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Physical review. B, Condensed matter

Ultrashort x-ray pulse propagation through resonant attenuating media

F. N. Chukhovskiǐ, Ulrich Teubner, Eckhart Forster

Published Feb 1, 1997• 0 citations
Publisher

Abstract

The propagation of ultrashort x-ray pulses through a resonant attenuating two-level atom medium is investigated on the basis of the temporal point-source (the Green-function) formalism. A general case of the small-area pulse (SAP) approximation of a traveling coherent wave is considered. The patterns of the SAP envelope E(t,z) and energy U(z) evolution within the medium are calculated in the cases of incident Lorentzian and exponential pulses and their dependence on the temporal bandwidth ${\mathrm{\ensuremath{\tau}}}_{\mathrm{band}}$ in comparison with the total dissipative relaxation time (lifetime) ${\mathrm{T}}_{2}$ . It is shown that if ${\mathrm{\ensuremath{\tau}}}_{\mathrm{band}}$ is the same order or smaller than ${\mathrm{T}}_{2}$ , the reshaping (oscillations) of the pulse envelope and/or low energy-loss effects occur in accord with the general conclusions pointed out by Crisp [Phys. Rev. A 1, 1604 (1970)] in the case of the SAP for coherent light traveling through a resonant medium. The experimental conditions for the observation of penetration effects of the SAP of x rays are discussed. Based on the theoretical study, it is found that an ultrashort x-ray pulse emitted by an ultrashort laser-produced plasma propagates through thin resonant medium foils with low energy loss.

DOI
10.1103/physrevb.55.3419

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The propagation of ultrashort x-ray pulses through a resonant attenuating two-level atom medium is investigated on the basis of the temporal point-source (the Green-function) formalism. A general case of the small-area pulse (SAP) approximation of a traveling coherent wave is considered. The patterns of the SAP envelope E(t,z) and energy U(z) evolution within the medium are calculated in the cases of incident Lorentzian and exponential pulses and their dependence on the temporal bandwidth \ensuremathτband{\mathrm{\ensuremath{\tau}}}_{\mathrm{band}}\ensuremathτband​ in comparison with the total dissipative relaxation time (lifetime) T2{\mathrm{T}}_{2}T2​ . It is shown that if \ensuremathτband{\mathrm{\ensuremath{\tau}}}_{\mathrm{band}}\ensuremathτband​ is the same order or smaller than T2{\mathrm{T}}_{2}T2​ , the reshaping (oscillations) of the pulse envelope and/or low energy-loss effects occur in accord with the general conclusions pointed out by Crisp [Phys. Rev. A 1, 1604 (1970)] in the case of the SAP for coherent light traveling through a resonant medium. The experimental conditions for the observation of penetration effects of the SAP of x rays are discussed. Based on the theoretical study, it is found that an ultrashort x-ray pulse emitted by an ultrashort laser-produced plasma propagates through thin resonant medium foils with low energy loss.
This article presents a study of the propagation of small-area pulses of coherent light through matter. It is found that the small-area pulses exactly obey an area theorem which, in the case of an attenuating medium, requires that the pulse area decay to zero exponentially with increasing distance of propagation. This, however, does not necessarily imply that the pulse energy decays exponentially. Instead, it is found that pulses of duration comparable to or shorter than the transverse relaxation time of the medium T2{T}_{2}T2​ (including both homogeneous and inhomogeneous broadening) propagate with low energy loss. The results are explained in terms of simple physical arguments which indicate that the pulse envelope should oscillate between positive and negative values, causing the area to decrease without a comparable decrease in the pulse energy. Analytic solutions are presented for the case of a pulse whose envelope varies as ${t}^{k}{e}^{\ensuremath{-}t}$ for t>0t>0t>0, a rectangular pulse, an ultrashort pulse (i.e., pulse width much less than T2{T}_{2}T2​), and the leading portion of a step-function pulse. The propagation of a small-area Gaussian pulse is studied numerically.
This article presents a study of the propagation of small-area pulses of coherent light through matter. It is found that the small-area pulses exactly obey an area theorem which, in the case of an attenuating medium, requires that the pulse area decay to zero exponentially with increasing distance of propagation. This, however, does not necessarily imply that the pulse energy decays exponentially. Instead, it is found that pulses of duration comparable to or shorter than the transverse relaxation time of the medium T2{T}_{2}T2​ (including both homogeneous and inhomogeneous broadening) propagate with low energy loss. The results are explained in terms of simple physical arguments which indicate that the pulse envelope should oscillate between positive and negative values, causing the area to decrease without a comparable decrease in the pulse energy. Analytic solutions are presented for the case of a pulse whose envelope varies as ${t}^{k}{e}^{\ensuremath{-}t}$ for tg0tg0tg0, a rectangular pulse, an ultrashort pulse (i.e., pulse width much less than T2{T}_{2}T2​), and the leading portion of a step-function pulse. The propagation of a small-area Gaussian pulse is studied numerically.
Propagation of an ultrashort, small-area (circularly polarized) pulse through a gas medium of three-level atoms near one-photon resonance is studied. The expression for the propagating pulse shape is obtained within the rotating wave and dipole approximations. Results are compared, both analytically and numerically, with those for two-level model. Sinusoidal and Gaussian shapes of input pulses are compared, and a high sensitivity of modulation of the light pulse for envelope to its input shape is revealed.
Propagation and amplification of an ultrashort laser pulse in a two-level medium is numerically investigated with the use of the finite-difference time-domain (FDTD) procedure simultaneously solving Maxwell and Schrodinger equations with no assumptions characteristic of slowly varying envelope approximation. Comparison of the results of FDTD numerical simulations with the predictions of the pulse area theorem has demonstrated that the developed numerical procedure provides an adequate description of pulse evolution in a two-level medium. Amplification of ultrashort light pulses in a two-level medium is analyzed. Two methods of improving the gain of ultrashort pulses in a two-level medium by modulating the spatial distribution of dipole moments of resonant transitions and using initially chirped frequency-detuned pulses are explored.
An ultrashort weak pulse that propagates resonantly on the $\ensuremath{\mid}a⟩\ensuremath{\rightarrow}\ensuremath{\mid}b⟩$ transition of a three-level system $(\ensuremath{\mid}a⟩,\ensuremath{\mid}b⟩,\ensuremath{\mid}c⟩)$ experiences reshaping effects on a time scale longer than its duration. When a strong field is applied (nonresonantly) on the $\ensuremath{\mid}b⟩\ensuremath{\rightarrow}\ensuremath{\mid}c⟩$ transition, important light shifts are induced. We have theoretically studied the novel behavior of both the medium and weak propagating laser pulses in such conditions. For the transmitted field profile, drastic changes occur: at long times, efficient reduction of the distortion is obtained, while strong oscillations appear for short times, mapping out the dynamical light shift. These shaping effects, which are accompanied by new features in the spectrum for the propagating pulse, are interpreted as the result of the interference between incident field and induced dipole radiated field, whose frequency sweeps in time because of the induced light shift.
Summary form only given. A small-area femtosecond pulse propagates in a dispersive medium in a coherent fashion, if the relaxation times of the medium are compared with the pulse length for a long time. As a result, the pulse will be reshaped. This has been described by linear dispersion theory. Using Rydberg states of a molecular or an atomic gas as dispersive medium, the large spectral width of the femtosecond pulse can overlap with more than one level simultaneously. In this case, the shape of the propagated pulse reflects the temporal evolution of the Rydberg wave packet formed by the resonant Rydberg states.