Optical pulse propagation in resonantly absorbing medium and a new definition of group velocity

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The purpose of the present research is to establish a new definition of a group velocity : which has a good meaning even in the long pulse propagation distance where the conventional definition of the group velocity breaks down, This new definition takes the effect of the imaginary part of the refractive index into account. The imaginary part, which inevitably exists owing to the Kromas-Kronig relation, is very essential in the pulse propagation in the resonant regions. Chirped pulses show a large Reshaping Delay owing to the spectral shift caused by the imaginary part of the refractive index. In incoherent pulses, there was no way to discuss the pulse velocity. In the present research, we define the position of the incoherent pulses by the centre of gravity, and discussed the meaning of the propagation velocity. While the Reshaping Delay in the individual incoherent pulses appears randomly, this delay is the ensemble averaged and the pulse propagates with a Net Delay.In order to verify the above theoretical predictions, we constructed an experiment system based on a modified Michelson interferometer and a TiO2-Safire laser, and performed systematic experiments on the femtosecond pulse propagation. Form these results, we consider that the new definition of the group velocity has well meaning even in the phase modulated pulses.