A simple acoustic device consisting of two dangling side resonators grafted at two sites on a slender tube is designed possibly to obtain transmission stop bands (where the propagation of longitudinal acoustic waves is forbidden). In contrast to all known systems of this kind, a spectral transmission gap of nonzero width occurs here even with this simple structure. This is obtained by combining appropriately the zeros of transmission of the side resonators. Sharp resonant states inside the gaps can be achieved without introducing any defects in the structure. This results from an internal resonance of the structure when such a resonance is situated in the vicinity of a zero of transmission or placed between two zeros of transmission, the so-called Fano resonances. A general analytical expression for the transmission coefficient is given for various systems of this kind within the framework of the Green's function method. The amplitude and the phase of the transmission are discussed as a function of frequency and it is shown that the width of the stop bands is very sensitive to the number of side resonators. These results should have important consequences for the suppression of low-frequency noise and for designing filters.
We report the existence of large gaps in the band structure of a comblike structure composed of a onedimensional magnonic waveguide along which NЈ dangling side branches are grafted at N equidistant sites. These gaps originate not only from the periodicity of the system but also from the resonance states of the grafted branches ͑which play the role of resonators͒. The width of these gaps is sensitive to the length of the side branches as well as to the numbers N and NЈ. The presence of defect branches in the comblike structure can give rise to localized states inside the gaps. We show that these states are very sensitive to the length of the side branches, to the periodicity, to N or/and NЈ and to the length of the defect branches. Analytic expressions are given for the band structure of combs for large N and for the transmission coefficient for an arbitrary value of N and NЈ with and without defects.
No abstract
The acoustic band structures and transmissions through a one-dimensional (1D) monomode waveguide made of asymmetric slender tube loops pasted together with slender tubes of finite length are investigated theoretically. These monomode circuits may exhibit large stop bands where the propagation of acoustic waves is forbidden. These stop bands (gaps) originate both from the periodicity of the system and the resonant modes of the loops. The width of these bandgaps depends on the geometrical parameters of the structure and may be drastically increased in a tandem geometry made of several successive asymmetric serial loop structures (ASLSs) which differ in their geometrical characteristics. These ASLSs may have potential applications as ultra-wideband filters.The discovery of photonic crystals has laid the foundation of bandgap engineering in mesoscopic systems. The keynote behind the proposal of photonic crystals was the possibility of modifying the propagation of electromagnetic waves by creating photonic bandgaps in the band structure of synthetic periodic dielectric structures. Within a complete photonic bandgap, optical waves, spontaneous emission and zero-point fluctuations are all absent. Because of its promised ability to influence spontaneous emission [1], and to pave the way to light localization [2], the pursuit of photonic bandgaps has been the major motivation for studying photonic crystals. These materials are composed of periodically modulated dielectrics with the length scale of the periodicity approaching the wavelength of light. This constitutes an important part of mesoscopic physics, which is just beginning to be explored [3].It did not take long before photonic crystals aroused interest in their phononic counterparts, namely, 'phononic crystals'-artificial two-and three-dimensional (3D) periodic elastic/acoustic composites [4]. In analogy to photonic crystals, the emphasis was laid on
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