Analysis and optimization of channelization architecture for wideband slow light in atomic vapors

We carry out an analysis of an earlier proposed "channelization" architecture for wideband slow light propagation and pulse delays in atomic vapors using electromagnetically induced transparency (EIT). In the channelization architecture, a wideband input signal pulse is spatially dispersed in the transverse dimension, sent through an EIT medium consisting of an initially spin-polarized atomic vapor illuminated by a monochromatic, co-propagating pump laser, then spatially recombined. An inhomogenous magnetic field is used to Zeeman shift the atomic vapor into two-photon (Raman) resonance with the signal-pump transitions at all locations. Extending on previous analyses, we show in detail how the reconstructed pulse will be delayed only if a slight mis-match from the two-photon resonance is introduced. If the desired delay is taken as a constrained parameter, we find the bandwidth can be increased by large factor. We present an analytic treatment which optimizes the bandwidth given a desired delay and constraints on the pump power and focusing. We find bandwidth increases on the order of 5 times (100 MHz versus 20 MHz) should be possible for delays of interest (10 ns) to applications in telecommunications and radar. Interestingly, due to the mis-match requirement, we find the channelization can not increase the optimal delay-bandwidth product over conventional slow light.