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Summary form only given. We study the interaction between intense (50 MW peak power), shaped ultrafast laser pulses and optically dense samples of Rb vapor. In particular, we concentrate our attention on laser pulses with a the complex hyperbolic secant envelope, or equivalently, a sech electric field envelope with a tanh frequency sweep. In order to produce and characterize the shaped laser pulses used in our experiments, we exploited several new technologies: amplified, shaped laser pulses were generated using an acousto-optic modulator-based system combined with a chirped-pulse regenerative amplifier. The amplitude and phase of these pulses were then characterized by the STRUT (spectrally and temporally resolved upconversion technique). The STRUT was used to measure the laser pulses both before and after propagating through Rb vapor. Examples of such experimental STRUT images are presented. The complex sech pulse was selected because, in optically thin media, only it and rectangular pulses give complete analytical solutions to the Bloch equations. This shape has been found to generate complete population inversion over a well-defined and amplitude-insensitive bandwidth. In optically dense samples the excited state dynamics are not so straightforward. We have found, both in experiments and theoretically, that the extent and character of the population inversion is related to the frequency sweep of the laser pulses as does the amount of residual excited population after the pulse and any subsequent stimulated emission.