**9. Conclusions**

The quantum optical properties of an EIT medium has been discussed (in Section 2), and the formalism for treating wave propagation in a periodic structure has been reviewed (in Section 3). The band structure and the reflectance of a 1D photonic crystal consisting of both EIT medium layers and host dielectric layers can show extraordinary sensitivity to the frequency of a probe field because of a two-photon resonance relevant to destructive quantum interference between two transition pathways driven by the control and probe fields (in Sections 4 and 5). Such an EIT-based periodic layered material can also exhibit an effect of field-intensity-sensitive switching control (depending quite sensitively on the Rabi frequency of the control field) in the cases of large layer number *N* . Since the optical responses can be controlled by the tunable quantum interference induced by the external control field via two-photon resonance, the EIT-based layered medium under consideration shows more flexible optical responses than conventional photonic crystals because of the EIT two-photon resonance that gives rise to strong dispersion in the band of transparency window.

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As the microscopic electric polarizability as well as the electric permittivity of the EIT medium are caused by the atomic energy level transition processes from the ground state to the excited states, in which the quantum interference relevant to atomic phase coherence is involved, the reflectance and transmittance of an EIT-based periodic layered medium are shown to be quite sensitive to the probe frequency.

The LHM-EIT-based periodic layered medium has also been considered (in Sections 6 and 7). Since there are left-handed layers embedded in the layered medium, and the periodic EIT layers would act as a potential barrier for the incident electromagnetic wave, the absolute values of the real or imaginary part of the reflection coefficient in some frequency ranges would be more than unity due to the Klein tunneling. The present photonic analog of the Klein tunneling might be used for designing frequency-sensitive photonic transistors. We expect that some new photonic devices (e.g., logic and functional gates) and sensitively switchable devices (fundamental building blocks in, e.g., photonic microcircuits on silicon, in which light replaces electrons), which would find new applications in photonic quantum information processing, would be achieved by taking advantage of such an effect of *coherent switching control* (in Section 8).

The present scheme can be generalized to the cases of four-level EIT systems, where two control fields and one probe field drive the atomic level transitions (Shen, 2007; Shen & Zhang, 2007; Gharibi et al., 2009; Shen, 2010). Obviously, the optical response in such a four-level EITbased photonic crystal would be more sensitive to the probe frequency than in a three-level EIT photonic crystal presented in this paper. Apart from this intriguing property, there are also interesting applications based on the four-level EIT photonic crystal, e.g., some examples of photonic devices (e.g., multi-input logic gates), in which the control fields and the transmitted probe field act as the input and output signals, respectively, can be designed. We expect that all these new optical properties relevant to quantum coherence, including their applications to photonic devices, could be realized experimentally in the near future.
