Abstract

It is common understanding that multilayered dielectric metamaterials, in the regime of deeply subwavelength layers, are accurately described by simple effective-medium models based on mixing formulas that do not depend on the spatial arrangement. In the wake of recent studies that have shown counterintuitive examples of periodic and aperiodic (orderly or random) scenarios in which this premise breaks down, we study here the effects of deterministic disorder. With specific reference to a model based on Golay-Rudin-Shapiro sequences, we illustrate certain peculiar boundary effects that can occur in finite-size dielectric multilayers, leading to anomalous light-transport properties that are in stark contrast with the predictions from conventional effective-medium theory. Via parametric and comparative studies, we elucidate the underlying physical mechanisms, also highlighting similarities and differences with respect to previously studied geometries. Our outcomes may inspire potential applications to optical sensing, switching and lasing.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Finite-size scaling and disorder effect on the transmissivity of multilayered structures with metamaterials

E. M. Nascimento, F. A. B. F. de Moura, and M. L. Lyra
Opt. Express 16(10) 6860-6866 (2008)

Giant optical nonlocality near the Dirac point in metal-dielectric multilayer metamaterials

Lei Sun, Jie Gao, and Xiaodong Yang
Opt. Express 21(18) 21542-21555 (2013)

References

  • View by:
  • |
  • |
  • |

  1. F. Capolino, Theory and Phenomena of Metamaterials (CRC Press, Boca Raton, FL, 2009).
  2. M. G. Silveirinha, “Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters,” Phys. Rev. B 75(11), 115104 (2007).
    [Crossref]
  3. A. Alù, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84(7), 075153 (2011).
    [Crossref]
  4. A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84(11), 115438 (2011).
    [Crossref]
  5. R.-L. Chern, “Spatial dispersion and nonlocal effective permittivity for periodic layered metamaterials,” Opt. Express 21(14), 16514–16527 (2013).
    [Crossref]
  6. A. Ciattoni and C. Rizza, “Nonlocal homogenization theory in metamaterials: Effective electromagnetic spatial dispersion and artificial chirality,” Phys. Rev. B 91(18), 184207 (2015).
    [Crossref]
  7. A. Sihvola, Electromagnetic Mixing Formulas and Applications, Electromagnetics and Radar Series (IET, London, UK, 1999).
  8. H. Herzig Sheinfux, I. Kaminer, Y. Plotnik, G. Bartal, and M. Segev, “Subwavelength multilayer dielectrics: Ultrasensitive transmission and breakdown of effective-medium theory,” Phys. Rev. Lett. 113(24), 243901 (2014).
    [Crossref]
  9. S. V. Zhukovsky, A. Andryieuski, O. Takayama, E. Shkondin, R. Malureanu, F. Jensen, and A. V. Lavrinenko, “Experimental demonstration of effective medium approximation breakdown in deeply subwavelength all-dielectric multilayers,” Phys. Rev. Lett. 115(17), 177402 (2015).
    [Crossref]
  10. A. Andryieuski, A. V. Lavrinenko, and S. V. Zhukovsky, “Anomalous effective medium approximation breakdown in deeply subwavelength all-dielectric photonic multilayers,” Nanotechnology 26(18), 184001 (2015).
    [Crossref]
  11. V. Popov, A. V. Lavrinenko, and A. Novitsky, “Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation,” Phys. Rev. B 94(8), 085428 (2016).
    [Crossref]
  12. X. Lei, L. Mao, Y. Lu, and P. Wang, “Revisiting the effective medium approximation in all-dielectric subwavelength multilayers: Breakdown and rebuilding,” Phys. Rev. B 96(3), 035439 (2017).
    [Crossref]
  13. A. Maurel and J.-J. Marigo, “Sensitivity of a dielectric layered structure on a scale below the periodicity: A fully local homogenized model,” Phys. Rev. B 98(2), 024306 (2018).
    [Crossref]
  14. G. Castaldi, A. Alù, and V. Galdi, “Boundary effects of weak nonlocality in multilayered dielectric metamaterials,” Phys. Rev. Appl. 10(3), 034060 (2018).
    [Crossref]
  15. M. A. Gorlach and M. Lapine, “Boundary conditions for the effective-medium description of subwavelength multilayered structures,” Phys. Rev. B 101(7), 075127 (2020).
    [Crossref]
  16. H. Herzig Sheinfux, I. Kaminer, A. Z. Genack, and M. Segev, “Interplay between evanescence and disorder in deep subwavelength photonic structures,” Nat. Commun. 7(1), 12927 (2016).
    [Crossref]
  17. H. Herzig Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
    [Crossref]
  18. E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69(2), 397–441 (2006).
    [Crossref]
  19. L. Dal Negro and S. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photonics Rev. 6(2), 178–218 (2012).
    [Crossref]
  20. M. Coppolaro, G. Castaldi, and V. Galdi, “Aperiodic order induced enhancement of weak nonlocality in multilayered dielectric metamaterials,” Phys. Rev. B 98(19), 195128 (2018).
    [Crossref]
  21. M. J. E. Golay, “Static multislit spectrometry and its application to the panoramic display of infrared spectra,” J. Opt. Soc. Am. 41(7), 468–472 (1951).
    [Crossref]
  22. H. S. Shapiro, “Extremal problems for polynomials and power series,” Ph.D. thesis, Massachusetts Institute of Technology (1952).
  23. W. Rudin, “Some theorems on Fourier coefficients,” Proc. Am. Math. Soc. 10(6), 855 (1959).
    [Crossref]
  24. N. P. Fogg, V. Berthé, S. Ferenczi, C. Mauduit, and A. Siegel, eds., Substitutions in Dynamics, Arithmetics and Combinatorics, vol. 1794 of Lecture Notes in Mathematics (Springer, Berlin, 2002).
  25. G. Wolff and D. Levine, “Diffuse scattering and atomic order,” Europhys. Lett. 117(3), 36001 (2017).
    [Crossref]
  26. V. Berthé, “Conditional entropy of some automatic sequences,” J. Phys. A: Math. Gen. 27(24), 7993–8006 (1994).
    [Crossref]
  27. V. Galdi, V. Pierro, G. Castaldi, I. M. Pinto, and L. B. Felsen, “Radiation properties of one-dimensional random-like antenna arrays based on Rudin-Shapiro sequences,” IEEE Trans. Antennas Propag. 53(11), 3568–3575 (2005).
    [Crossref]
  28. A. la Cour-Harbo, “On the Rudin-Shapiro transform,” Appl. Comp. Harm. Anal. 24(3), 310–328 (2008).
    [Crossref]
  29. M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
    [Crossref]
  30. M. Moccia, C. Koral, G. P. Papari, S. Liu, L. Zhang, R. Y. Wu, G. Castaldi, T. J. Cui, V. Galdi, and A. Andreone, “Suboptimal coding metasurfaces for terahertz diffuse scattering,” Sci. Rep. 8(1), 11908 (2018).
    [Crossref]
  31. A. Gopinath, S. V. Boriskina, B. M. Reinhard, and L. Dal Negro, “Deterministic aperiodic arrays of metal nanoparticles for surface-enhanced Raman scattering (SERS),” Opt. Express 17(5), 3741–3753 (2009).
    [Crossref]
  32. C. Forestiere, G. Miano, S. V. Boriskina, and L. Dal Negro, “The role of nanoparticle shapes and deterministic aperiodicity for the design of nanoplasmonic arrays,” Opt. Express 17(12), 9648–9661 (2009).
    [Crossref]
  33. S. V. Boriskina, S. Y. K. Lee, J. J. Amsden, F. G. Omenetto, and L. Dal Negro, “Formation of colorimetric fingerprints on nano-patterned deterministic aperiodic surfaces,” Opt. Express 18(14), 14568–14576 (2010).
    [Crossref]
  34. F. Axel, J. P. Allouche, and Z.-Y. Wen, “On certain properties of high-resolution X-ray diffraction spectra of finite-size generalized Rudin-Shapiro multilayer heterostructures,” J. Phys.: Condens. Matter 4(45), 8713–8728 (1992).
    [Crossref]
  35. M. S. Vasconcelos and E. L. Albuquerque, “Transmission fingerprints in quasiperiodic dielectric multilayers,” Phys. Rev. B 59(17), 11128–11131 (1999).
    [Crossref]
  36. M. Hiltunen, L. Dal Negro, N.-N. Feng, L. C. Kimerling, and J. Michel, “Modeling of aperiodic fractal waveguide structures for multifrequency light transport,” J. Lightwave Technol. 25(7), 1841–1847 (2007).
    [Crossref]
  37. V. Agarwal, M. E. Mora-Ramos, and B. Alvarado-Tenorio, “Optical properties of multilayered period-doubling and Rudin-Shapiro porous silicon dielectric heterostructures,” Photonics Nanostructures: Fundam. Appl. 7(2), 63–68 (2009).
    [Crossref]
  38. Y. Bouazzi and M. Kanzari, “Optical Fabry-Perot filter based on photonic band gap quasi-periodic one-dimensional multilayer according to the definite Rudin-Shapiro distribution,” Opt. Commun. 285(12), 2774–2779 (2012).
    [Crossref]
  39. Y. Trabelsi, Y. Bouazzi, N. Benali, and M. Kanzari, “Narrow stop band optical filter using one-dimensional regular Fibonacci/Rudin Shapiro photonic quasicrystals,” Opt. Quantum Electron. 48(1), 54 (2016).
    [Crossref]
  40. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), 7th ed.
  41. L. Kroon, E. Lennholm, and R. Riklund, “Localization-delocalization in aperiodic systems,” Phys. Rev. B 66(9), 094204 (2002).
    [Crossref]
  42. L. Kroon and R. Riklund, “Absence of localization in a model with correlation measure as a random lattice,” Phys. Rev. B 69(9), 094204 (2004).
    [Crossref]
  43. X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: Extensions and applications,” Phys. Rev. B 62(21), 14020–14031 (2000).
    [Crossref]
  44. A. Dikopoltsev, A. Shaham, A. Pick, H. H. Sheinfux, and M. Segev, “Coaction of disorder and PT-symmetry in deep subwavelength multilayers,” in Frontiers in Optics + Laser Science APS/DLS (Optical Society of America, 2019), p. JTu4A.45.
  45. Y. Sharabi, E. Lustig, and M. Segev, “Light propagation in temporally disordered media,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2019), p. FF3B.1.

