Time-resolved light propoagation at the band-edge states of 1D Fibonacci quasicrystals
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Time-resolved light propoagation at the band-edge states of 1D Fibonacci quasicrystals L. Dal Negro , C. J. Oton , Z. Gaburro, L. Pavesi INFM and Department of Physics, University of Trento, Povo (TN), ITALY. P. J. Johnson , A. Lagendijk Van der Waals-Zeeman Institute, University of Amsterdam, Amsterdam, THE NETHERLANDS D. S. Wiersma European Laboratory of Nonlinear Spectroscopy, Florence, ITALY. ABSTRACT Infrared time-resolved interferometric transmission measurements have been performed on one dimensional porous silicon Fibonacci quasicrystals, obtained by electrochemical etching a p-type Si substrate, to address experimentally the problem of light transport and localization in deterministic aperiodic structures. Coherent beatings, pulse stretching and strong pulse delay on a picosecond time scale have been measured when the laser wavelength was tuned at the onedimensional band-edge of a 233-layers Fibonacci quasicrystal where quasi-localized states exist. The observation of these dramatic pulse distortion effects demonstrates the selective excitation of very-narrow localized optical modes. One dimensional transfer matrix and scattering states simulations yield the electromagnetic field distribution inside the structure and reproduce these experimental data supporting the general conclusion about the observation of quasi-localized photonics states. INTRODUCTION Interference of optical waves has primary importance in light propagation in complex media, i.e. media where the refractive index fluctuates over length scales comparable to the wavelength of light. In periodical, transitionally invariant media, Bragg scattering occurs, and the Bloch theorem allows the familiar description of energy states as band structures defined in Brillouin zones [1,2]. On the other hand, also random media exhibit phenomena where interference dominates [3,4], such as Anderson localization of light [5], in which light does not propagates through the medium and energy is stored in exponentially decaying modes [6]. A third class of complex materials are deterministic aperiodic (or quasiperiodic) structures, whose index of refraction is a non periodic function of space, but definable through the iteration of deterministic rules. Such materials are called quasicrystals [7]. Bloch theorem does not apply to quasicrystals because of the global lack of periodicity, nor exponentially localized states are present as in totally random media. Instead, the energy states in quasiperiodic structures are the so-called critical wave functions, i. e. spatially localized wave functions with self-similar structure and scaling. [8,9]. Their transmission spectra posses a rich fractal nature and very narrow resonance peaks separated by forbidden frequency regions, called “pseudobandgaps”. In this work, we address the light transport at the band-edge of a one-dimensional (1D) quasiperiodic structure. We report time-resolved coherent transmission experiments, which allow to probe the density of optical modes at the band-edge through the modifications in the pul
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