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.

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We investigate the electronic transport in a simple mesoscopic cross structure made of two wires (stubs) grafted at the same point along a quantum waveguide. We show that the structure may exhibit important phenomena such as bound in continuum (BIC) states. These states are transformed into electromagnetically induced transparency (EIT) resonance by detuning slightly the lengths of the stubs. The last phenomenon is used to propose and study a mesoscopic demultiplexer device with an input waveguide and two output waveguides. We give closed-form expressions of the geometrical parameters that allow a selective transfer of a given state in the first waveguide without perturbing the second waveguide. The effect of temperature on the transmission resonances is also examined by using Landauer–Büttiker formula. The analytical results of the dispersion relation and transmission and reflection coefficient are obtained using the Green’s function method.

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