Scaling Law, Confined and Surface Modes in Photonic Fibonacci Stub Structures: Theory and Experiment

Abstract

We investigate both theoretically and experimentally the properties of electromagnetic waves propagation and localization in periodic and quasi-periodic stub structures of Fibonacci type. Each block constituting the Fibonacci sequence (FS) is composed of an horizontal segment and a vertical stub. The origin of the primary and secondary gaps shown in such systems is discussed. The behaviors and scattering properties of the electromagnetic modes are studied in two geometries, when the FS is inserted horizontally between two semi-infinite waveguides or grafted vertically along a guide. Typical properties of the Fibonacci systems such as the fragmentation of the frequency spectrum, the self-similarity following a scaling law are analyzed and discussed. It is found that certain modes inside these two geometries decrease according to a power law rather than an exponential law and the localization of these modes displays the property of self-similarity around the central gap frequency of the periodic structure where the quasi-periodicity is most effective. Also, the eigenmodes of the FS of different generation order are studied depending on the boundary conditions imposed on its extremities. It is shown that both geometries provide complementary information on the localization of the different modes inside the FS. In particular, in addition to bulk modes, some localized modes induced by both extremities of the system exhibit different behaviors depending on which surface they are localized. The theory is carried out using the Green’s function approach through an analysis of the dispersion relation, transmission coefficient and electric field distribution through such finite structures. The theoretical findings are in good agreement with the experimental results performed by measuring in the radio-frequency range the transmission along a waveguide in which the FS is inserted horizontally or grafted vertically.

Spin-wave localization on phasonic defects in one-dimensional magnonic quasicrystal

“…The profile of this mode exhibits the pattern with amplitude concentrated on parts of the structure possessing locally the same set of strips. For very large structures, these modes can reveal a selfsimilar pattern [52,55]. By adding the defects, we can shift critically localized modes to the frequency gap.…”

“…We can identify the strongly localized defect modes with a large value of |λ| inside the frequency gap. It is worth noting that the localization of the modes at frequencies close to the edges of gaps with enhanced λ suggests that some of the critically localized modes [52][53][54][55] become defect modes.…”