2020 (1)

M. A. Gorlach and M. Lapine, “Boundary conditions for the effective-medium description of subwavelength multilayered structures,” Phys. Rev. B 101(7), 075127 (2020).
[Crossref]

2018 (4)

A. Maurel and J.-J. Marigo, “Sensitivity of a dielectric layered structure on a scale below the periodicity: A fully local homogenized model,” Phys. Rev. B 98(2), 024306 (2018).
[Crossref]

G. Castaldi, A. Alù, and V. Galdi, “Boundary effects of weak nonlocality in multilayered dielectric metamaterials,” Phys. Rev. Appl. 10(3), 034060 (2018).
[Crossref]

M. Coppolaro, G. Castaldi, and V. Galdi, “Aperiodic order induced enhancement of weak nonlocality in multilayered dielectric metamaterials,” Phys. Rev. B 98(19), 195128 (2018).
[Crossref]

M. Moccia, C. Koral, G. P. Papari, S. Liu, L. Zhang, R. Y. Wu, G. Castaldi, T. J. Cui, V. Galdi, and A. Andreone, “Suboptimal coding metasurfaces for terahertz diffuse scattering,” Sci. Rep. 8(1), 11908 (2018).
[Crossref]

2017 (4)

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

G. Wolff and D. Levine, “Diffuse scattering and atomic order,” Europhys. Lett. 117(3), 36001 (2017).
[Crossref]

X. Lei, L. Mao, Y. Lu, and P. Wang, “Revisiting the effective medium approximation in all-dielectric subwavelength multilayers: Breakdown and rebuilding,” Phys. Rev. B 96(3), 035439 (2017).
[Crossref]

H. Herzig Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref]

2016 (3)

H. Herzig Sheinfux, I. Kaminer, A. Z. Genack, and M. Segev, “Interplay between evanescence and disorder in deep subwavelength photonic structures,” Nat. Commun. 7(1), 12927 (2016).
[Crossref]

V. Popov, A. V. Lavrinenko, and A. Novitsky, “Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation,” Phys. Rev. B 94(8), 085428 (2016).
[Crossref]

Y. Trabelsi, Y. Bouazzi, N. Benali, and M. Kanzari, “Narrow stop band optical filter using one-dimensional regular Fibonacci/Rudin Shapiro photonic quasicrystals,” Opt. Quantum Electron. 48(1), 54 (2016).
[Crossref]

2015 (3)

A. Ciattoni and C. Rizza, “Nonlocal homogenization theory in metamaterials: Effective electromagnetic spatial dispersion and artificial chirality,” Phys. Rev. B 91(18), 184207 (2015).
[Crossref]

S. V. Zhukovsky, A. Andryieuski, O. Takayama, E. Shkondin, R. Malureanu, F. Jensen, and A. V. Lavrinenko, “Experimental demonstration of effective medium approximation breakdown in deeply subwavelength all-dielectric multilayers,” Phys. Rev. Lett. 115(17), 177402 (2015).
[Crossref]

A. Andryieuski, A. V. Lavrinenko, and S. V. Zhukovsky, “Anomalous effective medium approximation breakdown in deeply subwavelength all-dielectric photonic multilayers,” Nanotechnology 26(18), 184001 (2015).
[Crossref]

