An analytical method based on a two-mode approximation is here developed to study the optical response of a periodically modulated medium of ultracold atoms driven into a regime of standing-wave electromagnetically induced transparency. A systematic comparison with the usual approach based on the coupled Maxwell-Liouville equations shows that our method is very accurate in the frequency region of interest. Our method, in particular, explains in a straightforward manner the formation of a well-developed photonic bandgap in the optical Bloch wave vector dispersion. For ultracold (87)Rb atoms nearly perfect reflectivity may be attained and a light pulse whose frequency components are contained within the gap is seen to be reflected with little loss and deformation. (C) 2008 Optical Society of America
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