Electromagnetic wave propagation in quasi-periodic photonic circuits

E H El Boudouti,V R Velasco,Y El Hassouani,H Aynaou,B Djafari-Rouhani,A Akjouj

doi:10.1088/0953-8984/19/24/246217

Abstract

We study theoretically and experimentally the properties of quasiperiodic one-dimensionalserial loop structures made of segments and loops arranged according to a Fibonaccisequence (FS). Two systems are considered. (i) By inserting the FS horizontally betweentwo waveguides, we give experimental evidence of the scaling behaviour of theamplitude and the phase of the transmission coefficient. (ii) By grafting the FSvertically along a guide, we obtain from the maxima of the transmission coefficientthe eigenmodes of the finite structure (assuming the vanishing of the magneticfield at the boundaries of the FS). We show that these two systems (i) and (ii)exhibit the property of self-similarity of order three at certain frequencies where thequasiperiodicity is most effective. In addition, because of the different boundaryconditions imposed on the ends of the FS, we show that horizontal and verticalstructures give different information on the localization of the different modesinside the FS. Finally, we show that the eigenmodes of the finite FS coincideexactly with the surface modes of two semi-infinite superlattices obtained by thecleavage of an infinite superlattice formed by a periodic repetition of a givenFS.

Highlights

Photonic crystals (PCs) have been a subject of great interest during the last decade because of their interesting properties in the development of new optical circuits [1, 2]
[33], we have studied the propagation and localization of electromagnetic waves in a quasi-periodic coaxial photonic crystal made of loops and segments arranged to a Fibonacci sequence (FS) Sk+1 = Sk Sk−1 with the initial conditions S1 = A, S2 = B, where k is the generation number
We have presented theoretical and experimental results of propagation and localization of electromagnetic waves in Fibonacci structures made of coaxial cables

Summary

Introduction

Photonic crystals (PCs) have been a subject of great interest during the last decade because of their interesting properties in the development of new optical circuits [1, 2] These systems, constituted by periodic arrangements (cells) of dielectric materials according to one (1D), two (2D) and three (3D) dimensions, present characteristic frequency domains in the dispersion curves where light can propagate (bulk bands) and frequency domains where light cannot propagate (gaps). In their 1D version, PCs are well known as optical multilayers of alternating dielectric materials [5] Such structures exhibit multiple reflections and destructive interference giving rise to forbidden bands where light cannot propagate. The propagation in these structures is monomode [17] and one can obtain very accurate experimental results that may be fitted with a simple 1D theoretical model

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Conclusion