Transmission and reflection of electromagnetically induced absorption grating in homogeneous atomic media

We theoretically study the transmission and reflection of the probe travelling wave in an electromagnetically induced absorption grating (EIG), which is created in a three-level Lambda-type atomic system when the coupling field is a standing wave. Using the system, we show that a photonic stop band can exist on one side away from the resonance point in ultracold atomic gas, while there is an enhanced absorption at resonance and small reflection around it in the thermal atomic gas. Because our method can deal with such two cases, it is helpful to further understand the effects of the Doppler effect on atomic coherence and interference.