Abstract
A simple photonic device consisting of two dangling side resonators grafted at two sites on a waveguide is designed in order to obtain sharp resonant states inside the transmission gaps 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. The amplitude of the transmission is obtained following the Fano form. The full width at half maximum of the resonances as well as the asymmetric Fano parameter are discussed explicitly as function of the geometrical parameters of the system. In addition to the usual asymmetric Fano resonance, we show that this system may exhibit an electromagnetic induced transparency resonance as well as well as a particular case where such resonances collapse in the transmission coefficient. Also, we give a comparison between the phase of the determinant of the scattering matrix, the so-called Friedel phase, and the phase of the transmission amplitude. The analytical results are obtained by means of the Green's function method, whereas the experiments are carried out using coaxial cables in the radio-frequency regime. These results should have important consequences for designing integrated devices such as narrow-frequency optical or microwave filters and high-speed switches. This system is proposed as a simpler alternative to coupled-micoresonators.
Highlights
When the resonance falls between two anti-resonances, Fano resonance behaves like electromagnetic induced transparency (EIT) resonance
In addition to the usual asymmetric Fano resonance, we show that this system may exhibit an electromagnetic induced transparency resonance as well as well as a particular case where such resonances collapse in the transmission coefficient
We have clearly demonstrated that a simple geometry of an electromagnetic waveguide with dangling side resonators on both sides can pave the way to the obtention of gaps in the radio frequency domain
Summary
When the resonance falls between two anti-resonances, Fano resonance behaves like electromagnetic induced transparency (EIT) resonance. Recent works have shown that several properties of quantum graphs could be successfully simulated by microwave networks made of coaxial cables These structures are attractive since their production is more feasible at any wavelength scale and they require only simple analytical and numerical calculations. We have proposed a new simple filter structure to study theoretically Fano resonances for acoustic, mesoscopic, and magnonic 1D circuits. This structure consists of two side stubs, which play the role of resonators, grafted at two sites on an infinite waveguide (see Fig. 1).
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