2014 (1)

H. Herzig Sheinfux, I. Kaminer, Y. Plotnik, G. Bartal, and M. Segev, “Subwavelength multilayer dielectrics: Ultrasensitive transmission and breakdown of effective-medium theory,” Phys. Rev. Lett. 113(24), 243901 (2014).
[Crossref]

2013 (1)

2012 (2)

L. Dal Negro and S. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photonics Rev. 6(2), 178–218 (2012).
[Crossref]

Y. Bouazzi and M. Kanzari, “Optical Fabry-Perot filter based on photonic band gap quasi-periodic one-dimensional multilayer according to the definite Rudin-Shapiro distribution,” Opt. Commun. 285(12), 2774–2779 (2012).
[Crossref]

2011 (2)

A. Alù, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84(7), 075153 (2011).
[Crossref]

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84(11), 115438 (2011).
[Crossref]

2010 (1)

2009 (3)

2008 (1)

A. la Cour-Harbo, “On the Rudin-Shapiro transform,” Appl. Comp. Harm. Anal. 24(3), 310–328 (2008).
[Crossref]

2007 (2)

M. Hiltunen, L. Dal Negro, N.-N. Feng, L. C. Kimerling, and J. Michel, “Modeling of aperiodic fractal waveguide structures for multifrequency light transport,” J. Lightwave Technol. 25(7), 1841–1847 (2007).
[Crossref]

M. G. Silveirinha, “Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters,” Phys. Rev. B 75(11), 115104 (2007).
[Crossref]

2006 (1)

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69(2), 397–441 (2006).
[Crossref]

2005 (1)

V. Galdi, V. Pierro, G. Castaldi, I. M. Pinto, and L. B. Felsen, “Radiation properties of one-dimensional random-like antenna arrays based on Rudin-Shapiro sequences,” IEEE Trans. Antennas Propag. 53(11), 3568–3575 (2005).
[Crossref]

2004 (1)

L. Kroon and R. Riklund, “Absence of localization in a model with correlation measure as a random lattice,” Phys. Rev. B 69(9), 094204 (2004).
[Crossref]

2002 (1)

L. Kroon, E. Lennholm, and R. Riklund, “Localization-delocalization in aperiodic systems,” Phys. Rev. B 66(9), 094204 (2002).
[Crossref]

2000 (1)

X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: Extensions and applications,” Phys. Rev. B 62(21), 14020–14031 (2000).
[Crossref]

1999 (1)

M. S. Vasconcelos and E. L. Albuquerque, “Transmission fingerprints in quasiperiodic dielectric multilayers,” Phys. Rev. B 59(17), 11128–11131 (1999).
[Crossref]

1994 (1)

V. Berthé, “Conditional entropy of some automatic sequences,” J. Phys. A: Math. Gen. 27(24), 7993–8006 (1994).
[Crossref]

1992 (1)

F. Axel, J. P. Allouche, and Z.-Y. Wen, “On certain properties of high-resolution X-ray diffraction spectra of finite-size generalized Rudin-Shapiro multilayer heterostructures,” J. Phys.: Condens. Matter 4(45), 8713–8728 (1992).
[Crossref]

1959 (1)

W. Rudin, “Some theorems on Fourier coefficients,” Proc. Am. Math. Soc. 10(6), 855 (1959).
[Crossref]

1951 (1)

Agarwal, V.

V. Agarwal, M. E. Mora-Ramos, and B. Alvarado-Tenorio, “Optical properties of multilayered period-doubling and Rudin-Shapiro porous silicon dielectric heterostructures,” Photonics Nanostructures: Fundam. Appl. 7(2), 63–68 (2009).
[Crossref]

Albuquerque, E. L.

M. S. Vasconcelos and E. L. Albuquerque, “Transmission fingerprints in quasiperiodic dielectric multilayers,” Phys. Rev. B 59(17), 11128–11131 (1999).
[Crossref]

Allouche, J. P.

F. Axel, J. P. Allouche, and Z.-Y. Wen, “On certain properties of high-resolution X-ray diffraction spectra of finite-size generalized Rudin-Shapiro multilayer heterostructures,” J. Phys.: Condens. Matter 4(45), 8713–8728 (1992).
[Crossref]

Alù, A.

G. Castaldi, A. Alù, and V. Galdi, “Boundary effects of weak nonlocality in multilayered dielectric metamaterials,” Phys. Rev. Appl. 10(3), 034060 (2018).
[Crossref]

A. Alù, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84(7), 075153 (2011).
[Crossref]

Alvarado-Tenorio, B.

V. Agarwal, M. E. Mora-Ramos, and B. Alvarado-Tenorio, “Optical properties of multilayered period-doubling and Rudin-Shapiro porous silicon dielectric heterostructures,” Photonics Nanostructures: Fundam. Appl. 7(2), 63–68 (2009).
[Crossref]

Amsden, J. J.

Andreone, A.

M. Moccia, C. Koral, G. P. Papari, S. Liu, L. Zhang, R. Y. Wu, G. Castaldi, T. J. Cui, V. Galdi, and A. Andreone, “Suboptimal coding metasurfaces for terahertz diffuse scattering,” Sci. Rep. 8(1), 11908 (2018).
[Crossref]

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

Andryieuski, A.

S. V. Zhukovsky, A. Andryieuski, O. Takayama, E. Shkondin, R. Malureanu, F. Jensen, and A. V. Lavrinenko, “Experimental demonstration of effective medium approximation breakdown in deeply subwavelength all-dielectric multilayers,” Phys. Rev. Lett. 115(17), 177402 (2015).
[Crossref]

A. Andryieuski, A. V. Lavrinenko, and S. V. Zhukovsky, “Anomalous effective medium approximation breakdown in deeply subwavelength all-dielectric photonic multilayers,” Nanotechnology 26(18), 184001 (2015).
[Crossref]

Ankonina, G.

H. Herzig Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref]

Axel, F.

F. Axel, J. P. Allouche, and Z.-Y. Wen, “On certain properties of high-resolution X-ray diffraction spectra of finite-size generalized Rudin-Shapiro multilayer heterostructures,” J. Phys.: Condens. Matter 4(45), 8713–8728 (1992).
[Crossref]

Bartal, G.

H. Herzig Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref]

H. Herzig Sheinfux, I. Kaminer, Y. Plotnik, G. Bartal, and M. Segev, “Subwavelength multilayer dielectrics: Ultrasensitive transmission and breakdown of effective-medium theory,” Phys. Rev. Lett. 113(24), 243901 (2014).
[Crossref]

Belov, P. A.

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84(11), 115438 (2011).
[Crossref]

Benali, N.

Y. Trabelsi, Y. Bouazzi, N. Benali, and M. Kanzari, “Narrow stop band optical filter using one-dimensional regular Fibonacci/Rudin Shapiro photonic quasicrystals,” Opt. Quantum Electron. 48(1), 54 (2016).
[Crossref]

Berthé, V.

