9 Aperiodic Order in Nanoplasmonics
373
27. D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Metallic phase with long-range orientational
order and no translational symmetry. Phys. Rev. Lett. 53(20), 1951 (1984)
28. D. Levine, P.J. Steinhardt, Quasicrystals: a new class of ordered structures. Phys. Rev. Lett.
53(26), 2477 (1984)
29. R. Penrose, The role of aesthetic in pure and applied mathematical research. Inst. Math. Appl.
7(8), 10 (1974)
30. Z. Cheng, R. Savit, R. Merlin, Structure and electronic properties of Thue–Morse lattices.
Phys. Rev. B 37(9), 4375 (1988)
31. L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L.C. Kimerling, J. LeBlanc, J. Haavisto, Photon band gap properties and omnidirectional reflectance in Si/ SiO Thue–Morse
quasicrystals. Appl. Phys. Lett. 84, 5186 (2004)
32. L. Dal Negro, N.N. Feng, A. Gopinath, Electromagnetic coupling and plasmon localization
in deterministic aperiodic arrays. J. Optics A. Pure Appl. Opt. 10, 064013 (2008)
33. M. Kolar, M.K. Ali, F. Nori, Generalized Thue–Morse chains and their physical properties.
Phys. Rev. B 43(1), 1034 (1991)
34. M.E. Prouhet, Mémoire sur quelques relations entre les puissances des nombres. CR Acad.
Sci. Paris 33, 225 (1851)
35. H.M. Morse, Recurrent geodesics on a surface of negative curvature. J. Math. 42, 84–100
(1920)
36. H.S. Shapiro, Extremal problems for polynomials and power series. M. Sc. Thesis, Massachusetts Institute of Technology, 1951
37. F. Axel, J. Allouche, On certain properties of high-resolution X-ray diffraction spectra of
finite-size generalized Rudin–Shapiro multilayer heterostructures. J. Phys. Cond. Mat. 4,
8713 (1992)
38. L. Kroon, E. Lennholm, R. Riklund, Localization-delocalization in aperiodic systems. Phys.
Rev. B 66(9), 094204 (2002)
39. L. Kroon, R. Riklund, Absence of localization in a model with correlation measure as a
random lattice. Phys. Rev. B 69(9), 094204 (2004)
40. A. Barbé, F. Haeseler, Correlation and spectral properties of higher-dimensional paperfolding
and Rudin–Shapiro sequences. J. Phys. A Math. Gen. 38, 2599 (2005)
41. A. Barbé, F. Von Haeseler, Correlation and spectral properties of multidimensional Thue–
Morse sequences I. J. Bifurcat. Chaos 17(4), 1265–1303 (2007)
42. A. Barbé, F. Haeseler, Correlation functions of higher-dimensional automatic sequences. J.
Phys. A Math. Gen. 37, 10879 (2004)
43. A. Gopinath, S.V. Boriskina, N.N. Feng, B.M. Reinhard, L. Dal Negro, Photonic-plasmonic
scattering resonances in deterministic aperiodic structures. Nano Lett. 8(8), 2423–2431 (2008)
44. J.M. Luck, Cantor spectra and scaling of gap widths in deterministic aperiodic systems. Phys.
Rev. B 39(9), 5834 (1989)
45. C. Godreche, J.M. Luck, Indexing the diffraction spectrum of a non-Pisot self-similar structure. Phys. Rev. B 45(1), 176 (1992)
46. M. Kolar, F. Nori, Trace maps of general substitutional sequences. Phys. Rev. B 42(1), 1062
(1990)
47. G. Gumbs, M.K. Ali, Dynamical maps, Cantor spectra, and localization for Fibonacci and
related quasiperiodic lattices. Phys. Rev. Lett. 60(11), 1081 (1988)
48. X. Wang, U. Grimm, M. Schreiber, Trace and antitrace maps for aperiodic sequences: extensions and applications. Phys. Rev. B 62(21), 14020 (2000)
49. E. Bombieri, J.E. Taylor, Quasicrystals, tilings, and algebraic number theory: some preliminary connections. Contemp. Math. 64, 241–264 (1987)
50. E. Bombieri, J.E. Taylor, Which distributions of matter diffract? An initial investigation. J.
Phys. Colloques 47(C3), C3-19–C13-28 (1986)
51. M. Dulea, M. Johansson, R. Riklund, Localization of electrons and electromagnetic waves in
a deterministic aperiodic system. Phys. Rev. B 45(1), 105 (1992)
52. M. Kohmoto, Localization problem and mapping of one-dimensional wave equations in random and quasiperiodic media. Phys. Rev. B 34(8), 5043 (1986)
373
27. D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Metallic phase with long-range orientational
order and no translational symmetry. Phys. Rev. Lett. 53(20), 1951 (1984)
