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 demonstrate analytically and numerically the possibility of existence of the analogues of electromagnetic induced transparency (EIT) and electromagnetic induced reflection (EIR) in a simple mesoscopic structure. The latter consists of a ring of length 2d attached vertically to two semi-infinite leads (waveguide) by a wire of length d 1 . The ring is threaded by a magnetic flux Φ, the so-called Aharonov-Bohm effect. The number of dangling wire-ring resonators attached at the same point can be increased to N. First, we demonstrate analytically that in the absence of the magnetic flux (Φ ¼ 0) and for particular values of d 1 , the structure may present some states that are confined in the ring and do not interact with the waveguide states. These trapped states fall in the continuum states of the two leads and therefore represent bound in continuum (BIC) states. These states are characterized by a zero width resonance (i.e., infinite life-time) in the transmission and reflection spectra. In presence of a weak magnetic flux (Φ 6 ¼ 0), the BIC states transform to EIT or EIR resonances for specific values of the lengths d 1 and d of the wire and the ring respectively. In addition to the numerical results, we have developed Taylor expansion calculations of the transmission and reflection coefficients around EIT and EIR resonances to show that the latter can be written following a Fano shape. In particular, we have deduced the Fano parameter q and the quality factor Q of these resonances as function of N and the flux Φ. We have found that Q decreases as function of Φ for both EIT and EIR resonances, whereas it increases (decreases) as function of N for EIT (EIR) resonances. These results show the possibility of tuning EIT and EIR resonances by means of the magnetic flux Φ and the number of dangling resonators N. The effect of temperature on EIT and EIR resonances is also considered through an analysis of the Landauer-Buttiker conductance formula obtained from transmission. The theoretical results are obtained within the framework of the Green's function method which enables us to deduce analytically the dispersion relation, transmission and reflection coefficients. These results may have important applications for electronic transport in mesoscopic systems such as filters and demultiplexers.
In the frame of long-wavelength Heisenberg model, a simple magnonic device is designed to obtain possibly transmission stop bands ͑where the propagation of spin waves is forbidden͒. This simple device is composed of an infinite one-dimensional mono-mode waveguide ͑the backbone͒ along which N͑NЈ͒ side resonators are grafted at two sites. Contrary 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, the phase, and the phase time 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 the side resonators. These results should have important consequences for designing integrated devices such as narrow-frequency optical or microwave filters and high-speed switches.
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