V. Berthé, “Conditional entropy of some automatic sequences,” J. Phys. A: Math. Gen. 27(24), 7993–8006 (1994).
[Crossref]

Boriskina, S.

L. Dal Negro and S. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photonics Rev. 6(2), 178–218 (2012).
[Crossref]

Boriskina, S. V.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), 7th ed.

Bouazzi, Y.

Y. Trabelsi, Y. Bouazzi, N. Benali, and M. Kanzari, “Narrow stop band optical filter using one-dimensional regular Fibonacci/Rudin Shapiro photonic quasicrystals,” Opt. Quantum Electron. 48(1), 54 (2016).
[Crossref]

Y. Bouazzi and M. Kanzari, “Optical Fabry-Perot filter based on photonic band gap quasi-periodic one-dimensional multilayer according to the definite Rudin-Shapiro distribution,” Opt. Commun. 285(12), 2774–2779 (2012).
[Crossref]

Capolino, F.

F. Capolino, Theory and Phenomena of Metamaterials (CRC Press, Boca Raton, FL, 2009).

Castaldi, G.

M. Coppolaro, G. Castaldi, and V. Galdi, “Aperiodic order induced enhancement of weak nonlocality in multilayered dielectric metamaterials,” Phys. Rev. B 98(19), 195128 (2018).
[Crossref]

G. Castaldi, A. Alù, and V. Galdi, “Boundary effects of weak nonlocality in multilayered dielectric metamaterials,” Phys. Rev. Appl. 10(3), 034060 (2018).
[Crossref]

M. Moccia, C. Koral, G. P. Papari, S. Liu, L. Zhang, R. Y. Wu, G. Castaldi, T. J. Cui, V. Galdi, and A. Andreone, “Suboptimal coding metasurfaces for terahertz diffuse scattering,” Sci. Rep. 8(1), 11908 (2018).
[Crossref]

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

V. Galdi, V. Pierro, G. Castaldi, I. M. Pinto, and L. B. Felsen, “Radiation properties of one-dimensional random-like antenna arrays based on Rudin-Shapiro sequences,” IEEE Trans. Antennas Propag. 53(11), 3568–3575 (2005).
[Crossref]

Chebykin, A. V.

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84(11), 115438 (2011).
[Crossref]

Chern, R.-L.

Ciattoni, A.

A. Ciattoni and C. Rizza, “Nonlocal homogenization theory in metamaterials: Effective electromagnetic spatial dispersion and artificial chirality,” Phys. Rev. B 91(18), 184207 (2015).
[Crossref]

Coppolaro, M.

M. Coppolaro, G. Castaldi, and V. Galdi, “Aperiodic order induced enhancement of weak nonlocality in multilayered dielectric metamaterials,” Phys. Rev. B 98(19), 195128 (2018).
[Crossref]

Cui, T. J.

M. Moccia, C. Koral, G. P. Papari, S. Liu, L. Zhang, R. Y. Wu, G. Castaldi, T. J. Cui, V. Galdi, and A. Andreone, “Suboptimal coding metasurfaces for terahertz diffuse scattering,” Sci. Rep. 8(1), 11908 (2018).
[Crossref]

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

Dal Negro, L.

Dikopoltsev, A.

A. Dikopoltsev, A. Shaham, A. Pick, H. H. Sheinfux, and M. Segev, “Coaction of disorder and PT-symmetry in deep subwavelength multilayers,” in Frontiers in Optics + Laser Science APS/DLS (Optical Society of America, 2019), p. JTu4A.45.

Felsen, L. B.

V. Galdi, V. Pierro, G. Castaldi, I. M. Pinto, and L. B. Felsen, “Radiation properties of one-dimensional random-like antenna arrays based on Rudin-Shapiro sequences,” IEEE Trans. Antennas Propag. 53(11), 3568–3575 (2005).
[Crossref]

Feng, N.-N.

Forestiere, C.

Galdi, V.

M. Moccia, C. Koral, G. P. Papari, S. Liu, L. Zhang, R. Y. Wu, G. Castaldi, T. J. Cui, V. Galdi, and A. Andreone, “Suboptimal coding metasurfaces for terahertz diffuse scattering,” Sci. Rep. 8(1), 11908 (2018).
[Crossref]

M. Coppolaro, G. Castaldi, and V. Galdi, “Aperiodic order induced enhancement of weak nonlocality in multilayered dielectric metamaterials,” Phys. Rev. B 98(19), 195128 (2018).
[Crossref]

G. Castaldi, A. Alù, and V. Galdi, “Boundary effects of weak nonlocality in multilayered dielectric metamaterials,” Phys. Rev. Appl. 10(3), 034060 (2018).
[Crossref]

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

V. Galdi, V. Pierro, G. Castaldi, I. M. Pinto, and L. B. Felsen, “Radiation properties of one-dimensional random-like antenna arrays based on Rudin-Shapiro sequences,” IEEE Trans. Antennas Propag. 53(11), 3568–3575 (2005).
[Crossref]

Genack, A. Z.

H. Herzig Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref]

H. Herzig Sheinfux, I. Kaminer, A. Z. Genack, and M. Segev, “Interplay between evanescence and disorder in deep subwavelength photonic structures,” Nat. Commun. 7(1), 12927 (2016).
[Crossref]

Golay, M. J. E.

Gopinath, A.

Gorlach, M. A.

M. A. Gorlach and M. Lapine, “Boundary conditions for the effective-medium description of subwavelength multilayered structures,” Phys. Rev. B 101(7), 075127 (2020).
[Crossref]

Grimm, U.

X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: Extensions and applications,” Phys. Rev. B 62(21), 14020–14031 (2000).
[Crossref]

Herzig Sheinfux, H.

H. Herzig Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref]

H. Herzig Sheinfux, I. Kaminer, A. Z. Genack, and M. Segev, “Interplay between evanescence and disorder in deep subwavelength photonic structures,” Nat. Commun. 7(1), 12927 (2016).
[Crossref]

H. Herzig Sheinfux, I. Kaminer, Y. Plotnik, G. Bartal, and M. Segev, “Subwavelength multilayer dielectrics: Ultrasensitive transmission and breakdown of effective-medium theory,” Phys. Rev. Lett. 113(24), 243901 (2014).
[Crossref]

Hiltunen, M.

Jensen, F.

S. V. Zhukovsky, A. Andryieuski, O. Takayama, E. Shkondin, R. Malureanu, F. Jensen, and A. V. Lavrinenko, “Experimental demonstration of effective medium approximation breakdown in deeply subwavelength all-dielectric multilayers,” Phys. Rev. Lett. 115(17), 177402 (2015).
[Crossref]

Kaminer, I.

