Theory and group velocity of ultrashort, tightly focused laser pulses

Journal Article · Fri Sep 01 04:00:00 EDT 1995 · Journal of the Optical Society of America, Part B: Optical Physics

DOI:https://doi.org/10.1364/JOSAB.12.001695· OSTI ID:165725

Esarey, E; Sprangle, P; Pilloff, M; Krall, J ^[1]

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1. Beam Physics Branch, Plasma Physics Division, Naval Research Laboratory, Washington, D.C. 20375-5346 (United States)

The wave equation describing an ultrashort, tightly focused laser pulse in vacuum is solved analytically. Plasma dispersive effects are also included. Based on exact short-pulse solutions, analytical expressions are obtained for the pulse-length evolution, the pulse centroid motion, and the group velocity. Approximate short-pulse solutions are obtained to arbitrary order in the parameter {lambda}/2{pi}{ital L}{lt}1, where {lambda} is the pulse wavelength and {ital 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 analytical expression for the pulse group velocity {ital v}{sub {ital g}}, which is correctly determined from the motion of the pulse centroid, is in excellent agreement with the numerical solution. In vacuum, 1{minus}{ital v}{sub {ital g}}/{ital c}{congruent}({lambda}/2{pi}{ital r}{sub 0}){sup 2}, where {ital r}{sub 0} is the laser spot size at focus. Estimates for the quantity 1{minus}{ital v}{sub {ital g}}/{ital c}, based on the paraxial wave equation, are found to be in error by a factor of 2. {copyright} 1995 Optical Society of America

• Sponsoring Organization: USDOE
• OSTI ID: 165725
• Journal Information: Journal of the Optical Society of America, Part B: Optical Physics, Journal Name: Journal of the Optical Society of America, Part B: Optical Physics Journal Issue: 9 Vol. 12; ISSN JOBPDE; ISSN 0740-3224
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
FOURIER ANALYSIS
LASER RADIATION
PULSE TECHNIQUES
WAVE EQUATIONS