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Physical Review A

Effects of ultrashort laser-pulse durations on Fano resonances in atomic spectra

FRANK B. ROSMEJ, Valery Alexandrovich Astapenko, Valerii S. Lisitsa

Published Oct 31, 2014• 26 citations
Publisher

Abstract

The Fano resonance theory is modified to account for photoionization by ultrashort laser pulses where the probability definition due to the nonlinear dependence on time is no longer valid. We employ the exact integrals over the Fourier transform of the photoionization cross section including the Fano resonances and a corrected Gaussian pulse shape that has vanishing electric field for zero frequency. Numerical results are presented for neutral helium that allow us to deduce the spectral distribution of the Fano resonance for different parameters and to identify the cases where the linear regime is invalid. Analytical approximations are given that provide a clear understanding of the linear and nonlinear regime related to the Fano parameter $q$, the detuned carrier frequencies, and pulse durations.

DOI
10.1103/physreva.90.043421

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In this reply we amend the effect of misusing an analytical formula derived in 2007 Phys. Rev. A 75 013407, but containing a misprint subsequently corrected in a recently published erratum, 2013 Phys. Rev. A 87 069905(E). Two new corrected figures are included in this reply with the gradual formation of the resonance Fano profile for the lowest and third-lowest He 1P o resonant states. The comparison between our ab initio time-dependent Feshbach method and the analytical perturbative formula is rather good in the temporal domain for the time sequence shown during and after the laser pulse up to 50 fs, although still far from reaching the final asymptotic form. Other comments are also replied to. Finally, we emphasize that in the LabTalk published on 4 June 2013, we do not mention the inadequacy of any analytical formula whatsoever and the figure caption clearly refers to the asymptotic form of the Fano profile.

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The Fano resonance theory is modified to account for photoionization by ultrashort laser pulses where the probability definition due to the nonlinear dependence on time is no longer valid. We employ the exact integrals over the Fourier transform of the photoionization cross section including the Fano resonances and a corrected Gaussian pulse shape that has vanishing electric field for zero frequency. Numerical results are presented for neutral helium that allow us to deduce the spectral distribution of the Fano resonance for different parameters and to identify the cases where the linear regime is invalid. Analytical approximations are given that provide a clear understanding of the linear and nonlinear regime related to the Fano parameter qqq, the detuned carrier frequencies, and pulse durations.
The paper is devoted to the investigation of the absorption of ultrashort laser pulses on atoms in plasmas, accounting for the different broadening mechanisms of atomic resonant transitions. The analysis is made in terms of the absorption probability during the entire interaction between the laser pulse and atom. Attention is mainly given to dependence of probability upon the pulse duration and the carrier frequency of the pulse. The results are presented via dimensionless parameters and functions describing the effect of finite pulse duration on atomic spectra for different broadening mechanisms, namely Doppler, Voigt, Holtsmark and their combinations, as well as the Stark line broadening of Rydberg atomic lines.
In this reply we amend the effect of misusing an analytical formula derived in 2007 Phys. Rev. A 75 013407, but containing a misprint subsequently corrected in a recently published erratum, 2013 Phys. Rev. A 87 069905(E). Two new corrected figures are included in this reply with the gradual formation of the resonance Fano profile for the lowest and third-lowest He 1P o resonant states. The comparison between our ab initio time-dependent Feshbach method and the analytical perturbative formula is rather good in the temporal domain for the time sequence shown during and after the laser pulse up to 50 fs, although still far from reaching the final asymptotic form. Other comments are also replied to. Finally, we emphasize that in the LabTalk published on 4 June 2013, we do not mention the inadequacy of any analytical formula whatsoever and the figure caption clearly refers to the asymptotic form of the Fano profile.
The development of methods of generation of ultrashort pulses (USP) of femto- and attosecond duration ranges with controlled parameters necessitates the theoretical study of features of their interaction with a matter [1]. Among such features that do not exist in case of “long” pulses should first of all be the nonlinear dependence of the photoprocess probability W on the USP duration (τ) [2] as well as the dependence on the carrier phase with respect to the pulse envelope (φ) [3-4]. It should be noted that if the dependence of the probability W on the phase φ manifests itself either only for very short pulses, when ωτ < 1 (ω is carrier frequency of the pulse), or in case of a nonlinear photoprocess [3], the function W(τ) can differ from a linear function in the limit ωτ> 1 too for fields of moderate strength, when the perturbation theory is applicable [2].
Abstract In the framework of the consistent microscopic theory, universal analytic expressions describing absorption of laser pulses of an arbitrary duration in an optically dense medium have been derived, and their limiting cases have been considered. For the Gaussian and Lorentzian spectral profiles, simple expressions have been obtained for the absorption coefficient as a function of dimensionless parameters (optical thickness of the medium, the pulse duration and carrier frequency). Based on the performed calculations, the effect of the optical thickness of the medium on the dependences of the absorption coefficient on the pulse parameters has been revealed.
In the present paper, we investigate the time-resolved transient absorption spectroscopy of doubly excited states of helium atoms by solving the time-dependent two-electron Schr\"odinger equation numerically based on a one-dimensional model. The helium atoms are subjected to an extreme ultraviolet (XUV) attosecond pulse and a time-delayed infrared (IR) few-cycle laser pulse. A superposition of doubly excited states populated by the XUV pulse is identified, which interferes with the direct ionization pathway leading to Fano resonance profiles in the photoabsorption spectrum. In the presence of an IR laser, however, the Fano line profiles are strongly modified: A shifting, splitting, and broadening of the original absorption lines is observed when the XUV attosecond pulse and infrared few-cycle laser pulse overlap in time, which is in good agreement with recent experimental results. At certain time delays, we observe symmetric Lorentz, inverted Fano profiles, and even negative absorption cross sections indicating that the XUV light can be amplified during the interaction with atoms. We further prove that the above pictures are general for different doubly excited states by suitably varying the frequency of the IR field to coherently couple the corresponding states.