Electromagnetic wave propagation in quasiperiodic photonic circuits
Résumé
We study theoretically and experimentally the properties of quasiperiodic
one-dimensional serial loop structures made of segments and loops arranged
according to a Fibonacci sequence (FS). Two systems are considered. (i) By
inserting the FS horizontally between two waveguides, we give experimental
evidence of the scaling behaviour of the amplitude and the phase of the
transmission coefficient. (ii) By grafting the FS vertically along a guide, we
obtain from the maxima of the transmission coefficient the eigenmodes of the
finite structure (assuming the vanishing of the magnetic field 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 the quasiperiodicity
is most effective. In addition, because of the different boundary conditions
imposed on the ends of the FS, we show that horizontal and vertical structures
give different information on the localization of the different modes inside the
FS. Finally, we show that the eigenmodes of the finite FS coincide exactly with
the surface modes of two semi-infinite superlattices obtained by the cleavage of
an infinite superlattice formed by a periodic repetition of a given FS.
Domaines
Physique [physics]
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