P. Hugonin, 2018, “Light interaction with photonic and plasmonic resonances,” Laser Photonics Rev. 12, 1700113.
  281. LAMMPS Collaboration, 2019, computer code lammps, https://lammps.sandia.gov/.
  282. Lan, Y., et al., 2018, “Unexpected stability of aqueous dispersions of raspberry-like colloids,” Nat. Commun. 9, 3614.
  283. Landau, L. D., and E. M. Lifshitz, 1980, Statistical Physics, 3rd ed. Course of Theoretical Physics Vol. 5 (Butterworth-Heinemann, Oxford), Chap. XII, pp. 333–400.
  284. Landau, L. D., E. M. Lifshitz, and J. B. Sykes, 2013, Electrodynamics of Continuous Media, Vol. 8 (Elsevier, New York).
  285. Larsen, E. W., and R. Vasques, 2011, “A generalized linear Boltzmann equation for non-classical particle transport,” J. Quant. Spectrosc. Radiat. Transfer 112, 619–631.
  286. Laverdant, J., S. Buil, B. Bérini, and X. Quélin, 2008, “Polarization dependent near-field speckle of random gold films,” Phys. Rev. B 77, 165406.
  287. Lax, M., 1951, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287.
  288. Lax, M., 1952, “Multiple scattering of waves. II. The effective field in dense systems,” Phys. Rev. 85, 621.
  289. Lebowitz, J. L., and J. K. Percus, 1963, “Integral equations and inequalities in the theory of fluids,” J. Math. Phys. (N.Y.) 4, 1495–1506.
  290. Ledermann, A., L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. Von Freymann, 2006, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5, 942.
  291. Lee, C.-Y., Z. H. Stachurski, and T. R. Welberry, 2010, “The geometry, topology and structure of amorphous solids,” Acta Mater. 58, 615–625.
  292. Lee, M., S. Callard, C. Seassal, and H. Jeon, 2019, “Taming of random lasers,” Nat. Photonics 13, 445–448.
  293. Lee, S. H., S. M. Han, and S. E. Han, 2020, “Anisotropic diffusion in cyphochilus white beetle scales,” APL Photonics 5, 056103.
  294. Lee, W.-K., S. Yu, C. J. Engel, T. Reese, D. Rhee, W. Chen, and T. W. Odom, 2017, “Concurrent design of quasi-random photonic nanostructures,” Proc. Natl. Acad. Sci. U.S.A. 114, 8734–8739.
  295. Leedumrongwatthanakun, S., L. Innocenti, H. Defienne, T. Juffmann, A. Ferraro, M. Paternostro, and S. Gigan, 2020, “Programmable linear quantum networks with a multimode fibre,” Nat. Photonics 14, 139–142.
  296. Leistikow, M. D., A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, 2011, “Inhibited Spontaneous Emission of Quantum Dots Observed in a 3D Photonic Band Gap,” Phys. Rev. Lett. 107, 193903.
  297. Leonetti, M., C. Conti, and C. Lopez, 2011, “The mode-locking transition of random lasers,” Nat. Photonics 5, 615.
  298. Leonetti, M., L. Pattelli, S. De Panfilis, D. S. Wiersma, and G. Ruocco, 2021, “Spatial coherence of light inside three-dimensional media,” Nat. Commun. 12, 4199.
  299. Lepri, S., C. Trono, and G. Giacomelli, 2017, “Complex Active Optical Networks as a New Laser Concept,” Phys. Rev. Lett. 118, 123901.
  300. Leseur, O., R. Pierrat, and R. Carminati, 2016, “High-density hyperuniform materials can be transparent,” Optica 3, 763–767.
  301. Leseur, O., R. Pierrat, and R. Carminati, 2017, “Spatial correlations of the spontaneous decay rate as a probe of dense and correlated disordered materials,” Eur. Phys. J. Special Topics 226, 1423–1432.
  302. Leseur, O., R. Pierrat, J. J. Sáenz, and R. Carminati, 2014, “Probing two-dimensional Anderson localization without statistics,” Phys. Rev. A 90, 053827.
  303. Letokhov, V. S., 1968, “Generation of light by a scattering medium with negative resonance absorption,” Sov. Phys. JETP 26, 835–840, http://jetp.ras.ru/cgi-bin/e/index/e/26/4/p835?a=list.
  304. Lidorikis, E., M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 2000, “Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,” Phys. Rev. B 61, 13458.
  305. Liew, S. F., J.-K. Yang, H. Noh, C. F. Schreck, E. R. Dufresne, C. S. O’Hern, and H. Cao, 2011, “Photonic band gaps in three-dimensional network structures with short-range order,” Phys. Rev. A 84, 063818.
  306. Lima, J. R. F., L. F. C. Pereira, and A. L. R. Barbosa, 2019, “Dirac wave transmission in Lévy-disordered systems,” Phys. Rev. E 99, 032118.
  307. Lin, H.-C., Z. Wang, and C. W. Hsu, 2022, “Fast multi-source nanophotonic simulations using augmented partial factorization,” Nat. Comput. Sci. 2, 815–822.
  308. Lin, M. Y., H. M. Lindsay, D. A. Weitz, R. C. Ball, R. Klein, and P. Meakin, 1989, “Universality of fractal aggregates as probed by light scattering,” Proc. R. Soc. A, 423, 71–87.
  309. Lin, S.-y., J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, 1998, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature (London) 394, 251.
  310. Liu, J., H.-J. Schöpe, and T. Palberg, 2000, “An improved empirical relation to determine the particle number density of fluid-like ordered charge-stabilized suspensions,” Part. Part. Syst. Charact. 17, 206–212.
  311. Liu, J., P. D. Garcia, S. Ek, N. Gregersen, T. Suhr, M. Schubert, J. Mørk, S. Stobbe, and P. Lodahl, 2014, “Random nanolasing in the Anderson localized regime,” Nat. Nanotechnol. 9, 285.
  312. Liu, M. Q., C. Y. Zhao, B. X. Wang, and X. Fang, 2018, “Role of short-range order in manipulating light absorption in disordered media,” J. Opt. Soc. Am. B 35, 504–513.
  313. Lodahl, P., A. F. Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, 2004, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature (London) 430, 654.
  314. López, C., 2003, “Materials aspects of photonic crystals,” Adv. Mater. 15, 1679–1704.
  315. Lorentz, H. A., 1880, “Ueber die beziehung zwischen der fortpflanzungsgeschwindigkeit des lichtes und der körperdichte,” Ann. Phys. (Berlin) 245, 641–665.
  316. Lorenz, L., 1880, “Ueber die refractionsconstante,” Ann. Phys. (Berlin) 247, 70–103.
  317. Lubachevsky, B. D., and F. H. Stillinger, 1990, “Geometric properties of random disk packings,” J. Stat. Phys. 60, 561–583.
  318. Luke, S. M., B. T. Hallam, and P. Vukusic, 2010, “Structural optimization for broadband scattering in several ultra-thin white beetle scales,” Appl. Opt. 49, 4246–4254.
  319. Ma, Y., V. K. Varadan, and V. V. Varadan, 1990, “Enhanced absorption due to dependent scattering,” J. Heat Transfer 112, 402–407.
  320. Mackay, T. G., and A. Lakhtakia, 2020, Modern Analytical Electromagnetic Homogenization with Mathematica, 2nd ed. (IOP Publishing, Bristol, England).
  321. Mackowski, D. W., 2008, “Exact solution for the scattering and absorption properties of sphere clusters on a plane surface,” J. Quant. Spectrosc. Radiat. Transfer 109, 770–788.
  322. Mackowski, D. W., 2022, computer code mstm, https://github.com/dmckwski/MSTM (accessed December 23, 2022).
  323. Mackowski, D. W., and M. I. Mishchenko, 2011, “A multiple sphere t-matrix fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transfer 112, 2182–2192.
  324. Magerle, R., 2000, “Nanotomography,” Phys. Rev. Lett. 85, 2749.
  325. Magkiriadou, S., J.-G. Park, Y.-S. Kim, and V. N. Manoharan, 2012, “Disordered packings of core-shell particles with angle-independent structural colors,” Opt. Mater. Express 2, 1343–1352.
  326. Magkiriadou, S., J.-G. Park, Y.-S. Kim, and V. N. Manoharan, 2014, “Absence of red structural color in photonic glasses, bird feathers, and certain beetles,” Phys. Rev. E 90, 062302.
