Omnidirectional reflection from generalized Fibonacci quasicrystals

Abstract

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.

Octonacci photonic quasicrystals

“…Note that this sequence is classified as Pisot-Vijayaraghavan (PV), when we take the negative eigenvalue of the substitution matrix 36 , i e., σ − = 1 − √ 2, with |σ − | ≤ 1. On other hand, differently of the Fibonacci case, the ratio τ between the number of building blocks A and building blocks B is different of the positive eigenvalue σ + = 1 + √ 2, as usually is found in the Fibonacci generalizations 25,37 . Although several theoretical techniques have been used to study the transmission spectra in these structures, like spectral analysis 38 , in the present work we make use of the transfer-matrix approach to analyze them (for a review see Ref.…”

Omnidirectional Reflection From Generalized Kolakoski Multilayers

“…Since 1987, a broad range of photonic aperiodic structures arranged according to different substitutional rules and made of different kinds of materials have been investigated, (see, for instance [1,2,5,10,11]). Particularly, the optical behaviors of both the classical Kolakoski multilayers and OmniGuide structure constructed on their basis have been studied for the first time in [4,12,13].…”

“…Thus, the presence of several omnidirectional PBGs in a period of the reciprocal space has been theoretically and experimentally confirmed for a number of aperiodic multilayer configurations. For instance, the possibility of achieving omnidirectional reflection (ODR) in Thue-Morse [15], Fibonacci [16,17], generalized Fibonacci [10] and classical Kolakoski [4] aperiodic structures has been put forward lately. At the same time, the omnidirectional properties of the generalized Kolakoski multilayers K (p, q) have not been studied yet; such is the first goal of this paper.…”

Lempel-Ziv Complexity of Photonic Quasicrystals

“…This has developed into a cool topic [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56], which besides is underpinned by remarkable mathematical properties [57]. This confirms that the deterministic aperiodic nanostructures is a highly interdisciplinary and fascinating research field, conceptually rooted in several branches of mathematics.…”