THEORY AND GROUP-VELOCITY OF ULTRASHORT, TIGHTLY FOCUSED LASER-PULSES

The wave equation describing an ultrashort, tightly focused laser puls e in vacuum is solved analytically. Plasma dispersive effects are also included. Based on exact short-pulse solutions, analytical expression s are obtained for the pulse-length evolution, the pulse centroid moti on, and the group velocity. Approximate short-pulse solutions are obta ined to arbitrary order in the parameter lambda/2 pi L < 1, where lamb da is the pulse wavelength and L is the length of the pulse envelope. Comparisons are made to the solutions of the paraxial wave equation an d to numerical solutions of the full wave equation. The exact analytic al expression for the pulse group velocity upsilon(g), which is correc tly determined from the motion of the pulse centroid, is in excellent agreement with the numerical solution. In vacuum, 1 - upsilon(g)/c con gruent to (lambda/2 pi r(0))(2), where r(0) is the laser spot size at focus. Estimates for the quantity 1 - upsilon(g)/c, based on the parax ial wave equation, are found to be in error by a factor of 2.