  327. Maimouni, I., M. Morvaridi, M. Russo, G. Lui, K. Morozov, J. Cossy, M. Florescu, M. Labousse, and P. Tabeling, 2020, “Micrometric monodisperse solid foams as complete photonic bandgap materials,” ACS Appl. Mater. Interfaces 12, 32061–32068.
  328. Man, W., M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, 2013, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. U.S.A. 110, 15886–15891.
  329. Mandel, L., and E. Wolf, 1995, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, England).
  330. Mandelbrot, B., 1967, “How long is the coast of Britain? Statistical self-similarity and fractional dimension,” Science 156, 636–638.
  331. Manoharan, V. N., M. T. Elsesser, and D. J. Pine, 2003, “Dense packing and symmetry in small clusters of microspheres,” Science 301, 483–487.
  332. Marichy, C., N. Muller, L. S. Froufe-Pérez, and F. Scheffold, 2016, “High-quality photonic crystals with a nearly complete band gap obtained by direct inversion of woodpile templates with titanium dioxide,” Sci. Rep. 6, 21818.
  333. Markel, V. A., 2016, “Introduction to the Maxwell Garnett approximation: Tutorial,” J. Opt. Soc. Am. A 33, 1244–1256.
  334. Marshak, A., and A. Davis, 2005, 3D Radiative Transfer in Cloudy Atmospheres (Springer Science+Business Media, New York).
  335. Marshak, A., A. Davis, W. Wiscombe, and R. Cahalan, 1998, “Radiative effects of sub-mean free path liquid water variability observed in stratiform clouds,” J. Geophys. Res. Atmos. 103, 19557–19567.
  336. Martin, Ph. A., and T. Yalcin, 1980, “The charge fluctuations in classical Coulomb systems,” J. Stat. Phys. 22, 435–463.
  337. Martins, E. R., J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, 2013, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665.
  338. Maurice, D. M., 1957, “The structure and transparency of the cornea,” J. Physiol. 136, 263–286.
  339. Mavidis, C. P., A. C. Tasolamprou, S. B. Hasan, T. Koschny, E. N. Economou, M. Kafesaki, C. M. Soukoulis, and W. L. Vos, 2020, “Local density of optical states in the three-dimensional band gap of a finite photonic crystal,” Phys. Rev. B 101, 235309.
  340. Máximo, C. E., N. Piovella, Ph. W. Courteille, R. Kaiser, and R. Bachelard, 2015, “Spatial and temporal localization of light in two dimensions,” Phys. Rev. A 92, 062702.
  341. Maxwell Garnett, J. C., 1904, “XII. Colours in metal glasses and in metallic films,” Phil. Trans. R. Soc. A 203, 385–420.
  342. Meakin, P., 1987, “Fractal aggregates,” Adv. Colloid Interface Sci. 28, 249–331.
  343. Meakin, P., and R. Jullien, 1992, “Random sequential adsorption of spheres of different sizes,” Physica (Amsterdam) 187A, 475–488.
  344. Mello, P. A., and N. Kumar, 2004, Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations, a Maximum-Entropy Viewpoint, Vol. 4 (Oxford University Press, New York).
  345. Mercadier, N., W. Guerin, M. Chevrollier, and R. Kaiser, 2009, “Lévy flights of photons in hot atomic vapours,” Nat. Phys. 5, 602–605.
  346. Meseguer, F., A. Blanco, H. Míguez, F. García-Santamaría, M. Ibisate, and C. López, 2002, “Synthesis of inverse opals,” Colloids Surf. A 202, 281–290.
  347. Michel, B., and A. Lakhtakia, 1995, “Strong-property-fluctuation theory for homogenizing chiral particulate composites,” Phys. Rev. E 51, 5701.
  348. Michielsen, K., H. De Raedt, and D. G. Stavenga, 2010, “Reflectivity of the gyroid biophotonic crystals in the ventral wing scales of the green hairstreak butterfly, Callophrys rubi,” J. R. Soc. Interface 7, 765–771.
  349. Michielsen, K., and D. G. Stavenga, 2008, “Gyroid cuticular structures in butterfly wing scales: Biological photonic crystals,” J. R. Soc. Interface 5, 85–94.
  350. Mie, G., 1908, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Ann. Phys. (Berlin) 330, 377–445.
  351. Mirlin, A. D., Yu. V. Fyodorov, A. Mildenberger, and F. Evers, 2006, “Exact Relations between Multifractal Exponents at the Anderson Transition,” Phys. Rev. Lett. 97, 046803.
  352. Mishchenko, M. I., 2008, “Multiple scattering by particles embedded in an absorbing medium. 1. Foldy-Lax equations, order-of-scattering expansion, and coherent field,” Opt. Express 16, 2288–2301.
  353. Mishchenko, M. I., J. W. Hovenier, and L. D. Travis, 1999, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Elsevier, New York).
  354. Mishchenko, M. I., L. D. Travis, and D. W. Mackowski, 1996, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575.
  355. Mokkapati, S., and K. R. Catchpole, 2012, “Nanophotonic light trapping in solar cells,” J. Appl. Phys. 112, 101101.
  356. Monsarrat, R., R. Pierrat, A. Tourin, and A. Goetschy, 2022, “Pseudogap and Anderson localization of light in correlated disordered media,” Phys. Rev. Res. 4, 033246.
  357. Moon, J. H., G.-R. Yi, S.-M. Yang, D. J. Pine, and S. B. Park, 2004, “Electrospray-assisted fabrication of uniform photonic balls,” Adv. Mater. 16, 605–609.
  358. Moyroud, E., et al., 2017, “Disorder in convergent floral nanostructures enhances signalling to bees,” Nature (London) 550, 469–474.
  359. Muljarov, E. A., and W. Langbein, 2016, “Exact mode volume and Purcell factor of open optical systems,” Phys. Rev. B 94, 235438.
  360. Muller, N., J. Haberko, C. Marichy, and F. Scheffold, 2014, “Silicon hyperuniform disordered photonic materials with a pronounced gap in the shortwave infrared,” Adv. Opt. Mater. 2, 115–119.
  361. Muller, N., J. Haberko, C. Marichy, and F. Scheffold, 2017, “Photonic hyperuniform networks obtained by silicon double inversion of polymer templates,” Optica 4, 361–366.
  362. Mupparapu, R., K. Vynck, T. Svensson, M. Burresi, and D. S. Wiersma, 2015, “Path length enhancement in disordered media for increased absorption,” Opt. Express 23, A1472–A1484.
  363. Musbach, A., G. W. Meyer, F. Reitich, and S.-H. Oh, 2013, “Full wave modelling of light propagation and reflection,” Comput. Graphics Forum 32, 24–37.
  364. Muskens, O. L., J. Gómez Rivas, R. E. Algra, E. P. A. M. Bakkers, and A. Lagendijk, 2008, “Design of light scattering in nanowire materials for photovoltaic applications,” Nano Lett. 8, 2638–2642.
  365. Nakayama, T., K. Yakubo, and R. L. Orbach, 1994, “Dynamical properties of fractal networks: Scaling, numerical simulations, and physical realizations,” Rev. Mod. Phys. 66, 381.
  366. Naraghi, R. R., and A. Dogariu, 2016, “Phase Transitions in Diffusion of Light,” Phys. Rev. Lett. 117, 263901.
  367. Naraghi, R. R., S. Sukhov, and A. Dogariu, 2016, “Disorder fingerprint: Intensity distributions in the near field of random media,” Phys. Rev. B 94, 174205.
  368. Naraghi, R. R., S. Sukhov, J. J. Sáenz, and A. Dogariu, 2015, “Near-Field Effects in Mesoscopic Light Transport,” Phys. Rev. Lett. 115, 203903.
  369. Natta, A., and N. Panagia, 1984, “Extinction in inhomogeneous clouds,” Astrophys. J. 287, 228–237.
  370. Nelson, E. C., et al., 2011, “Epitaxial growth of three-dimensionally architectured optoelectronic devices,” Nat. Mater. 10, 676–681.
  371. Noh, H., S. F. Liew, V. Saranathan, S. G. J. Mochrie, R. O. Prum, E. R. Dufresne, and H. Cao, 2010, “How noniridescent colors are generated by quasi-ordered structures of bird feathers,” Adv. Mater. 22, 2871–2880.
  372. Noh, H., J.-K. Yang, S. F. Liew, M. J. Rooks, G. S. Solomon, and H. Cao, 2011, “Control of Lasing in Biomimetic Structures with Short-Range Order,” Phys. Rev. Lett. 106, 183901.
