Omnidirectional reflectance and optical gap properties of Si/SiO 2 Thue-Morse quasicrystals
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Omnidirectional reflectance and optical gap properties of Si/SiO2 Thue-Morse quasicrystals L. Dal Negro1, M. Stolfi1,2, Y. Yi1, J. Michel1, X. Duan1, L.C. Kimerling1 J. LeBlanc2, J. Haavisto2 1 2
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 Charles Stark Draper Laboratory, 555 Technology Square, Cambridge, MA 02139
ABSTRACT Aperiodic one dimensional Si/SiO2 Thue-Morse (T-M) multilayer structures have been fabricated, for the first time, in order to investigate both the band-gap behavior, with respect to the system size (band-gap scaling), and the omnidirectional reflectance of the fundamental optical band-gap. Variable angle reflectance data have experimentally demonstrated a large reflectance band-gap in the optical spectrum of a T-M quasicrystal, in agreement with transfer matrix simulations. We have explained the physical origin of the T-M omnidirectional band-gap as a result of periodic spatial correlations in the self-similar T-M structure, as revealed by Fourier Transform and Wavelet analysis. The unprecedented degree of structural flexibility showed by T-M systems can provide an attractive alternative to photonic crystals for the fabrication of photonic devices. INTRODUCTION Photonic quasicrystals (PQ’s) are deterministically generated dielectric structures with nonperiodic refractive index modulation. PQ’s represent an intermediate organization stage between periodic dielectric materials, namely photonic crystal structures[1-3], and random media[4-7]. One dimensional PQ’s can be generated by stacking together layers of different dielectric materials, A and B, according to simple rules, encoding a fascinating complexity. PQ’s show peculiar physical properties like the formation of multiple frequency band-gap regions, called pseudo band-gaps[8,9], the presence of fractal transmission resonances[10,11] and the occurrence of critically localized states[12,13] (field states that decay weaker than exponentially, typically by a power law, and have a rich self similar structure). The presence of large band-gap regions in photonic structures without translational symmetry shows close analogies with the electron behavior in amorphous semiconductors or glass materials. Since the first experimental realization by Gellermann et al. [14] of an optical Fibonacci quasicrystal, the Fibonacci system has been predominantly investigated leading to the experimental demonstration of transmission scaling[14,15], symmetry induced resonances[16], complex light dispersion[17] and strong band-edge group velocity reduction[18]. Fibonacci quasicrystals are an example of quasi-periodic structures with delta-like Fourier power spectrum (FPS) characterized by nonperiodic self-similar Bragg peaks which are responsible for the location and width of the energy pseudo band-gaps[19]. However, there are other classes of quasicrystals that exhibit a “more complex” structure than the Fibonacci ones. In particular, deterministic aperiodic structures are
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characterized by singular continuous
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