H. Herzig Sheinfux, I. Kaminer, A. Z. Genack, and M. Segev, “Interplay between evanescence and disorder in deep subwavelength photonic structures,” Nat. Commun. 7(1), 12927 (2016).
[Crossref]

H. Herzig Sheinfux, I. Kaminer, Y. Plotnik, G. Bartal, and M. Segev, “Subwavelength multilayer dielectrics: Ultrasensitive transmission and breakdown of effective-medium theory,” Phys. Rev. Lett. 113(24), 243901 (2014).
[Crossref]

Kanzari, M.

Y. Trabelsi, Y. Bouazzi, N. Benali, and M. Kanzari, “Narrow stop band optical filter using one-dimensional regular Fibonacci/Rudin Shapiro photonic quasicrystals,” Opt. Quantum Electron. 48(1), 54 (2016).
[Crossref]

Y. Bouazzi and M. Kanzari, “Optical Fabry-Perot filter based on photonic band gap quasi-periodic one-dimensional multilayer according to the definite Rudin-Shapiro distribution,” Opt. Commun. 285(12), 2774–2779 (2012).
[Crossref]

Kimerling, L. C.

Kivshar, Y. S.

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84(11), 115438 (2011).
[Crossref]

Koral, C.

M. Moccia, C. Koral, G. P. Papari, S. Liu, L. Zhang, R. Y. Wu, G. Castaldi, T. J. Cui, V. Galdi, and A. Andreone, “Suboptimal coding metasurfaces for terahertz diffuse scattering,” Sci. Rep. 8(1), 11908 (2018).
[Crossref]

Kroon, L.

L. Kroon and R. Riklund, “Absence of localization in a model with correlation measure as a random lattice,” Phys. Rev. B 69(9), 094204 (2004).
[Crossref]

L. Kroon, E. Lennholm, and R. Riklund, “Localization-delocalization in aperiodic systems,” Phys. Rev. B 66(9), 094204 (2002).
[Crossref]

la Cour-Harbo, A.

A. la Cour-Harbo, “On the Rudin-Shapiro transform,” Appl. Comp. Harm. Anal. 24(3), 310–328 (2008).
[Crossref]

Lapine, M.

M. A. Gorlach and M. Lapine, “Boundary conditions for the effective-medium description of subwavelength multilayered structures,” Phys. Rev. B 101(7), 075127 (2020).
[Crossref]

Lavrinenko, A. V.

V. Popov, A. V. Lavrinenko, and A. Novitsky, “Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation,” Phys. Rev. B 94(8), 085428 (2016).
[Crossref]

S. V. Zhukovsky, A. Andryieuski, O. Takayama, E. Shkondin, R. Malureanu, F. Jensen, and A. V. Lavrinenko, “Experimental demonstration of effective medium approximation breakdown in deeply subwavelength all-dielectric multilayers,” Phys. Rev. Lett. 115(17), 177402 (2015).
[Crossref]

A. Andryieuski, A. V. Lavrinenko, and S. V. Zhukovsky, “Anomalous effective medium approximation breakdown in deeply subwavelength all-dielectric photonic multilayers,” Nanotechnology 26(18), 184001 (2015).
[Crossref]

Lee, S. Y. K.

Lei, X.

X. Lei, L. Mao, Y. Lu, and P. Wang, “Revisiting the effective medium approximation in all-dielectric subwavelength multilayers: Breakdown and rebuilding,” Phys. Rev. B 96(3), 035439 (2017).
[Crossref]

Lennholm, E.

L. Kroon, E. Lennholm, and R. Riklund, “Localization-delocalization in aperiodic systems,” Phys. Rev. B 66(9), 094204 (2002).
[Crossref]

Levine, D.

G. Wolff and D. Levine, “Diffuse scattering and atomic order,” Europhys. Lett. 117(3), 36001 (2017).
[Crossref]

Liu, S.

M. Moccia, C. Koral, G. P. Papari, S. Liu, L. Zhang, R. Y. Wu, G. Castaldi, T. J. Cui, V. Galdi, and A. Andreone, “Suboptimal coding metasurfaces for terahertz diffuse scattering,” Sci. Rep. 8(1), 11908 (2018).
[Crossref]

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

Lu, Y.

X. Lei, L. Mao, Y. Lu, and P. Wang, “Revisiting the effective medium approximation in all-dielectric subwavelength multilayers: Breakdown and rebuilding,” Phys. Rev. B 96(3), 035439 (2017).
[Crossref]

Lumer, Y.

H. Herzig Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref]

Lustig, E.

Y. Sharabi, E. Lustig, and M. Segev, “Light propagation in temporally disordered media,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2019), p. FF3B.1.

Maciá, E.

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69(2), 397–441 (2006).
[Crossref]

Malureanu, R.

S. V. Zhukovsky, A. Andryieuski, O. Takayama, E. Shkondin, R. Malureanu, F. Jensen, and A. V. Lavrinenko, “Experimental demonstration of effective medium approximation breakdown in deeply subwavelength all-dielectric multilayers,” Phys. Rev. Lett. 115(17), 177402 (2015).
[Crossref]

Mao, L.

X. Lei, L. Mao, Y. Lu, and P. Wang, “Revisiting the effective medium approximation in all-dielectric subwavelength multilayers: Breakdown and rebuilding,” Phys. Rev. B 96(3), 035439 (2017).
[Crossref]

Marigo, J.-J.

A. Maurel and J.-J. Marigo, “Sensitivity of a dielectric layered structure on a scale below the periodicity: A fully local homogenized model,” Phys. Rev. B 98(2), 024306 (2018).
[Crossref]

Maslovski, S. I.

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84(11), 115438 (2011).
[Crossref]

Maurel, A.

A. Maurel and J.-J. Marigo, “Sensitivity of a dielectric layered structure on a scale below the periodicity: A fully local homogenized model,” Phys. Rev. B 98(2), 024306 (2018).
[Crossref]

Miano, G.

Michel, J.

Moccia, M.

M. Moccia, C. Koral, G. P. Papari, S. Liu, L. Zhang, R. Y. Wu, G. Castaldi, T. J. Cui, V. Galdi, and A. Andreone, “Suboptimal coding metasurfaces for terahertz diffuse scattering,” Sci. Rep. 8(1), 11908 (2018).
[Crossref]

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

Mora-Ramos, M. E.

V. Agarwal, M. E. Mora-Ramos, and B. Alvarado-Tenorio, “Optical properties of multilayered period-doubling and Rudin-Shapiro porous silicon dielectric heterostructures,” Photonics Nanostructures: Fundam. Appl. 7(2), 63–68 (2009).
[Crossref]

Novitsky, A.

V. Popov, A. V. Lavrinenko, and A. Novitsky, “Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation,” Phys. Rev. B 94(8), 085428 (2016).
[Crossref]

Omenetto, F. G.

Orlov, A. A.