  373. Nolan, J., 2003, Stable Distributions: Models for Heavy-Tailed Data (Birkhäuser, Boston).
  374. Novotny, L., and B. Hecht, 2012, Principles of Nano-optics (Cambridge University Press, Cambridge, England).
  375. O’Brien, S., and J. B. Pendry, 2002, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14, 4035.
  376. Ohta, N., and A. Robertson, 2006, Colorimetry: Fundamentals and Applications (John Wiley & Sons, New York).
  377. Onelli, O. D., T. van de Kamp, J. N. Skepper, J. Powell, T. dos Santos Rolo, T. Baumbach, and S. Vignolini, 2017, “Development of structural colour in leaf beetles,” Sci. Rep. 7, 1373.
  378. Onsager, L., 1936, “Electric moments of molecules in liquids,” J. Am. Chem. Soc. 58, 1486–1493.
  379. Ornstein, L. S., and F. Zernike, 1914, “Accidental deviations of density and opalescence at the critical point of a single substance,” Proc. Akad. Sci. (Amsterdam) 17, 793–806, https://dwc.knaw.nl/DL/publications/PU00012727.pdf.
  380. Oskooi, A., P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, 2012, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100, 181110.
  381. Oskooi, A. F., D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, 2010, “meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702.
  382. Parigi, V., E. Perros, G. Binard, C. Bourdillon, A. Maître, R. Carminati, V. Krachmalnicoff, and Y. De Wilde, 2016, “Near-field to far-field characterization of speckle patterns generated by disordered nanomaterials,” Opt. Express 24, 7019–7027.
  383. Parisi, G., and F. Zamponi, 2010, “Mean-field theory of hard sphere glasses and jamming,” Rev. Mod. Phys. 82, 789.
  384. Park, J.-G., S.-H. Kim, S. Magkiriadou, T. M. Choi, Y.-S. Kim, and V. N. Manoharan, 2014, “Full-spectrum photonic pigments with non-iridescent structural colors through colloidal assembly,” Angew. Chem., Int. Ed. 53, 2899–2903.
  385. Pattelli, L., A. Egel, U. Lemmer, and D. S. Wiersma, 2018, “Role of packing density and spatial correlations in strongly scattering 3D systems,” Optica 5, 1037–1045.
  386. Pelton, M., 2015, “Modified spontaneous emission in nanophotonic structures,” Nat. Photonics 9, 427–435.
  387. Peng, X. T., and A. D. Dinsmore, 2007, “Light Propagation in Strongly Scattering, Random Colloidal Films: The Role of the Packing Geometry,” Phys. Rev. Lett. 99, 143902.
  388. Percus, J. K., and G. J. Yevick, 1958, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1.
  389. Pereira, E., J. M. G. Martinho, and M. N. Berberan-Santos, 2004, “Photon Trajectories in Incoherent Atomic Radiation Trapping as Lévy Flights,” Phys. Rev. Lett. 93, 120201.
  390. Peretti, R., G. Gomard, L. Lalouat, C. Seassal, and E. Drouard, 2013, “Absorption control in pseudodisordered photonic-crystal thin films,” Phys. Rev. A 88, 053835.
  391. Phillips, J. C., 1971, “Electronic structure and optical spectra of amorphous semiconductors,” Phys. Status Solidi B 44, K1–K4.
  392. Phillips, J. C., R. Braun, W. Wang, J. Gumbart, E. Tajkhorshid, E. Villa, C. Chipot, R. D. Skeel, L. Kale, and K. Schulten, 2005, “Scalable molecular dynamics with namd,” J. Comput. Chem. 26, 1781–1802.
  393. Piechulla, P. M., B. Fuhrmann, E. Slivina, C. Rockstuhl, R. B. Wehrspohn, and A. N. Sprafke, 2021, “Tailored light scattering through hyperuniform disorder in self-organized arrays of high-index nanodisks,” Adv. Opt. Mater. 9, 2100186.
  394. Piechulla, P. M., L. Muehlenbein, R. B. Wehrspohn, S. Nanz, A. Abass, C. Rockstuhl, and A. Sprafke, 2018, “Fabrication of nearly-hyperuniform substrates by tailored disorder for photonic applications,” Adv. Opt. Mater. 6, 1701272.
  395. Piechulla, P. M., E. Slivina, D. Bätzner, I. Fernandez-Corbaton, P. Dhawan, R. B. Wehrspohn, A. N. Sprafke, and C. Rockstuhl, 2021, “Antireflective Huygens’ metasurface with correlated disorder made from high-index disks implemented into silicon heterojunction solar cells,” ACS Photonics 8, 3476–3485.
  396. Piechulla, P. M., R. B. Wehrspohn, and A. N. Sprafke, 2023, “Toward hyperuniform disorder via self-assembly of bidisperse colloidal patterns at an electrode,” Adv. Mater. Interfaces 10, 2201395.
  397. Pierrat, R., P. Ambichl, S. Gigan, A. Haber, R. Carminati, and S. Rotter, 2014, “Invariance property of wave scattering through disordered media,” Proc. Natl. Acad. Sci. U.S.A. 111, 17765–17770.
  398. Pierrat, R., and R. Carminati, 2007, “Threshold of random lasers in the incoherent transport regime,” Phys. Rev. A 76, 023821.
  399. Pierrat, R., and R. Carminati, 2010, “Spontaneous decay rate of a dipole emitter in a strongly scattering disordered environment,” Phys. Rev. A 81, 063802.
  400. Plimpton, S., 1995, “Fast parallel algorithms for short-range molecular dynamics,” J. Comput. Phys. 117, 1–19.
  401. Pomerantz, A. F., R. H. Siddique, E. I. Cash, Y. Kishi, C. Pinna, K. Hammar, D. Gomez, M. Elias, and N. H. Patel, 2021, “Developmental, cellular and biochemical basis of transparency in clearwing butterflies,” J. Exp. Biol. 224, jeb237917.
  402. Pomraning, G. C., 1991, Linear Kinetic Theory and Particle Transport in Stochastic Mixtures, Vol. 7 (World Scientific, Singapore).
  403. Poon, W., 2004, “Colloids as big atoms,” Science 304, 830–831.
  404. Pratesi, F., M. Burresi, F. Riboli, K. Vynck, and D. S. Wiersma, 2013, “Disordered photonic structures for light harvesting in solar cells,” Opt. Express 21, A460–A468.
  405. Priya, O. Schöps, U. Woggon, R. V. Nair, 2018, “Inhibited spontaneous emission using gaplike resonance in disordered photonic structures,” Phys. Rev. A 98, 043835.
  406. Prum, R. O., E. R. Dufresne, T. Quinn, and K. Waters, 2009, “Development of colour-producing β-keratin nanostructures in avian feather barbs,” J. R. Soc. Interface 6, S253–S265.
  407. Prum, R. O., T. Quinn, and R. H. Torres, 2006, “Anatomically diverse butterfly scales all produce structural colours by coherent scattering,” J. Exp. Biol. 209, 748–765.
  408. Prum, R. O., and R. Torres, 2003, “Structural colouration of avian skin: Convergent evolution of coherently scattering dermal collagen arrays,” J. Exp. Biol. 206, 2409–2429.
  409. Prum, R. O., and R. Torres, 2004, “Structural colouration of mammalian skin: Convergent evolution of coherently scattering dermal collagen arrays,” J. Exp. Biol. 207, 2157–2172.
  410. Prum, R. O., R. H. Torres, S. Williamson, and J. Dyck, 1998, “Coherent light scattering by blue feather barbs,” Nature (London) 396, 28.
  411. Pusey, P. N., 1987, “The effect of polydispersity on the crystallization of hard spherical colloids,” J. Phys. (Paris) 48, 709–712.
  412. Pusey, P. N., 1991, “Colloidal suspensions,” in Liquids, Freezing and the Glass Transition, Proceedings of the 1989 Les Houches Winter School, edited by J. P. Hansen, D. Levesque, and J. Zinn-Justin (Elsevier, New York).
  413. Pusey, P. N., and W. Van Megen, 1986, “Phase behaviour of concentrated suspensions of nearly hard colloidal spheres,” Nature (London) 320, 340.
  414. Pusey, P. N., W. Van Megen, P. Bartlett, B. J. Ackerson, J. G. Rarity, and S. M. Underwood, 1989, “Structure of Crystals of Hard Colloidal Spheres,” Phys. Rev. Lett. 63, 2753.
