Ultrashort Gaussian Pulses Research Articles

Generalized asymptotic description of the propagated field dynamics in Gaussian pulse propagation in a linear, causally dispersive medium

As the initial pulse envelope width of an input Gaussian pulse-modulated harmonic wave is increased above the characteristic relaxation time of a single resonance Lorentz model dielectric, the classical asymptotic description of the propagated field becomes increasingly inaccurate at a fixed propagation distance and must then be generalized in order to become uniformly valid with respect to the initial pulse width. The required generalization results in a modified complex phase function that depends not only upon the dispersive medium parameters and the propagation distance, but also upon the initial pulse width. The resultant modified asymptotic description of Gaussian pulse propagation is shown to be uniformly valid in the initial pulse width. The modified asymptotic description presented here reduces to the classical asymptotic result presented in an earlier paper [Phys. Rev. E 47, 3645 (1993)] in the limit of an input ultrashort Gaussian pulse. In the opposite limit of a very broad input pulse, the modified asymptotic description reduces to that obtained with the well-known quasimonochromatic or slowly varying envelope approximation. Furthermore, the modified asymptotic description provides a clear description of the transition from the ultrashort limit to the quasimonochromatic regime for Gaussian pulse propagation.

Propagation of radius-tailored laser pulses over extended distances in a uniform plasma*

A Maxwell-fluid model is described, which allows simulation of laser pulses over extended distances (multiple diffraction lengths) in an underdense plasma. This model is used to simulate radius-tailored laser pulses, which can propagate over such distances with minimal distortion in a uniform plasma. Theoretical model equations governing the choice of radius tailoring are also given. A radius-tailored pulse has constant power approximately equal to the critical power for relativistic guiding over the length of the pulse and a spot size at focus that varies over the length of the pulse. A laser pulse configuration of this type can be constructed from a series of ultrashort Gaussian pulses.

Uniform asymptotic description of ultrashort Gaussian-pulse propagation in a causal, dispersive dielectric.

The complete asymptotic description of ultrashort Gaussian-pulse propagation in a single-resonance Lorentz medium in the mature-dispersion regime is presented and compared with the results of two independent numerical experiments of the propagated-field evolution. The nonuniform asymptotic method of Olver [Stud. Appl. Math. Rev. 12, 228 (1970)] (an extension of the method of steepest descents) is first applied to obtain the standard asymptotic description of the propagated field that is due to the given input Gaussian-modulated field. The description afforded by this asymptotic method, although nonuniform in certain space-time regions, is found to be in excellent agreement with purely numerical results, especially when exact, numerically determined saddle-point locations, and exact expressions for the derivatives of the phase function are used in the implementation of the theoretical approach. Modern uniform asymptotic techniques, which generalize Olver's nonuniform description, are then employed to obtain a rigorous description of ultrashort Gaussian-pulse propagation that is uniformly valid for all space-time points in the mature-dispersion regime. This asymptotic description clearly shows that the propagated field can be expressed solely in terms of a generalized Sommerfeld and a generalized Brillouin precursor field, the first of which dominates the total propagated field when the carrier frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ is well above resonance while the second generalized precursor field dominates when ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ is below or near resonance. It is further shown that the pulse distortion is due solely to the manner in which the precursor field amplitude is modified by the initial Gaussian-pulse envelope spectrum. Finally, the frequency dependence of the signal velocity of the input ultrashort, Gaussian-modulated harmonic field in a single-resonance Lorentz medium is discussed.