Wave propagation in a quasi-periodic waveguide network

Abstract

We investigate the transport properties of a classical wave propagating through a quasi-periodic Fibonacci array of waveguide segments in the form of loops. The formulation is general, and applicable for electromagnetic or acoustic waves through such structures. We examine the conditions for resonant transmission in a Fibonacci waveguide structure. The local positional correlation between the loops are found to be responsible for the resonance. We also show that, depending on the number of segments attached to a particular loop, the intensity at the nodes displays a perfectly periodic or a self-similar pattern. The former pattern corresponds to a perfectly extended mode of propagation, which is to be contrasted to the electron or phonon characteristics of a pure one dimensional Fibonacci quasi-crystal.

Engineering wave localization in a fractal waveguide network

“…As one can easily appreciate, the geometry of a diamond-Vicsek network provides an interesting culmination of the 'open' character of a typical Vicsek pattern and closed loops at shorter scales of length. This is in marked contrast to the much studied Sierpinski gasket waveguide network [34], which is a closed structure, or to the other deterministic waveguide networks [36,37]. The presence of the loops generates a possibility of an effectively long ranged propagation of waves between the various vertices, and its effect on the localization or delocalization of waves is worth studying.…”

“…Photonic gaps, apart from materials with a large di- * E-mail: arunava chakrabarti@yahoo.co.in electric constant, can also be observed in waveguide networks, as proposed by several groups over the past years [30][31][32][33][34][35][36][37][38]. Anderson localized eigenmodes are observed inside the photonic gaps and excellent agreement between theory and experiments has been obtained [30].…”

“…The network models are able to localize a propagating wave by virtue of the geometrical arrangement of the waveguide segments. Of particular interest are a wide variety of models based on waveguide networks designed following a deterministic fractal geometry [34][35][36][37][38], where the gaps result from the typical topology exhibited the hierarchical arrangement of the waveguide segments. The present communication also deals with a hierarchically designed (fractal geometry) waveguide network, but addresses a deeper fundamental question regarding wave localization in such systems, as explained below.…”

Real Space Theory for Electron and Phonon Transport in Aperiodic Lattices via Renormalization

“…For instance, V. Sánchez et al developed, in 2001, a sophisticated and exact RSRM for the Kubo-Greenwood formula (3) applied to the mixing Fibonacci problem [47], and then its AC conductivity spectra were carefully analyzed [48,49] beyond those obtained from approximants [50]. The renormalization technique was also used for the study of localization [51][52][53], electronic spectra of GaAs/Ga x Al 1−x As superlattices [54], and arrays of quantum dot [55], as well as for a unified transport theory of phonon [56], photon [57], and fermionic atom [58] based on the tight-binding model. On the other hand, by means of RSRM, the fine structure of energy spectra [59] and electronic transport in Hubbard Fibonacci chains [60,61] were investigated, and a new universality class was found in spin-one-half Heisenberg quasiperiodic chains [62].…”

Effect of diffusion layers and defect layer on acoustic phonons transport through the structure consisting of different films

“…The localized surface or interface acous- tic phonon modes in finite or semi-infinites SLs [27][28][29] have also been reported. Recently, acoustic phonons transmission and thermal conductance in quantum waveguides were investigated [30][31][32][33][34][35]. The calculated results show that the transmission probability and thermal conductance can be artificially controlled to a certain degree by adjusting the structural parameters.…”