  415. Rabinowitch, E. I., 1951, Photosynthesis and Related Processes, Vol. 2 (Interscience, New York).
  416. Randall, C. H., 1962, “Stochastic models for heterogeneous materials. I. (Large scale inhomogeneities and neutron transmission),” Knolls Atomic Power Laboratory Report No. KAPL-M-CHR-6, 10.2172/4754972.
  417. Rayleigh, L., 1899, “XXXIV. On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky,” London Edinburgh Dublin Philos. Mag. J. Sci. 47, 375–384.
  418. Rechtsman, M., A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, 2011, “Amorphous Photonic Lattices: Band Gaps, Effective Mass, and Suppressed Transport,” Phys. Rev. Lett. 106, 193904.
  419. Rechtsman, M. C., J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, 2013, “Photonic Floquet topological insulators,” Nature (London) 496, 196–200.
  420. Redding, B., S. F. Liew, R. Sarma, and H. Cao, 2013, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7, 746.
  421. Rengarajan, R., D. Mittleman, C. Rich, and V. Colvin, 2005, “Effect of disorder on the optical properties of colloidal crystals,” Phys. Rev. E 71, 016615.
  422. Renner, M., and G. Von Freymann, 2015, “Spatial correlations and optical properties in three-dimensional deterministic aperiodic structures,” Sci. Rep. 5, 13129.
  423. Reufer, M., L. Fernando Rojas-Ochoa, S. Eiden, J. J. Sáenz, and F. Scheffold, 2007, “Transport of light in amorphous photonic materials,” Appl. Phys. Lett. 91, 171904.
  424. Riboli, F., P. Barthelemy, S. Vignolini, F. Intonti, A. De Rossi, S. Combrie, and D. S. Wiersma, 2011, “Anderson localization of near-visible light in two dimensions,” Opt. Lett. 36, 127–129.
  425. Riboli, F., F. Uccheddu, G. Monaco, N. Caselli, F. Intonti, M. Gurioli, and S. E. Skipetrov, 2017, “Tailoring Correlations of the Local Density of States in Disordered Photonic Materials,” Phys. Rev. Lett. 119, 043902.
  426. Riboli, F., et al., 2014, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13, 720.
  427. Ricouvier, J., R. Pierrat, R. Carminati, P. Tabeling, and P. Yazhgur, 2017, “Optimizing Hyperuniformity in Self-Assembled Bidisperse Emulsions,” Phys. Rev. Lett. 119, 208001.
  428. Ricouvier, J., P. Tabeling, and P. Yazhgur, 2019, “Foam as a self-assembling amorphous photonic band gap material,” Proc. Natl. Acad. Sci. U.S.A. 116, 9202–9207.
  429. Rohfritsch, A., J.-M. Conoir, T. Valier-Brasier, and R. Marchiano, 2020, “Impact of particle size and multiple scattering on the propagation of waves in stealthy-hyperuniform media,” Phys. Rev. E 102, 053001.
  430. Rojas-Ochoa, L. F., J. M. Mendez-Alcaraz, J. J. Sáenz, P. Schurtenberger, and F. Scheffold, 2004, “Photonic Properties of Strongly Correlated Colloidal Liquids,” Phys. Rev. Lett. 93, 073903.
  431. Rojas-Ochoa, L. F., S. Romer, F. Scheffold, and P. Schurtenberger, 2002, “Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions,” Phys. Rev. E 65, 051403.
  432. Rothemund, P. W. K., 2006, “Folding DNA to create nanoscale shapes and patterns,” Nature (London) 440, 297.
  433. Rothenberger, G., P. Comte, and M. Grätzel, 1999, “A contribution to the optical design of dye-sensitized nanocrystalline solar cells,” Sol. Energy Mater. Sol. Cells 58, 321–336.
  434. Rotter, S., and S. Gigan, 2017, “Light fields in complex media: Mesoscopic scattering meets wave control,” Rev. Mod. Phys. 89, 015005.
  435. Ruppin, R., 2000, “Evaluation of extended Maxwell-Garnett theories,” Opt. Commun. 182, 273–279.
  436. Rusek, M., A. Orłowski, and J. Mostowski, 1996, “Localization of light in three-dimensional random dielectric media,” Phys. Rev. E 53, 4122.
  437. Rustomji, K., M. Dubois, P. Jomin, S. Enoch, J. Wenger, C. Martijn de Sterke, and R. Abdeddaim, 2021, “Complete Electromagnetic Dyadic Green Function .Characterization in a Complex Environment—Resonant Dipole-Dipole Interaction and Cooperative Effects,” Phys. Rev. X 11, 021004.
  438. Rytov, S. M., Y. A. Kravtsov, and V. I. Tatarskii, 1989, Principles of Statistical Radiophysics, Vol. 4 (Springer-Verlag, Berlin).
  439. Ryzhik, L., G. Papanicolaou, and J. B. Keller, 1996, “Transport equations for elastic and other waves in random media,” Wave Motion 24, 327.
  440. Ryzhov, Yu. A., and V. V. Tamoikin, 1970, “Radiation and propagation of electromagnetic waves in randomly inhomogeneous media,” Radiophys. Quantum Electron. 13, 273–300.
  441. Ryzhov, Yu. A., V. V. Tamoikin, and V. I. Tatarskii, 1965, “Spatial dispersion of inhomogeneous media,” Sov. Phys. JETP 21, 433–438, http://jetp.ras.ru/cgi-bin/e/index/e/21/2/p433?a=list.
  442. Saito, A., K. Ishibashi, J. Ohga, Y. Hirai, and Y. Kuwahara, 2018, “Replication of large-area morpho-color material using flexible mold,” in Bioinspiration, Biomimetics, and Bioreplication VIII, SPIE Proceedings Vol. 10593 (SPIE—International Society for Optical Engineering, Bellingham, WA), pp. 82–88, 10.1117/12.2296532.
  443. Salameh, C., et al., 2020, “Origin of transparency in scattering biomimetic collagen materials,” Proc. Natl. Acad. Sci. U.S.A. 117, 11947–11953.
  444. Salpeter, E. E., and H. A. Bethe, 1951, “A relativistic equation for bound-state problems,” Phys. Rev. 84, 1232.
  445. Salvalaglio, M., et al., 2020, “Hyperuniform Monocrystalline Structures by Spinodal Solid-State Dewetting,” Phys. Rev. Lett. 125, 126101.
  446. Salvarezza, R. C., L. Vázquez, H. Miguez, R. Mayoral, C. López, and F. Meseguer, 1996, “Edward-Wilkinson Behavior of Crystal Surfaces Grown by Sedimentation of SiO2 Nanospheres,” Phys. Rev. Lett. 77, 4572.
  447. Sanders, D. P., 2010, “Advances in patterning materials for 193 nm immersion lithography,” Chem. Rev. 110, 321–360.
  448. Sapienza, R., 2019, “Determining random lasing action,” Nat. Rev. Phys. 1, 690–695.
  449. Sapienza, R., P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. Van Hulst, 2011, “Long-Tail Statistics of the Purcell Factor in Disordered Media Driven by Near-Field Interactions,” Phys. Rev. Lett. 106, 163902.
  450. Sapienza, R., P. D. García, J. Bertolotti, M. D. Martin, A. Blanco, L. Vina, C. López, and D. S. Wiersma, 2007, “Observation of Resonant Behavior in the Energy Velocity of Diffused Light,” Phys. Rev. Lett. 99, 233902.
  451. Saranathan, V., J. D. Forster, H. Noh, S.-F. Liew, S. G. J. Mochrie, H. Cao, E. R. Dufresne, and R. O. Prum, 2012, “Structure and optical function of amorphous photonic nanostructures from avian feather barbs: A comparative small angle x-ray scattering (SAXS) analysis of 230 bird species,” J. R. Soc. Interface 9, 2563–2580.
  452. Saulnier, P. M., M. P. Zinkin, and G. H. Watson, 1990, “Scatterer correlation effects on photon transport in dense random media,” Phys. Rev. B 42, 2621.
  453. Sauvan, C., J.-P. Hugonin, R. Carminati, and P. Lalanne, 2014, “Modal representation of spatial coherence in dissipative and resonant photonic systems,” Phys. Rev. A 89, 043825.
  454. Sauvan, C., J.-P. Hugonin, I. S. Maksymov, and P. Lalanne, 2013, “Theory of the Spontaneous Optical Emission of Nanosize Photonic and Plasmon Resonators,” Phys. Rev. Lett. 110, 237401.
