Theory and Group Velocity of Ultrashort, Tightly-Focused Laser Pulses

摘要

The wave equation describing an ultrashort, tightly focused laser pulse in vacuumis solved analytically. Plasma dispersive effects are also included. Based on exact short-pulse solutions, analytic expressions are obtained for pulse length evolution, pulse centroid motion and group velocity. Approximate short pulse solutions are obtained to arbitrary order in the parameter lambda/2xL <1, where lamda is the pulse wavelength and L is the length of the pulse envelope. Comparisons are made to the solutions of the paraxial wave equation and to numerical solutions of the full wave equation.The exact analytic expression for the pulse group velocity vg, which is correctly determined from the motion of the pulse centroid, is in excellent agreement with the numerical solution. In vacuum,