Forbidden gaps in finite periodic and quasi-periodic Cantor-like dielectric multilayers at normal incidence

Cojocaru, E.

doi:10.1364/ao.40.006319

Cited by 9 publications

(10 citation statements)

References 16 publications

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“…Subsequently, a wealth of photonic quasicrystals have been conceived, the most outstanding ones being Thue-Morse [19][20][21] and Cantor [22][23][24][25][26]. Both classical (light) and quantum (electrons) waves in these media have been shown to have a self-similar energy spectrum [27], a pseudo-bandgap of forbidden frequencies [28], and critically localized states [29] whose wave functions are distinguished by power law asymptotes and selfsimilarity [30,31].…”

Section: Introductionmentioning

confidence: 99%

Omnidirectional reflection from generalized Fibonacci quasicrystals

et al. 2013

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Abstract:We determine the optimal thicknesses for which omnidirectional reflection from generalized Fibonacci quasicrystals occurs. By capitalizing on the idea of wavelength-and angle-averaged reflectance, we assess in a consistent way the performance of the different systems. Our results indicate that some of these aperiodic arrangements can largely overperform the conventional photonic crystals as omnidirectional reflection is concerned. 143-215 (1996). 6. B. A. van Tiggelen, "Transverse diffusion of light in Faraday-active media," Phys. Rev. Lett. 75, 422-424 (1995). 7. W. Steurer and D. Sutter-Widmer, "Photonic and phononic quasicrystals," J. Phys. D 40, R229-R247 (2007). 8. A. Poddubny and E. Ivchenko, "Photonic quasicrystalline and aperiodic structures," Physica E 42, 1871-1895 (2010). 9. L. Dal Negro and S. V. Boriskina, "Deterministic aperiodic nanostructures for photonics and plasmonics applications," Laser Photon. Rev. 6, 178-218 (2012). 10. P. J. Steinhardt and S. Ostlund, The Physics of Quasicrystals (World Scientific, 1987). 11. M. Senechal, Quasicrystals and Geometry (Cambridge University, 1995). 12. C. Janot, Quasicrystals: A Primer (Oxford University, 2012). 13. Z. V. Vardeny, A. Nahata, and A. Agrawal, "Optics of photonic quasicrystals," Nat. Photonics 7, 177-187 (2013). 14. E. Maciá, "The role of aperiodic order in science and technology," Rep. Prog. Phys. 69, 397-441 (2006 1768-1770 (1985). 17. M. Kohmoto, L. P. Kadanoff, and C. Tang, "Localization problem in one dimension: Mapping and escape," Phys.Rev. Lett. 50, 1870-1872 (1983). 18. M. Kohmoto, B. Sutherland, and K. Iguchi, "Localization in optics: Quasiperiodic media," Phys. Rev. Lett. 58, 2436-2438 (1987). 19. N.-H. Liu, "Propagation of light waves in Thue-Morse dielectric multilayers," Phys. Rev. B 55, 3543-3547 (1997). 20. S. Tamura and F. Nori, "Transmission and frequency spectra of acoustic phonons in Thue-Morse superlattices,"Phys. Rev. B 40, 9790-9801 (1989 1947-1952 (1998). 24. E. Cojocaru, "Forbidden gaps in finite periodic and quasi-periodic Cantor-like dielectric multilayers at normal incidence," Appl. one-dimensional magnonic quasicrystals," J.

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Section: Introductionmentioning

confidence: 99%

Omnidirectional reflection from generalized Fibonacci quasicrystals

et al. 2013

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“…As anticipated in the Introduction, an infinite multilayer is unrealistic in practice, and one should consider N -period finite structures, for which the previous standard approach fails [17,18].…”

Section: Finite Periodic Structures and Iwasawa Decompositionmentioning

confidence: 99%

Characterizing the reflectance of periodic layered media

Monzón

Yonte

Sánchez-Soto

2003

Optics Communications

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It has recently been shown that periodic layered media can reflect strongly for all incident angles and polarizations in a given frequency range. The standard treatment gets these band gaps from an eigenvalue equation for the Bloch factor in an infinite periodic structure. We argue that such a procedure may become meaningless when dealing with structures with not very many periods. We propose an alternative approach based on a factorization of the multilayer transfer matrix in terms of three fundamental matrices of simple interpretation. We show that the trace of the transfer matrix sorts the periodic structures into three types with properties closely related to one (and only one) of the three fundamental matrices. We present the reflectance associated to each one of these types, which can be considered as universal features of the reflection in these media.Comment: 4 pages. 1 eps figure. To be published in Optics Communication

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“…Subsequently, a wealth of other photonic quasicrystals have been conceived, the most outstanding ones being Thue-Morse [37][38][39] and Cantor [40,41].…”

Section: Introductionmentioning

confidence: 99%

Lempel-Ziv Complexity of Photonic Quasicrystals

Monzón¹,

Felipe²,

Sánchez-Soto

2017

Preprint

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The properties of photonic quasicrystals ultimate rely on their inherent long-range order, a hallmark that can be quantified in many ways depending on the specific aspects to be studied. We use the Lempel-Ziv measure, a basic tool for information theoretic problems, to characterize the complexity of the specific structure under consideration. Using the generalized Fibonacci quasicrystals as our thread, we adress the relation between the optical response and the associated complexity.

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Forbidden gaps in finite periodic and quasi-periodic Cantor-like dielectric multilayers at normal incidence

Cited by 9 publications

References 16 publications

Omnidirectional reflection from generalized Fibonacci quasicrystals

Omnidirectional reflection from generalized Fibonacci quasicrystals

Characterizing the reflectance of periodic layered media

Lempel-Ziv Complexity of Photonic Quasicrystals

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