Electromagnetic wave propagation in quasiperiodic photonic circuits

Abstract

International audienceWe study theoretically and experimentally the properties of quasiperiodicone-dimensional serial loop structures made of segments and loops arrangedaccording to a Fibonacci sequence (FS). Two systems are considered. (i) Byinserting the FS horizontally between two waveguides, we give experimentalevidence of the scaling behaviour of the amplitude and the phase of thetransmission coefficient. (ii) By grafting the FS vertically along a guide, weobtain from the maxima of the transmission coefficient the eigenmodes of thefinite structure (assuming the vanishing of the magnetic field at the boundariesof the FS). We show that these two systems (i) and (ii) exhibit the property ofself-similarity of order three at certain frequencies where the quasiperiodicityis most effective. In addition, because of the different boundary conditionsimposed on the ends of the FS, we show that horizontal and vertical structuresgive different information on the localization of the different modes inside theFS. Finally, we show that the eigenmodes of the finite FS coincide exactly withthe surface modes of two semi-infinite superlattices obtained by the cleavage ofan infinite superlattice formed by a periodic repetition of a given FS