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84(11), 115438 (2011).
[Crossref]

Papari, G. P.

M. Moccia, C. Koral, G. P. Papari, S. Liu, L. Zhang, R. Y. Wu, G. Castaldi, T. J. Cui, V. Galdi, and A. Andreone, “Suboptimal coding metasurfaces for terahertz diffuse scattering,” Sci. Rep. 8(1), 11908 (2018).
[Crossref]

Pick, A.

A. Dikopoltsev, A. Shaham, A. Pick, H. H. Sheinfux, and M. Segev, “Coaction of disorder and PT-symmetry in deep subwavelength multilayers,” in Frontiers in Optics + Laser Science APS/DLS (Optical Society of America, 2019), p. JTu4A.45.

Pierro, V.

V. Galdi, V. Pierro, G. Castaldi, I. M. Pinto, and L. B. Felsen, “Radiation properties of one-dimensional random-like antenna arrays based on Rudin-Shapiro sequences,” IEEE Trans. Antennas Propag. 53(11), 3568–3575 (2005).
[Crossref]

Pinto, I. M.

V. Galdi, V. Pierro, G. Castaldi, I. M. Pinto, and L. B. Felsen, “Radiation properties of one-dimensional random-like antenna arrays based on Rudin-Shapiro sequences,” IEEE Trans. Antennas Propag. 53(11), 3568–3575 (2005).
[Crossref]

Plotnik, Y.

H. Herzig Sheinfux, I. Kaminer, Y. Plotnik, G. Bartal, and M. Segev, “Subwavelength multilayer dielectrics: Ultrasensitive transmission and breakdown of effective-medium theory,” Phys. Rev. Lett. 113(24), 243901 (2014).
[Crossref]

Popov, V.

V. Popov, A. V. Lavrinenko, and A. Novitsky, “Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation,” Phys. Rev. B 94(8), 085428 (2016).
[Crossref]

Reinhard, B. M.

Riklund, R.

L. Kroon and R. Riklund, “Absence of localization in a model with correlation measure as a random lattice,” Phys. Rev. B 69(9), 094204 (2004).
[Crossref]

L. Kroon, E. Lennholm, and R. Riklund, “Localization-delocalization in aperiodic systems,” Phys. Rev. B 66(9), 094204 (2002).
[Crossref]

Rizza, C.

A. Ciattoni and C. Rizza, “Nonlocal homogenization theory in metamaterials: Effective electromagnetic spatial dispersion and artificial chirality,” Phys. Rev. B 91(18), 184207 (2015).
[Crossref]

Rudin, W.

W. Rudin, “Some theorems on Fourier coefficients,” Proc. Am. Math. Soc. 10(6), 855 (1959).
[Crossref]

Schreiber, M.

X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: Extensions and applications,” Phys. Rev. B 62(21), 14020–14031 (2000).
[Crossref]

Segev, M.

H. Herzig Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref]

H. Herzig Sheinfux, I. Kaminer, A. Z. Genack, and M. Segev, “Interplay between evanescence and disorder in deep subwavelength photonic structures,” Nat. Commun. 7(1), 12927 (2016).
[Crossref]

H. Herzig Sheinfux, I. Kaminer, Y. Plotnik, G. Bartal, and M. Segev, “Subwavelength multilayer dielectrics: Ultrasensitive transmission and breakdown of effective-medium theory,” Phys. Rev. Lett. 113(24), 243901 (2014).
[Crossref]

A. Dikopoltsev, A. Shaham, A. Pick, H. H. Sheinfux, and M. Segev, “Coaction of disorder and PT-symmetry in deep subwavelength multilayers,” in Frontiers in Optics + Laser Science APS/DLS (Optical Society of America, 2019), p. JTu4A.45.

Y. Sharabi, E. Lustig, and M. Segev, “Light propagation in temporally disordered media,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2019), p. FF3B.1.

Shaham, A.

A. Dikopoltsev, A. Shaham, A. Pick, H. H. Sheinfux, and M. Segev, “Coaction of disorder and PT-symmetry in deep subwavelength multilayers,” in Frontiers in Optics + Laser Science APS/DLS (Optical Society of America, 2019), p. JTu4A.45.

Shapiro, H. S.

H. S. Shapiro, “Extremal problems for polynomials and power series,” Ph.D. thesis, Massachusetts Institute of Technology (1952).

Sharabi, Y.

Y. Sharabi, E. Lustig, and M. Segev, “Light propagation in temporally disordered media,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2019), p. FF3B.1.

Sheinfux, H. H.

A. Dikopoltsev, A. Shaham, A. Pick, H. H. Sheinfux, and M. Segev, “Coaction of disorder and PT-symmetry in deep subwavelength multilayers,” in Frontiers in Optics + Laser Science APS/DLS (Optical Society of America, 2019), p. JTu4A.45.

Shkondin, E.

S. V. Zhukovsky, A. Andryieuski, O. Takayama, E. Shkondin, R. Malureanu, F. Jensen, and A. V. Lavrinenko, “Experimental demonstration of effective medium approximation breakdown in deeply subwavelength all-dielectric multilayers,” Phys. Rev. Lett. 115(17), 177402 (2015).
[Crossref]

Sihvola, A.

A. Sihvola, Electromagnetic Mixing Formulas and Applications, Electromagnetics and Radar Series (IET, London, UK, 1999).

Silveirinha, M. G.

M. G. Silveirinha, “Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters,” Phys. Rev. B 75(11), 115104 (2007).
[Crossref]

Takayama, O.

S. V. Zhukovsky, A. Andryieuski, O. Takayama, E. Shkondin, R. Malureanu, F. Jensen, and A. V. Lavrinenko, “Experimental demonstration of effective medium approximation breakdown in deeply subwavelength all-dielectric multilayers,” Phys. Rev. Lett. 115(17), 177402 (2015).
[Crossref]

Trabelsi, Y.

Y. Trabelsi, Y. Bouazzi, N. Benali, and M. Kanzari, “Narrow stop band optical filter using one-dimensional regular Fibonacci/Rudin Shapiro photonic quasicrystals,” Opt. Quantum Electron. 48(1), 54 (2016).
[Crossref]

Vasconcelos, M. S.

M. S. Vasconcelos and E. L. Albuquerque, “Transmission fingerprints in quasiperiodic dielectric multilayers,” Phys. Rev. B 59(17), 11128–11131 (1999).
[Crossref]

Vozianova, A. V.

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84(11), 115438 (2011).
[Crossref]

Wang, P.

X. Lei, L. Mao, Y. Lu, and P. Wang, “Revisiting the effective medium approximation in all-dielectric subwavelength multilayers: Breakdown and rebuilding,” Phys. Rev. B 96(3), 035439 (2017).
[Crossref]

Wang, X.

X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: Extensions and applications,” Phys. Rev. B 62(21), 14020–14031 (2000).
[Crossref]

Wen, Z.-Y.

