Slow light transmission in one-dimensional periodic structures

We have analyzed the transmission properties of pulses through one-dimensional periodic structures in order to systematically explore the best conditions to achieve the maximum delay with the minimum possible distortion. In the absence of absorption and no layer variation, the transmission coefficient $t_N$ can be well approximated by a sum of Lorentzian resonances. The ratio between their width $\Gamma_{\rm r}$ and their separation $\Delta\omega_{\rm r}$ is a crucial parameter to characterize the distortion of the transmitted pulse. For typical values of the parameters used in telecommunications and high index of refraction contrasts $n_2 / n_1$, the distortion of the transmitted pulse is unacceptably large for frequencies near the edge of the transmission window. We estimate fractional delays achievables in terms of the central frequency used and the pulse bandwidth.