  455. Savo, R., M. Burresi, T. Svensson, K. Vynck, and D. S. Wiersma, 2014, “Walk dimension for light in complex disordered media,” Phys. Rev. A 90, 023839.
  456. Savo, R., R. Pierrat, U. Najar, R. Carminati, S. Rotter, and S. Gigan, 2017, “Observation of mean path length invariance in light-scattering media,” Science 358, 765–768.
  457. Sbalbi, N., Q. Li, and E. M. Furst, 2022, “Effect of scatterer interactions on photon transport in diffusing wave spectroscopy,” Phys. Rev. E 106, 064609.
  458. Scheffold, F., J. Haberko, S. Magkiriadou, and L. S. Froufe-Pérez, 2022, “Transport through Amorphous Photonic Materials with Localization and Bandgap Regimes,” Phys. Rev. Lett. 129, 157402.
  459. Scheffold, F., R. Lenke, R. Tweer, and G. Maret, 1999, “Localization or classical diffusion of light?,” Nature (London) 398, 206.
  460. Scheffold, F., and G. Maret, 1998, “Universal Conductance Fluctuations of Light,” Phys. Rev. Lett. 81, 5800.
  461. Scheffold, F., and T. G. Mason, 2009, “Scattering from highly packed disordered colloids,” J. Phys. Condens. Matter 21, 332102.
  462. Scheffold, F., and D. Wiersma, 2013, “Inelastic scattering puts in question recent claims of Anderson localization of light,” Nat. Photonics 7, 934–934.
  463. Schertel, L., G. T. van de Kerkhof, G. Jacucci, L. Catón, Y. Ogawa, B. D. Wilts, C. J. Ingham, S. Vignolini, and V. E. Johansen, 2020, “Complex photonic response reveals three-dimensional self-organization of structural coloured bacterial colonies,” J. R. Soc. Interface 17, 20200196.
  464. Schertel, L., L. Siedentop, J.-M. Meijer, P. Keim, C. M. Aegerter, G. J. Aubry, and G. Maret, 2019, “The structural colors of photonic glasses,” Adv. Opt. Mater. 7, 1900442.
  465. Schertel, L., I. Wimmer, P. Besirske, C. M. Aegerter, G. Maret, S. Polarz, and G. J. Aubry, 2019, “Tunable high-index photonic glasses,” Phys. Rev. Mater. 3, 015203.
  466. Schilder, N. J., C. Sauvan, J.-P. Hugonin, S. Jennewein, Y. R. P. Sortais, A. Browaeys, and J.-J. Greffet, 2016, “Polaritonic modes in a dense cloud of cold atoms,” Phys. Rev. A 93, 063835.
  467. Schilder, N. J., C. Sauvan, Y. R. P. Sortais, A. Browaeys, and J.-J. Greffet, 2017, “Homogenization of an ensemble of interacting resonant scatterers,” Phys. Rev. A 96, 013825.
  468. Schröder-Turk, G. E., S. Wickham, H. Averdunk, F. Brink, J. D. Fitz Gerald, L. Poladian, M. C. J. Large, and S. T. Hyde, 2011, “The chiral structure of porous chitin within the wing-scales of Callophrys rubi,” J. Struct. Biol. 174, 290–295.
  469. Schwartz, T., G. Bartal, S. Fishman, and M. Segev, 2007, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature (London) 446, 52–55.
  470. Seago, A. E., P. Brady, J.-P. Vigneron, and T. D. Schultz, 2009, “Gold bugs and beyond: A review of iridescence and structural colour mechanisms in beetles (Coleoptera),” J. R. Soc. Interface 6, S165–S184.
  471. Seal, K., A. K. Sarychev, H. Noh, D. A. Genov, A. Yamilov, V. M. Shalaev, Z. C. Ying, and H. Cao, 2005, “Near-Field Intensity Correlations in Semicontinuous Metal-Dielectric Films,” Phys. Rev. Lett. 94, 226101.
  472. Segev, M., Y. Silberberg, and D. N. Christodoulides, 2013, “Anderson localization of light,” Nat. Photonics 7, 197–204.
  473. Sellers, S. R., W. Man, S. Sahba, and M. Florescu, 2017, “Local self-uniformity in photonic networks,” Nat. Commun. 8, 14439.
  474. Setälä, T., K. Blomstedt, M. Kaivola, and A. T. Friberg, 2003, “Universality of electromagnetic-field correlations within homogeneous and isotropic sources,” Phys. Rev. E 67, 026613.
  475. Sgrignuoli, F., S. Torquato, and L. Dal Negro, 2022, “Subdiffusive wave transport and weak localization transition in three-dimensional stealthy hyperuniform disordered systems,” Phys. Rev. B 105, 064204.
  476. Shalaev, V. M., 2002, Optical Properties of Nanostructured Random Media, Topics in Applied Physics Vol. 82 (Springer Science+Business Media, New York).
  477. Shalaev, V. M., 2007, Nonlinear Optics of Random Media: Fractal Composites and Metal-Dielectric Films, Springer Tracts in Modern Physics Vol. 158 (Springer, New York).
  478. Shang, G., L. Maiwald, H. Renner, D. Jalas, M. Dosta, S. Heinrich, A. Petrov, and M. Eich, 2018, “Photonic glass for high contrast structural color,” Sci. Rep. 8, 7804.
  479. Shapiro, B., 1986, “Large Intensity Fluctuations for Wave Propagation in Random Media,” Phys. Rev. Lett. 57, 2168.
  480. Shapiro, B., 1999, “New Type of Intensity Correlation in Random Media,” Phys. Rev. Lett. 83, 4733.
  481. Sheng, P., 2006, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena, Springer Series in Materials Science Vol. 88 (Springer Science+Business Media, New York).
  482. Sheremet, A., R. Pierrat, and R. Carminati, 2020, “Absorption of scalar waves in correlated disordered media and its maximization using stealth hyperuniformity,” Phys. Rev. A 101, 053829.
  483. Shi, L., Y. Zhang, B. Dong, T. Zhan, X. Liu, and J. Zi, 2013, “Amorphous photonic crystals with only short-range order,” Adv. Mater. 25, 5314–5320.
  484. Siddique, R. H., G. Gomard, and H. Hölscher, 2015, “The role of random nanostructures for the omnidirectional anti-reflection properties of the glasswing butterfly,” Nat. Commun. 6, 6909.
  485. Sigalas, M. M., C. M. Soukoulis, C.-T. Chan, and D. Turner, 1996, “Localization of electromagnetic waves in two-dimensional disordered systems,” Phys. Rev. B 53, 8340.
  486. Skipetrov, S. E., and J. H. Page, 2016, “Red light for Anderson localization,” New J. Phys. 18, 021001.
  487. Skipetrov, S. E., and I. M. Sokolov, 2014, “Absence of Anderson Localization of Light in a Random Ensemble of Point Scatterers,” Phys. Rev. Lett. 112, 023905.
  488. Skipetrov, S. E., and B. A. van Tiggelen, 2006, “Dynamics of Anderson Localization in Open 3D Media,” Phys. Rev. Lett. 96, 043902.
  489. Skoge, M., A. Donev, F. H. Stillinger, and S. Torquato, 2006, “Packing hyperspheres in high-dimensional Euclidean spaces,” Phys. Rev. E 74, 041127.
  490. Smoluchowski, M. v., 1908, “Molekular-kinetische theorie der opaleszenz von gasen im kritischen zustande, sowie einiger verwandter erscheinungen,” Ann. Phys. (Berlin) 330, 205–226.
  491. Solomon, T. H., E. R. Weeks, and H. L. Swinney, 1993, “Observation of Anomalous Diffusion and Lévy Flights in a Two-Dimensional Rotating Flow,” Phys. Rev. Lett. 71, 3975.
  492. Soneira, R. M., and P. J. E. Peebles, 1977, “Is there evidence for a spatially homogeneous population of field galaxies,” Astrophys. J. 211, 1–15.
  493. Song, C., P. Wang, and H. A. Makse, 2008, “A phase diagram for jammed matter,” Nature (London) 453, 629.
  494. Song, D.-P., G. Jacucci, F. Dundar, A. Naik, H.-F. Fei, S. Vignolini, and J. J. Watkins, 2018, “Photonic resins: Designing optical appearance via block copolymer self-assembly,” Macromolecules 51, 2395–2400.