F. Axel, J. P. Allouche, and Z.-Y. Wen, “On certain properties of high-resolution X-ray diffraction spectra of finite-size generalized Rudin-Shapiro multilayer heterostructures,” J. Phys.: Condens. Matter 4(45), 8713–8728 (1992).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), 7th ed.

Wolff, G.

G. Wolff and D. Levine, “Diffuse scattering and atomic order,” Europhys. Lett. 117(3), 36001 (2017).
[Crossref]

Wu, R. Y.

M. Moccia, C. Koral, G. P. Papari, S. Liu, L. Zhang, R. Y. Wu, G. Castaldi, T. J. Cui, V. Galdi, and A. Andreone, “Suboptimal coding metasurfaces for terahertz diffuse scattering,” Sci. Rep. 8(1), 11908 (2018).
[Crossref]

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

Zhang, L.

M. Moccia, C. Koral, G. P. Papari, S. Liu, L. Zhang, R. Y. Wu, G. Castaldi, T. J. Cui, V. Galdi, and A. Andreone, “Suboptimal coding metasurfaces for terahertz diffuse scattering,” Sci. Rep. 8(1), 11908 (2018).
[Crossref]

Zhukovsky, S. V.

A. Andryieuski, A. V. Lavrinenko, and S. V. Zhukovsky, “Anomalous effective medium approximation breakdown in deeply subwavelength all-dielectric photonic multilayers,” Nanotechnology 26(18), 184001 (2015).
[Crossref]

S. V. Zhukovsky, A. Andryieuski, O. Takayama, E. Shkondin, R. Malureanu, F. Jensen, and A. V. Lavrinenko, “Experimental demonstration of effective medium approximation breakdown in deeply subwavelength all-dielectric multilayers,” Phys. Rev. Lett. 115(17), 177402 (2015).
[Crossref]

Adv. Opt. Mater. (1)

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

Appl. Comp. Harm. Anal. (1)

A. la Cour-Harbo, “On the Rudin-Shapiro transform,” Appl. Comp. Harm. Anal. 24(3), 310–328 (2008).
[Crossref]

Europhys. Lett. (1)

G. Wolff and D. Levine, “Diffuse scattering and atomic order,” Europhys. Lett. 117(3), 36001 (2017).
[Crossref]

IEEE Trans. Antennas Propag. (1)

V. Galdi, V. Pierro, G. Castaldi, I. M. Pinto, and L. B. Felsen, “Radiation properties of one-dimensional random-like antenna arrays based on Rudin-Shapiro sequences,” IEEE Trans. Antennas Propag. 53(11), 3568–3575 (2005).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

J. Phys. A: Math. Gen. (1)

V. Berthé, “Conditional entropy of some automatic sequences,” J. Phys. A: Math. Gen. 27(24), 7993–8006 (1994).
[Crossref]

J. Phys.: Condens. Matter (1)

F. Axel, J. P. Allouche, and Z.-Y. Wen, “On certain properties of high-resolution X-ray diffraction spectra of finite-size generalized Rudin-Shapiro multilayer heterostructures,” J. Phys.: Condens. Matter 4(45), 8713–8728 (1992).
[Crossref]

Laser Photonics Rev. (1)

L. Dal Negro and S. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photonics Rev. 6(2), 178–218 (2012).
[Crossref]

Nanotechnology (1)

A. Andryieuski, A. V. Lavrinenko, and S. V. Zhukovsky, “Anomalous effective medium approximation breakdown in deeply subwavelength all-dielectric photonic multilayers,” Nanotechnology 26(18), 184001 (2015).
[Crossref]

Nat. Commun. (1)

H. Herzig Sheinfux, I. Kaminer, A. Z. Genack, and M. Segev, “Interplay between evanescence and disorder in deep subwavelength photonic structures,” Nat. Commun. 7(1), 12927 (2016).
[Crossref]

Opt. Commun. (1)

Y. Bouazzi and M. Kanzari, “Optical Fabry-Perot filter based on photonic band gap quasi-periodic one-dimensional multilayer according to the definite Rudin-Shapiro distribution,” Opt. Commun. 285(12), 2774–2779 (2012).
[Crossref]

Opt. Express (4)

Opt. Quantum Electron. (1)

Y. Trabelsi, Y. Bouazzi, N. Benali, and M. Kanzari, “Narrow stop band optical filter using one-dimensional regular Fibonacci/Rudin Shapiro photonic quasicrystals,” Opt. Quantum Electron. 48(1), 54 (2016).
[Crossref]

Photonics Nanostructures: Fundam. Appl. (1)

V. Agarwal, M. E. Mora-Ramos, and B. Alvarado-Tenorio, “Optical properties of multilayered period-doubling and Rudin-Shapiro porous silicon dielectric heterostructures,” Photonics Nanostructures: Fundam. Appl. 7(2), 63–68 (2009).
[Crossref]

Phys. Rev. Appl. (1)

G. Castaldi, A. Alù, and V. Galdi, “Boundary effects of weak nonlocality in multilayered dielectric metamaterials,” Phys. Rev. Appl. 10(3), 034060 (2018).
[Crossref]

Phys. Rev. B (13)

M. A. Gorlach and M. Lapine, “Boundary conditions for the effective-medium description of subwavelength multilayered structures,” Phys. Rev. B 101(7), 075127 (2020).
[Crossref]

V. Popov, A. V. Lavrinenko, and A. Novitsky, “Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation,” Phys. Rev. B 94(8), 085428 (2016).
[Crossref]

X. Lei, L. Mao, Y. Lu, and P. Wang, “Revisiting the effective medium approximation in all-dielectric subwavelength multilayers: Breakdown and rebuilding,” Phys. Rev. B 96(3), 035439 (2017).
[Crossref]

A. Maurel and J.-J. Marigo, “Sensitivity of a dielectric layered structure on a scale below the periodicity: A fully local homogenized model,” Phys. Rev. B 98(2), 024306 (2018).
[Crossref]

M. G. Silveirinha, “Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters,” Phys. Rev. B 75(11), 115104 (2007).
[Crossref]

A. Alù, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84(7), 075153 (2011).
[Crossref]

A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84(11), 115438 (2011).
[Crossref]

A. Ciattoni and C. Rizza, “Nonlocal homogenization theory in metamaterials: Effective electromagnetic spatial dispersion and artificial chirality,” Phys. Rev. B 91(18), 184207 (2015).
[Crossref]

M. Coppolaro, G. Castaldi, and V. Galdi, “Aperiodic order induced enhancement of weak nonlocality in multilayered dielectric metamaterials,” Phys. Rev. B 98(19), 195128 (2018).
[Crossref]

M. S. Vasconcelos and E. L. Albuquerque, “Transmission fingerprints in quasiperiodic dielectric multilayers,” Phys. Rev. B 59(17), 11128–11131 (1999).
[Crossref]

