Ultrashort Pulse Propagation in the Linear Regime

First, we investigate the Bouguer-Lambert-Beer (BLB) law as applied to the transmission of ultrashort pulses through water in the linear absorption regime. We present a linear theory for propagation of ultrashort laser pulses, and related experimental results are in excellent agreement with this theory. Thus we conclude that recent claims of the BLB law violations are inconsistent with the experimental data obtained by our group. Second, we study the dynamics of ultrashort pulses in a Lorentz medium and in water via the saddle point method. It shows that the saddle point method is a more efficient and faster method than the direct integration method to study one-dimensional pulse propagation over macroscopic distances (that is, distance comparable to the wavelength) in a general dielectric medium. Comments are also made about the exponential attenuation of the generalized Sommerfeld and Brillouin precursors. By applying the saddle point method, we also determined that the pulse duration estimated by the group velocity dispersion (GVD) approximation is within 2% of the value computed with the actual refractive index for a propagation distance of 6 m in water.