  495. Song, D.-P., T. H. Zhao, G. Guidetti, S. Vignolini, and R. M. Parker, 2019, “Hierarchical photonic pigments via the confined self-assembly of bottlebrush block copolymers,” ACS Nano 13, 1764–1771.
  496. Soukoulis, C. M., 2012, Photonic Crystals and Light Localization in the 21st Century, NATO Science Series C Vol. 563 (Springer Science+Business Media, New York).
  497. Soukoulis, C. M., S. Datta, and E. N. Economou, 1994, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800.
  498. Soukoulis, C. M., and M. Wegener, 2011, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523.
  499. Sperling, T., W. Buehrer, C. M. Aegerter, and G. Maret, 2013, “Direct determination of the transition to localization of light in three dimensions,” Nat. Photonics 7, 48–52.
  500. Spry, R. J., and D. J. Kosan, 1986, “Theoretical analysis of the crystalline colloidal array filter,” Appl. Spectrosc. 40, 782–784.
  501. Staude, I., M. Thiel, S. Essig, C. Wolff, K. Busch, G. Von Freymann, and M. Wegener, 2010, “Fabrication and characterization of silicon woodpile photonic crystals with a complete bandgap at telecom wavelengths,” Opt. Lett. 35, 1094–1096.
  502. Stavenga, D. G., J. Tinbergen, H. L. Leertouwer, and B. D. Wilts, 2011, “Kingfisher feathers—Colouration by pigments, spongy nanostructures and thin films,” J. Exp. Biol. 214, 3960–3967.
  503. Stefik, M., S. Guldin, S. Vignolini, U. Wiesner, and U. Steiner, 2015, “Block copolymer self-assembly for nanophotonics,” Chem. Soc. Rev. 44, 5076–5091.
  504. Stein, S., 1961, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24.
  505. Stephenson, A. B., et al., 2023, “Predicting the structural colors of films of disordered photonic balls,” ACS Photonics 10, 58–70.
  506. Stillinger, F. H., and T. A. Weber, 1985, “Computer simulation of local order in condensed phases of silicon,” Phys. Rev. B 31, 5262.
  507. Stover, J. C., 1995, Optical Scattering: Measurement and Analysis, Vol. 2 (SPIE—International Society for Optical Engineering, Bellingham, WA).
  508. Sullivan, D. M., 2013, Electromagnetic Simulation Using the FDTD Method (John Wiley & Sons, New York).
  509. Sullivan, D. E., and J. M. Deutch, 1976, “Local field models for light scattering and the dielectric constant of nonpolar fluids,” J. Chem. Phys. 64, 3870–3878.
  510. Sun, H.-B., S. Matsuo, and H. Misawa, 1999, “Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin,” Appl. Phys. Lett. 74, 786–788.
  511. Svensson, T., K. Vynck, E. Adolfsson, A. Farina, A. Pifferi, and D. S. Wiersma, 2014, “Light diffusion in quenched disorder: Role of step correlations,” Phys. Rev. E 89, 022141.
  512. Svensson, T., K. Vynck, M. Grisi, R. Savo, M. Burresi, and D. S. Wiersma, 2013, “Holey random walks: Optics of heterogeneous turbid composites,” Phys. Rev. E 87, 022120.
  513. Ta, V. D., S. Caixeiro, D. Saxena, and R. Sapienza, 2021, “Biocompatible polymer and protein microspheres with inverse photonic glass structure for random micro-biolasers,” Adv. Photonics Res. 2, 2100036.
  514. Taflove, A., and S. C. Hagness, 2005, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, London).
  515. Takeoka, Y., 2012, “Angle-independent structural coloured amorphous arrays,” J. Mater. Chem. 22, 23299–23309.
  516. Takeoka, Y., S. Yoshioka, A. Takano, S. Arai, K. Nueangnoraj, H. Nishihara, M. Teshima, Y. Ohtsuka, and T. Seki, 2013, “Production of colored pigments with amorphous arrays of black and white colloidal particles,” Angew. Chem. 125, 7402–7406.
  517. Tarasov, V. E., 2015, “Fractal electrodynamics via non-integer dimensional space approach,” Phys. Lett. A 379, 2055–2061.
  518. Tavakoli, N., et al., 2022, “Over 65% sunlight absorption in a 1  μm Si slab with hyperuniform texture,” ACS Photonics 9, 1206–1217.
  519. Tétreault, N., G. von Freymann, M. Deubel, M. Hermatschweiler, F. Pérez-Willard, S. John, M. Wegener, and G. A. Ozin, 2006, “New route to three-dimensional photonic bandgap materials: Silicon double inversion of polymer templates,” Adv. Mater. 18, 457–460.
  520. Thorpe, M. F., 1973, “A note on band gaps in amorphous semiconductors (relation to structure),” J. Phys. C 6, L75.
  521. Toninelli, C., E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, 2008, “Exceptional Reduction of the Diffusion Constant in Partially Disordered Photonic Crystals,” Phys. Rev. Lett. 101, 123901.
  522. Torquato, S., 2013, Random Heterogeneous Materials: Microstructure and Macroscopic Properties, Interdisciplinary Applied Mathematics Vol. 16 (Springer Science+Business Media, New York).
  523. Torquato, S., 2018, “Hyperuniform states of matter,” Phys. Rep. 745, 1–95.
  524. Torquato, S., and J. Kim, 2021, “Nonlocal Effective Electromagnetic Wave Characteristics of Composite Media: Beyond the Quasistatic Regime,” Phys. Rev. X 11, 021002.
  525. Torquato, S., and G. Stell, 1982, “Microstructure of two-phase random media. I. The n-point probability functions,” J. Chem. Phys. 77, 2071–2077.
  526. Torquato, S., and F. H. Stillinger, 2003, “Local density fluctuations, hyperuniformity, and order metrics,” Phys. Rev. E 68, 041113.
  527. Torquato, S., and F. H. Stillinger, 2010, “Jammed hard-particle packings: From Kepler to Bernal and beyond,” Rev. Mod. Phys. 82, 2633.
  528. Torquato, S., T. M. Truskett, and P. G. Debenedetti, 2000, “Is Random Close Packing of Spheres Well Defined?,” Phys. Rev. Lett. 84, 2064.
  529. Trompoukis, C., I. Massiot, V. Depauw, O. El Daif, K. Lee, A. Dmitriev, I. Gordon, R. Mertens, and J. Poortmans, 2016, “Disordered nanostructures by hole-mask colloidal lithography for advanced light trapping in silicon solar cells,” Opt. Express 24, A191–A201.
  530. Tsang, L., C.-T. Chen, A. T. C. Chang, J. Guo, and K.-H. Ding, 2000, “Dense media radiative transfer theory based on quasicrystalline approximation with applications to passive microwave remote sensing of snow,” Radio Sci. 35, 731–749.
  531. Tsang, L., and A. Ishimaru, 1984, “Backscattering enhancement of random discrete scatterers,” J. Opt. Soc. Am. A 1, 836–839.
  532. Tsang, L., and J. A. Kong, 1980, “Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism,” J. Appl. Phys. 51, 3465–3485.
  533. Tsang, L., and J. A. Kong, 1981, “Scattering of electromagnetic waves from random media with strong permittivity fluctuations,” Radio Sci. 16, 303–320.
  534. Tsang, L., and J. A. Kong, 1982, “Effective propagation constants for coherent electromagnetic wave propagation in media embedded with dielectric scatters,” J. Appl. Phys. 53, 7162–7173.
  535. Tsang, L., and J. A. Kong, 2001, Scattering of Electromagnetic Waves—Advanced Topics (John Wiley & Sons, New York).
  536. Tsang, L., J. A. Kong, and K.-H. Ding, 2004, Scattering of Electromagnetic Waves: Theories and Applications, Vol. 27 (John Wiley & Sons, New York).
  537. Türeci, H. E., L. Ge, S. Rotter, and A. D. Stone, 2008, “Strong interactions in multimode random lasers,” Science 320, 643–646.
  538. Twersky, V., 1964, “On propagation in random media of discrete scatterers,” in Stochastic Processes in Mathematical Physics and Engineering, Vol. 16, edited by R. E. Bellmann (American Mathematical Society, Providence), pp. 84–116.
  539. Twersky, V., 1975, “Transparency of pair-correlated, random distributions of small scatterers, with applications to the cornea,” J. Opt. Soc. Am. 65, 524–530.
