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Propagation and localization of electromagnetic waves in quasiperiodic serial loop structures

AuthorsAynaou, H.; El Boudouti, E. H.; Velasco, V. R. CSIC ORCID; El Hassouani, Y.; Akjouj, A.; Djafari-Rouhani, B.; Vasseur, J.; Benomar, A.
KeywordsElectromagnetic wave propagation
Photonic band gap
Localised modes
Fibonacci sequences
Issue Date3-Nov-2005
PublisherAmerican Physical Society
CitationPhysical Review E 72, 056601 (2005)
AbstractWe study the propagation of electromagnetic waves in one-dimensional quasiperiodic photonic band gap structures made of serial loop structures separated by segments. Different quasiperiodic structures such as Fibonacci, Thue-Morse, Rudin-Shapiro, and double period are investigated with special focus on the Fibonacci structure. Depending on the lengths of the two arms constituting the loops, one can distinguish two particular cases. (i) There are symmetric loop structures, which are shown to be equivalent to impedance-modulated mediums. In this case, it is found that besides the existence of extended and forbidden modes, some narrow frequency bands appear as defect modes in the transmission spectrum inside the gaps. These modes are shown to be localized within only one of the two types of blocks constituting the structure. An analysis of the transmission phase time enables us to derive the group velocity as well as the density of states in these structures. In particular, the stop bands (localized modes) may give rise to unusual (strong normal) dispersion in the gaps, yielding fast (slow) group velocities above (below) the velocity of light. (ii) There are also asymmetric loop structures, where the loops play the role of resonators that may introduce transmission zeros and hence additional gaps unnoticed in the case of simple impedance-modulated mediums. A comparison of the transmission amplitude and phase time of Fibonacci systems with those of other quasiperiodic systems is also outlined. In particular, it was shown that these structures present similar behaviors in the transmission spectra inside the regions of extended modes, whereas they present different localized modes inside the gaps. Experiments and numerical calculations are in very good agreement.
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