28. D. Levine, P.J. Steinhardt, Quasicrystals: a new class of ordered structures. Phys. Rev. Lett.
53(26), 2477 (1984)
29. R. Penrose, The role of aesthetic in pure and applied mathematical research. Inst. Math. Appl.
7(8), 10 (1974)
30. Z. Cheng, R. Savit, R. Merlin, Structure and electronic properties of Thue–Morse lattices.
Phys. Rev. B 37(9), 4375 (1988)
31. L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L.C. Kimerling, J. LeBlanc, J. Haavisto, Photon band gap properties and omnidirectional reflectance in Si/ SiO Thue–Morse
quasicrystals. Appl. Phys. Lett. 84, 5186 (2004)
32. L. Dal Negro, N.N. Feng, A. Gopinath, Electromagnetic coupling and plasmon localization
in deterministic aperiodic arrays. J. Optics A. Pure Appl. Opt. 10, 064013 (2008)
33. M. Kolar, M.K. Ali, F. Nori, Generalized Thue–Morse chains and their physical properties.
Phys. Rev. B 43(1), 1034 (1991)
34. M.E. Prouhet, Mémoire sur quelques relations entre les puissances des nombres. CR Acad.
Sci. Paris 33, 225 (1851)
35. H.M. Morse, Recurrent geodesics on a surface of negative curvature. J. Math. 42, 84–100
(1920)
36. H.S. Shapiro, Extremal problems for polynomials and power series. M. Sc. Thesis, Massachusetts Institute of Technology, 1951
37. F. Axel, J. Allouche, On certain properties of high-resolution X-ray diffraction spectra of
finite-size generalized Rudin–Shapiro multilayer heterostructures. J. Phys. Cond. Mat. 4,
8713 (1992)
38. L. Kroon, E. Lennholm, R. Riklund, Localization-delocalization in aperiodic systems. Phys.
Rev. B 66(9), 094204 (2002)
39. L. Kroon, R. Riklund, Absence of localization in a model with correlation measure as a
random lattice. Phys. Rev. B 69(9), 094204 (2004)
40. A. Barbé, F. Haeseler, Correlation and spectral properties of higher-dimensional paperfolding
and Rudin–Shapiro sequences. J. Phys. A Math. Gen. 38, 2599 (2005)
41. A. Barbé, F. Von Haeseler, Correlation and spectral properties of multidimensional Thue–
Morse sequences I. J. Bifurcat. Chaos 17(4), 1265–1303 (2007)
42. A. Barbé, F. Haeseler, Correlation functions of higher-dimensional automatic sequences. J.
Phys. A Math. Gen. 37, 10879 (2004)
43. A. Gopinath, S.V. Boriskina, N.N. Feng, B.M. Reinhard, L. Dal Negro, Photonic-plasmonic
scattering resonances in deterministic aperiodic structures. Nano Lett. 8(8), 2423–2431 (2008)
44. J.M. Luck, Cantor spectra and scaling of gap widths in deterministic aperiodic systems. Phys.
Rev. B 39(9), 5834 (1989)
45. C. Godreche, J.M. Luck, Indexing the diffraction spectrum of a non-Pisot self-similar structure. Phys. Rev. B 45(1), 176 (1992)
46. M. Kolar, F. Nori, Trace maps of general substitutional sequences. Phys. Rev. B 42(1), 1062
(1990)
47. G. Gumbs, M.K. Ali, Dynamical maps, Cantor spectra, and localization for Fibonacci and
related quasiperiodic lattices. Phys. Rev. Lett. 60(11), 1081 (1988)
48. X. Wang, U. Grimm, M. Schreiber, Trace and antitrace maps for aperiodic sequences: extensions and applications. Phys. Rev. B 62(21), 14020 (2000)
49. E. Bombieri, J.E. Taylor, Quasicrystals, tilings, and algebraic number theory: some preliminary connections. Contemp. Math. 64, 241–264 (1987)
50. E. Bombieri, J.E. Taylor, Which distributions of matter diffract? An initial investigation. J.
Phys. Colloques 47(C3), C3-19–C13-28 (1986)
51. M. Dulea, M. Johansson, R. Riklund, Localization of electrons and electromagnetic waves in
a deterministic aperiodic system. Phys. Rev. B 45(1), 105 (1992)
52. M. Kohmoto, Localization problem and mapping of one-dimensional wave equations in random and quasiperiodic media. Phys. Rev. B 34(8), 5043 (1986)