The tight-binding model for a chain, where the hopping constants follow a Fibonacci sequence, predicts multifractality in the spectrum and wave functions. Experimentally, we realize this model by chains of small dielectric resonators with a high refractive index (Er ti 45) of cylindrical form that exhibit evanescent coupling. We show that the fractality of the measured local density of state (LDOS) is best understood when the sites are rearranged according to the similarities in their local surrounding, i.e., their conumbers. This allows us to deduce simple recursive construction schemes for the LDOS for the two cases of dominant strong and weak coupling, despite our limited resolution due to nonzero resonance width and size constraints. We measure the singularity spectrum and the fractal dimensions of the wave functions, and we find good agreement with theoretical predictions for the multifractality based on a perturbative description in the quasiperiodic limit.
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Natl Inst Adv Ind Sci & Technol, Nanotube Res Ctr, Tsukuba, Ibaraki 3058565, JapanNatl Inst Adv Ind Sci & Technol, Nanotube Res Ctr, Tsukuba, Ibaraki 3058565, Japan
Cretu, Ovidiu
Komsa, Hannu-Pekka
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Aalto Univ, Dept Appl Phys, Aalto 00076, FinlandNatl Inst Adv Ind Sci & Technol, Nanotube Res Ctr, Tsukuba, Ibaraki 3058565, Japan
Komsa, Hannu-Pekka
Lehtinen, Ossi
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Univ Ulm, Cent Facil Electron Microscopy, Grp Electron Microscopy Mat Sci, D-89081 Ulm, GermanyNatl Inst Adv Ind Sci & Technol, Nanotube Res Ctr, Tsukuba, Ibaraki 3058565, Japan
Lehtinen, Ossi
Algara-Siller, Gerardo
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Univ Ulm, Cent Facil Electron Microscopy, Grp Electron Microscopy Mat Sci, D-89081 Ulm, GermanyNatl Inst Adv Ind Sci & Technol, Nanotube Res Ctr, Tsukuba, Ibaraki 3058565, Japan
Algara-Siller, Gerardo
Kaiser, Ute
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Univ Ulm, Cent Facil Electron Microscopy, Grp Electron Microscopy Mat Sci, D-89081 Ulm, GermanyNatl Inst Adv Ind Sci & Technol, Nanotube Res Ctr, Tsukuba, Ibaraki 3058565, Japan
Kaiser, Ute
Suenaga, Kazu
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Natl Inst Adv Ind Sci & Technol, Nanotube Res Ctr, Tsukuba, Ibaraki 3058565, JapanNatl Inst Adv Ind Sci & Technol, Nanotube Res Ctr, Tsukuba, Ibaraki 3058565, Japan
Suenaga, Kazu
Krasheninnikov, Arkady V.
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Aalto Univ, Dept Appl Phys, Aalto 00076, Finland
Natl Univ Sci & Technol MISiS, Moscow 119049, RussiaNatl Inst Adv Ind Sci & Technol, Nanotube Res Ctr, Tsukuba, Ibaraki 3058565, Japan
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Univ Mohammed V Agdal, Fac Sci, Dept Math & Informat, BP 1014,Av Ibn Batata, Rabat, MoroccoUniv Mohammed V Agdal, Fac Sci, Dept Math & Informat, BP 1014,Av Ibn Batata, Rabat, Morocco
Benazzouz, H.
Mouline, M.
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Univ Mohammed V Agdal, Fac Sci, Dept Math & Informat, BP 1014,Av Ibn Batata, Rabat, MoroccoUniv Mohammed V Agdal, Fac Sci, Dept Math & Informat, BP 1014,Av Ibn Batata, Rabat, Morocco
Mouline, M.
Rachidi, M.
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Acad Reims, LEGT F Arago, Math Sect, F-51100 Reims, FranceUniv Mohammed V Agdal, Fac Sci, Dept Math & Informat, BP 1014,Av Ibn Batata, Rabat, Morocco
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S China Normal Univ, Inst Laser Life Sci, MOE Key Lab Laser Life Sci, Guangzhou 510631, Peoples R ChinaS China Normal Univ, Inst Laser Life Sci, MOE Key Lab Laser Life Sci, Guangzhou 510631, Peoples R China
Li, Liqin
Yang, Xiangbo
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S China Normal Univ, Inst Laser Life Sci, MOE Key Lab Laser Life Sci, Guangzhou 510631, Peoples R China
S China Normal Univ, Lab Photon Informat Technol, Guangzhou 510631, Peoples R ChinaS China Normal Univ, Inst Laser Life Sci, MOE Key Lab Laser Life Sci, Guangzhou 510631, Peoples R China