  540. Uche, O. U., F. H. Stillinger, and S. Torquato, 2004, “Constraints on collective density variables: Two dimensions,” Phys. Rev. E 70, 046122.
  541. Uppu, R., and S. Mujumdar, 2015, “Exponentially Tempered Lévy Sums in Random Lasers,” Phys. Rev. Lett. 114, 183903.
  542. Utel, F., L. Cortese, D. S. Wiersma, and L. Pattelli, 2019, “Optimized white reflectance in photonic-network structures,” Adv. Opt. Mater. 7, 1900043.
  543. Valantinas, L., and T. Vettenburg, 2022, “Computing coherent light scattering on the millimetre scale using a recurrent neural network without training,” arXiv:2208.01118.
  544. Van Albada, M. P., and A. Lagendijk, 1985, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55, 2692.
  545. Van Albada, M. P., B. A. van Tiggelen, A. Lagendijk, and A. Tip, 1991, “Speed of Propagation of Classical Waves in Strongly Scattering Media,” Phys. Rev. Lett. 66, 3132.
  546. Van Bladel, J., and J. Van Bladel, 1991, Singular Electromagnetic Fields and Sources (Clarendon Press, Oxford).
  547. Van Kranendonk, J., and J. E. Sipe, 1977, “Foundations of the macroscopic electromagnetic theory of dielectric media,” in Progress in Optics, Vol. 15, edited by E. Wolf (Elsevier, New York), Chap. V, pp. 245–350.
  548. van Rossum, M. C. W., and Th. M. Nieuwenhuizen, 1999, “Multiple scattering of classical waves: Microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313.
  549. van Soest, Gijs, and Ad Lagendijk, 2002, “β factor in a random laser,” Phys. Rev. E 65, 047601.
  550. van Tiggelen, B. A., A. Lagendijk, and D. S. Wiersma, 2000, “Reflection and Transmission of Waves near the Localization Threshold,” Phys. Rev. Lett. 84, 4333.
  551. van Tiggelen, B. A., and R. Maynard, 1998, “Reciprocity and coherent backscattering of light,” in Wave Propagation in Complex Media, edited by G. Papanicolaou (Springer, New York), pp. 247–271.
  552. van Tiggelen, B. A., and S. E. Skipetrov, 2021, “Longitudinal modes in diffusion and localization of light,” Phys. Rev. B 103, 174204.
  553. Városi, F., and E. Dwek, 1999, “Analytical approximations for calculating the escape and absorption of radiation in clumpy dusty environments,” Astrophys. J. 523, 265.
  554. Videen, G., 1991, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489.
  555. Vignolini, S., T. Gregory, M. Kolle, A. Lethbridge, E. Moyroud, U. Steiner, B. J. Glover, P. Vukusic, and P. J. Rudall, 2016, “Structural colour from helicoidal cell-wall architecture in fruits of Margaritaria nobilis,” J. R. Soc. Interface 13, 20160645.
  556. Vignolini, S., P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, 2012, “Pointillist structural color in Pollia fruit,” Proc. Natl. Acad. Sci. U.S.A. 109, 15712–15715.
  557. Vlasov, Yu. A., V. N. Astratov, A. V. Baryshev, A. A. Kaplyanskii, O. Z. Karimov, and M. F. Limonov, 2000, “Manifestation of intrinsic defects in optical properties of self-organized opal photonic crystals,” Phys. Rev. E 61, 5784.
  558. Vlasov, Yu. A., M. A. Kaliteevski, and V. V. Nikolaev, 1999, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B 60, 1555.
  559. Vogel, N., S. Utech, G. T. England, T. Shirman, K. R. Phillips, N. Koay, I. B. Burgess, M. Kolle, D. A. Weitz, and J. Aizenberg, 2015, “Color from hierarchy: Diverse optical properties of micron-sized spherical colloidal assemblies,” Proc. Natl. Acad. Sci. U.S.A. 112, 10845–10850.
  560. Vollhardt, D., and P. Wölfle, 1980, “Diagrammatic, self-consistent treatment of the Anderson localization problem in d≤2 dimensions,” Phys. Rev. B 22, 4666.
  561. Vollhardt, D., and P. Wölfle, 1982, “Scaling Equations from a Self-Consistent Theory of Anderson Localization,” Phys. Rev. Lett. 48, 699.
  562. Vukusic, P., B. Hallam, and J. Noyes, 2007, “Brilliant whiteness in ultrathin beetle scales,” Science 315, 348.
  563. Vynck, K., M. Burresi, F. Riboli, and D. S. Wiersma, 2012, “Photon management in two-dimensional disordered media,” Nat. Mater. 11, 1017.
  564. Vynck, K., D. Felbacq, E. Centeno, A. I. Cuabuz, D. Cassagne, and B. Guizal, 2009, “All-Dielectric Rod-Type Metamaterials at Optical Frequencies,” Phys. Rev. Lett. 102, 133901.
  565. Vynck, K., R. Pacanowski, A. Agreda, A. Dufay, X. Granier, and P. Lalanne, 2022, “The visual appearances of disordered optical metasurfaces,” Nat. Mater. 21, 1035–1041.
  566. Vynck, K., R. Pierrat, and R. Carminati, 2014, “Polarization and spatial coherence of electromagnetic waves in uncorrelated disordered media,” Phys. Rev. A 89, 013842.
  567. Vynck, K., R. Pierrat, and R. Carminati, 2016, .“Multiple scattering of polarized light in disordered media exhibiting short-range structural correlations,” Phys. Rev. A 94, 033851.
  568. Wales, D. J., and R. S. Berry, 1994, “Coexistence in Finite Systems,” Phys. Rev. Lett. 73, 2875.
  569. Wan, W., Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, 2011, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892.
  570. Wang, B. X., and C. Y. Zhao, 2018a, “Achieving a strongly negative scattering asymmetry factor in random media composed of dual-dipolar particles,” Phys. Rev. A 97, 023836.
  571. Wang, B. X., and C. Y. Zhao, 2018b, “Effect of dependent scattering on light absorption in highly scattering random media,” Int. J. Heat Mass Transfer 125, 1069–1078.
  572. Wang, B. X., and C. Y. Zhao, 2020, “The dependent scattering effect on radiative properties of micro/nanoscale discrete disordered media,” Annu. Rev. Heat Transfer 23, 231–353.
  573. Wang, J.-S., 2000, “Series expansion and computer simulation studies of random sequential adsorption,” Colloids Surf. A 165, 325–343.
  574. Wang, L., and S. L. Jacques, 1992, “Monte Carlo modeling of light transport in multi-layered tissues in standard C,” University of Texas, M. D. Anderson Cancer Center, technical report.
  575. Wang, Z.-s., and B.-w. Lu, 1994, “The scattering of electromagnetic waves in fractal media,” Waves Random Media 4, 97–103.
  576. Waterman, P. C., 1965, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812.
  577. Watson, D. F., 1981, “Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes,” Comput. J. 24, 167–172.
  578. Weaire, D., 1971, “Existence of a Gap in the Electronic Density of States of a Tetrahedrally Bonded Solid of Arbitrary Structure,” Phys. Rev. Lett. 26, 1541.
  579. Weijs, J. H., R. Jeanneret, R. Dreyfus, and D. Bartolo, 2015, “Emergent Hyperuniformity in Periodically Driven Emulsions,” Phys. Rev. Lett. 115, 108301.
  580. Weimann, S., M. Kremer, Y. Plotnik, Y. Lumer, S. Nolte, K. G. Makris, M. Segev, M. C. Rechtsman, and A. Szameit, 2017, “Topologically protected bound states in photonic parity–time-symmetric crystals,” Nat. Mater. 16, 433–438.
  581. Wertheim, M. S., 1963, “Exact Solution of the Percus-Yevick Integral Equation for Hard Spheres,” Phys. Rev. Lett. 10, 321.
  582. Wertheim, M. S., 1973, “Dielectric constant of non-polar fluids,” Mol. Phys. 25, 211–223.
  583. Whitney, H. M., M. Kolle, P. Andrew, L. Chittka, U. Steiner, and B. J. Glover, 2009, “Floral iridescence, produced by diffractive optics, acts as a cue for animal pollinators,” Science 323, 130–133.
  584. Widom, B., 1966, “Random sequential addition of hard spheres to a volume,” J. Chem. Phys. 44, 3888–3894.
  585. Wiersma, D. S., 2008, “The physics and applications of random lasers,” Nat. Phys. 4, 359.
  586. Wiersma, D. S., 2013, “Disordered photonics,” Nat. Photonics 7, 188–196.
  587. Wiersma, D. S., P. Bartolini, A. Lagendijk, and R. Righini, 1997, “Localization of light in a disordered medium,” Nature (London) 390, 671.
