Abstract

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 ${}^{87}\mathrm{Rb}$ 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.

© 2008 Optical Society of America

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