Ultrashort pulse propagation in a cubic medium including the Raman effect

A nonlinear evolution equation for sub-and a few-cycle pulse is derived in a cubic medium including the delayed nonlinear response. The equation is derived for the real electric field directly without separating the pulse into an envelope and the carrier wave. Using this equation, we numerically study the properties of eight-cycle pulse, at 0.39-mu m wavelength, propagating in a hollow-core fiber filled with D-2 gas.