  588. Wiersma, D. S., and A. Lagendijk, 1996, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256.
  589. Wilts, B. D., P. L. Clode, N. H. Patel, and G. E. Schröder-Turk, 2019, “Nature’s functional nanomaterials: Growth or self-assembly?,” MRS Bull. 44, 106–112.
  590. Wilts, B. D., K. Michielsen, J. Kuipers, H. De Raedt, and D. G. Stavenga, 2012, “Brilliant camouflage: Photonic crystals in the diamond weevil, Entimus imperialis,” Proc. R. Soc. B 279, 2524–2530.
  591. Wilts, B. D., K. Michielsen, H. De Raedt, and D. G. Stavenga, 2011, “Iridescence and spectral filtering of the gyroid-type photonic crystals in Parides sesostris wing scales,” Interface Focus 2, 681–687.
  592. Wilts, B. D., K. Michielsen, H. De Raedt, and D. G. Stavenga, 2014, “Sparkling feather reflections of a bird-of-paradise explained by finite-difference time-domain modeling,” Proc. Natl. Acad. Sci. U.S.A. 111, 4363–4368.
  593. Wilts, B. D., B. A. Zubiri, M. A. Klatt, B. Butz, M. G. Fischer, S. T. Kelly, E. Spiecker, U. Steiner, and G. E. Schröder-Turk, 2017, “Butterfly gyroid nanostructures as a time-frozen glimpse of intracellular membrane development,” Sci. Adv. 3, e1603119.
  594. Wilts, B. D., et al., 2018, “Evolutionary-optimized photonic network structure in white beetle wing scales,” Adv. Mater. 30, 1702057.
  595. Wolf, P.-E., and G. Maret, 1985, “Weak Localization and Coherent Backscattering of Photons in Disordered Media,” Phys. Rev. Lett. 55, 2696.
  596. Wooten, F., K. Winer, and D. Weaire, 1985, “Computer Generation of Structural Models of Amorphous Si and Ge,” Phys. Rev. Lett. 54, 1392.
  597. Wriedt, T., 2009a, Internet portal ScattPort, https://scattport.org/ (accessed December 23, 2022).
  598. Wriedt, T., 2009b, “Light scattering theories and computer codes,” J. Quant. Spectrosc. Radiat. Transfer 110, 833–843.
  599. Wright, A. C., and M. F. Thorpe, 2013, “Eighty years of random networks,” Phys. Status Solidi B 250, 931–936.
  600. Xiao, M., A. B. Stephenson, A. Neophytou, V. Hwang, D. Chakrabarti, and V. N. Manoharan, 2021, “Investigating the trade-off between color saturation and angle-independence in photonic glasses,” Opt. Express 29, 21212–21224.
  601. Yablonovitch, E., 1982, “Statistical ray optics,” J. Opt. Soc. Am. 72, 899–907.
  602. Yablonovitch, E., 1987, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059.
  603. Yaghjian, A. D., 1980, “Electric dyadic Green’s functions in the source region,” Proc. IEEE 68, 248–263.
  604. Yamilov, A., S. E. Skipetrov, T. W. Hughes, M. Minkov, Z. Yu, and H. Cao, 2022, “Anderson localization of electromagnetic waves in three dimensions,” arXiv:2203.02842.
  605. Yamilov, A. G., R. Sarma, B. Redding, B. Payne, H. Noh, and H. Cao, 2014, “Position-Dependent Diffusion of Light in Disordered Waveguides,” Phys. Rev. Lett. 112, 023904.
  606. Yan, W., R. Faggiani, and P. Lalanne, 2018, “Rigorous modal analysis of plasmonic nanoresonators,” Phys. Rev. B 97, 205422.
  607. Yang, J.-K., S. V. Boriskina, H. Noh, M. J. Rooks, G. S. Solomon, L. Dal Negro, and H. Cao, 2010, “Demonstration of laser action in a pseudorandom medium,” Appl. Phys. Lett. 97, 223101.
  608. Yang, J.-K., H. Noh, S. F. Liew, M. J. Rooks, G. S. Solomon, and H. Cao, 2011, “Lasing modes in polycrystalline and amorphous photonic structures,” Phys. Rev. A 84, 033820.
  609. Yang, J.-K., C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, 2010, “Photonic-band-gap effects in two-dimensional polycrystalline and amorphous structures,” Phys. Rev. A 82, 053838.
  610. Yazhgur, P., G. J. Aubry, L. S. Froufe-Pérez, and F. Scheffold, 2021, “Light scattering from colloidal aggregates on a hierarchy of length scales,” Opt. Express 29, 14367–14383.
  611. Yazhgur, P., G. J. Aubry, L. S. Froufe-Pérez, and F. Scheffold, 2022, “Scattering phase delay and momentum transfer of light in disordered media,” Phys. Rev. Res. 4, 023235.
  612. Yazhgur, P., N. Muller, and F. Scheffold, 2022, “Inkjet printing of structurally colored self-assembled colloidal aggregates,” ACS Photonics 9, 2809–2816.
  613. Yee, K., 1966, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307.
  614. Yeh, P., et al., 2005, Optical Waves in Layered Media, Wiley Series in Pure and Applied Optics (Wiley, New York).
  615. Yi, G.-R., S.-J. Jeon, T. Thorsen, V. N. Manoharan, S. R. Quake, D. J. Pine, and S.-M. Yang, 2003, “Generation of uniform photonic balls by template-assisted colloidal crystallization,” Synth. Met. 139, 803–806.
  616. Yin, H., B. Dong, X. Liu, T. Zhan, L. Shi, J. Zi, and E. Yablonovitch, 2012, “Amorphous diamond-structured photonic crystal in the feather barbs of the scarlet macaw,” Proc. Natl. Acad. Sci. U.S.A. 109, 10798–10801.
  617. Yu, S., C.-W. Qiu, Y. Chong, S. Torquato, and N. Park, 2021, “Engineered disorder in photonics,” Nat. Rev. Mater. 6, 226–243.
  618. Yu, Z., A. Raman, and S. Fan, 2010, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. 107, 17491–17496.
  619. Yvon, J., 1937, Recherches sur la Théorie Cinétique des Liquides: Fluctuations en Densité et Diffusion de la Lumière (Hermann et Cie, Paris).
  620. Zaburdaev, V., S. Denisov, and J. Klafter, 2015, “Lévy walks,” Rev. Mod. Phys. 87, 483.
  621. Zachary, C. E., Y. Jiao, and S. Torquato, 2011, “Hyperuniform Long-Range Correlations Are a Signature of Disordered Jammed Hard-Particle Packings,” Phys. Rev. Lett. 106, 178001.
  622. Zhang, C., N. Gnan, T. G. Mason, E. Zaccarelli, and F. Scheffold, 2016, “Dynamical and structural signatures of the glass transition in emulsions,” J. Stat. Mech. 094003.
  623. Zhang, F., and H. Yan, 2017, “DNA self-assembly scaled up,” Nature (London) 552, 34–35.
  624. Zhang, G., and S. Torquato, 2013, “Precise algorithm to generate random sequential addition of hard hyperspheres at saturation,” Phys. Rev. E 88, 053312.
  625. Zhao, T. H., G. Jacucci, X. Chen, D.-P. Song, S. Vignolini, and R. M. Parker, 2020, “Angular-independent photonic pigments via the controlled micellization of amphiphilic bottlebrush block copolymers,” Adv. Mater. 32, 2002681.
  626. Zhu, J., M. Li, R. Rogers, W. Meyer, R. H. Ottewill, W. B. Russel, P. M. Chaikin, and STS-73 Space Shuttle Crew, 1997, “Crystallization of hard-sphere colloids in microgravity,” Nature (London) 387, 883–885.
  627. Zito, G., G. Rusciano, G. Pesce, A. Malafronte, R. Di Girolamo, G. Ausanio, A. Vecchione, and A. Sasso, 2015, “Nanoscale engineering of two-dimensional disordered hyperuniform block-copolymer assemblies,” Phys. Rev. E 92, 050601.
  628. Zoorob, M. E., M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, 2000, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature (London) 404, 740.

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Rev. Mod. Phys. 95, 045003– Published 15 November, 2023
  • Received 27 June 2021
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