Stopping and filtering waves in phononic circuits

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

Photon, electron, magnon, phonon and plasmon mono-mode circuits

“…We address now the propagation of longitudinal acoustic waves through a quasi-one-dimensional structure, called asymmetric serial loop structure, of a mono-mode networked wave-guide [265]. The structure is composed of asymmetric slender tube loops pasted together with slender tubes of finite length (see Fig.…”

“…We focus on homogeneous loop structures where the media 1, 2 and 3 are made of the same material. The dispersion relation of the infinite loop structures, that relates the pulsation frequency o to the wave vector k, was derived [265]. It has the same expression (see Section 2.9) as that given above for the corresponding photon structure, as a function of L ¼ d 2 þ d 3 , DL ¼ d 2 À d 3 , and a ¼ o=v where v is the longitudinal speed of sound.…”

Effects of competition between the anisotropy and the spin quantum number on the magnon energy gap in a four-layer ferromagnetic superlattice

“…The band gap spectrum, being the signature of the periodicity, has been intensively studied in plasmonic crystals [13], phononic crystals [14], and periodic ferroelectric media [15]. Magnetic media, analogous to photonic crystals possessing a photonic gap (i.e., the frequency range where the wave propagation is completely forbidden), can be named as magnonic crystals.…”

Wave propagation in a quasi-periodic waveguide network

“…Recently, network models based on serial loop structures (SLS) are being studied in the context of propagation of electromagnetic and acoustic waves [10,11]. Experiment has been done [10] on systems consisting of loop structure made by slender tubes which are pasted on similar tubes of finite length.…”