9 - Electromagnetic Induced Transparency, Induced Absorption, and Fano Resonances in Photonic Circuits
Résumé
In this chapter, a simple photonic device consisting of two dangling side resonators grafted at two sites (U-shape) or at the same site (cross-shape) along 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 analytic 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 and the asymmetric Fano parameter are discussed explicitly as functions 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 (EIT) resonance, as well as a particular case where such resonances collapse in the transmission coefficient, giving rise to the so-called bound in continuum (BIC) states. 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. By taking into account the loss in the waveguides, we show that at the transmission resonance, the transmission (reflection) increases (decreases) as a function of the detuning δ between the lengths of the two stubs, whereas the absorption goes through a maximum around 0.5 for a threshold value δth, giving rise to electromagnetic induced absorption (EIA) resonance, which depends on the attenuation in the system and then falls to zero. The effect of the boundary conditions at the end of the resonators on the EIA resonance is also discussed. 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 microresonators.