L. Kroon, E. Lennholm, and R. Riklund, “Localization-delocalization in aperiodic systems,” Phys. Rev. B 66(9), 094204 (2002).
[Crossref]

L. Kroon and R. Riklund, “Absence of localization in a model with correlation measure as a random lattice,” Phys. Rev. B 69(9), 094204 (2004).
[Crossref]

X. Wang, U. Grimm, and M. Schreiber, “Trace and antitrace maps for aperiodic sequences: Extensions and applications,” Phys. Rev. B 62(21), 14020–14031 (2000).
[Crossref]

Phys. Rev. Lett. (2)

H. Herzig Sheinfux, I. Kaminer, Y. Plotnik, G. Bartal, and M. Segev, “Subwavelength multilayer dielectrics: Ultrasensitive transmission and breakdown of effective-medium theory,” Phys. Rev. Lett. 113(24), 243901 (2014).
[Crossref]

S. V. Zhukovsky, A. Andryieuski, O. Takayama, E. Shkondin, R. Malureanu, F. Jensen, and A. V. Lavrinenko, “Experimental demonstration of effective medium approximation breakdown in deeply subwavelength all-dielectric multilayers,” Phys. Rev. Lett. 115(17), 177402 (2015).
[Crossref]

Proc. Am. Math. Soc. (1)

W. Rudin, “Some theorems on Fourier coefficients,” Proc. Am. Math. Soc. 10(6), 855 (1959).
[Crossref]

Rep. Prog. Phys. (1)

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69(2), 397–441 (2006).
[Crossref]

Sci. Rep. (1)

M. Moccia, C. Koral, G. P. Papari, S. Liu, L. Zhang, R. Y. Wu, G. Castaldi, T. J. Cui, V. Galdi, and A. Andreone, “Suboptimal coding metasurfaces for terahertz diffuse scattering,” Sci. Rep. 8(1), 11908 (2018).
[Crossref]

Science (1)

H. Herzig Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref]

Other (7)

F. Capolino, Theory and Phenomena of Metamaterials (CRC Press, Boca Raton, FL, 2009).

A. Sihvola, Electromagnetic Mixing Formulas and Applications, Electromagnetics and Radar Series (IET, London, UK, 1999).

A. Dikopoltsev, A. Shaham, A. Pick, H. H. Sheinfux, and M. Segev, “Coaction of disorder and PT-symmetry in deep subwavelength multilayers,” in Frontiers in Optics + Laser Science APS/DLS (Optical Society of America, 2019), p. JTu4A.45.

Y. Sharabi, E. Lustig, and M. Segev, “Light propagation in temporally disordered media,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2019), p. FF3B.1.

N. P. Fogg, V. Berthé, S. Ferenczi, C. Mauduit, and A. Siegel, eds., Substitutions in Dynamics, Arithmetics and Combinatorics, vol. 1794 of Lecture Notes in Mathematics (Springer, Berlin, 2002).

H. S. Shapiro, “Extremal problems for polynomials and power series,” Ph.D. thesis, Massachusetts Institute of Technology (1952).

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), 7th ed.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1. Problem schematic (details in the text).
Fig. 2.
Fig. 2. Comparison between the transmittance responses of multilayered dielectric metamaterials with different geometrical arrangements, for $\varepsilon _a=1$, $\varepsilon _b=5$, $d_a=d_b=d$, $\varepsilon _e=4$, as a function of the layer electrical thickness $d/\lambda$ and incidence angle $\theta _i$. (a)–(c) $Q_{\nu }$-type GRS geometries at stages of growth $\nu =7$ ($N=128$ layers), $\nu =9$ ($N=512$ layers), and $\nu =11$ ($N=2048$ layers), respectively. (d)–(f) Corresponding EMT predictions (${\bar \varepsilon }_{\parallel }=3$). (g)–(i) Corresponding responses for periodic counterparts.
Fig. 3.
Fig. 3. (a) Representative transmittance cuts from Figs. 2(a) (GRS; blue-solid), 2(d) (EMT; green-dotted), and 2(g) (periodic; red-dashed), for $\theta _i=45.1^{o}$. (b) Corresponding electric-field (normalized-magnitude) distributions for $d/\lambda =0.01$.
Fig. 4.
Fig. 4. (a) Inverse localization length (scaled by the wavelength) for a GRS-type configuration with $N=2048$ layers and different electrical thicknesses (blue-solid: $d/\lambda =0.01$; red-dashed: $d/\lambda =0.02$; magenta-dotted: $d/\lambda =0.025$), as a function of the incidence angle. The inset shows the convergence to a constant value for increasing stages of growth and near-incidence conditions (continuous curves are guides to the eye only.). (b), (c), (d) Representative electric-field (normalized-magnitude) distributions inside the GRS-type multilayer for $N=128$ ($d/\lambda =0.02$, $\theta _i=58.35^{o}$), $N=512$ ($d/\lambda =0.01$, $\theta _i=58.35^{o}$), and $N=2048$ ($d/\lambda =0.01$, $\theta _i=58.1^{o}$), respectively.
Fig. 5.
Fig. 5. Representative electric-field (normalized-magnitude) distributions for localized states. (a) $N=128$, $d/\lambda =0.047$, $\theta _i=59.1^{o}$. (b) $N=512$, $d/\lambda =0.015$, $\theta _i=58.85^{o}$. (c) $N=2048$, $d/\lambda =0.02$, $\theta _i=46.6^{o}$.
Fig. 6.
Fig. 6. (a),(b),(c) Representative absorbance responses, in the presence of small losses ($\varepsilon _b=5+i10^{-4}$), as a function of electrical thickness, for $N=128$ ($\theta _i=59.1^{o}$), $N=512$ ($\theta _i=58.85^{o}$), and $N=2048$ ($\theta _i=46.6^{o}$), respectively. (d),(e),(f) Representative reflectance responses, in the presence of small gain ($\varepsilon _b=5-i10^{-3}$), as a function of electrical thickness, for $N=128$ ($\theta _i=56.85^{o}$), $N=512$ ($\theta _i=57.1^{o}$), and $N=2048$ ($\theta _i=36.1^{o}$), respectively.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

P ν + 1 ( X ) = P ν ( X ) + X 2 ν Q ν ( X ) ,
Q ν + 1 ( X ) = Q ν ( X ) X 2 ν P ν ( X ) ,
p 0 = 1 , p 2 n = p n , p 2 n + 1 = ( 1 ) n p n ,
q n = { p n , n = 0 , , N 2 1 , p n , n = N 2 , , N 1.
E y ( i ) ( x , z ) = exp [ i ( k x x + k z e z ) ] ,
ε ¯ = f a ε a d a + f b ε b d b f a d a + f b d b = ε a d a + ε b d b d a + d b ,
ξ = L log T ,