Enhancement of high-order harmonic generation by a two-color field: Influence of propagation effects

K. Schiessl, E. Persson, A. Scrinzi, and J. Burgdörfer

Phys. Rev. A 74, 053412 – Published 17 November 2006

Abstract

Recent calculations of the response of a single atom subjected to a two-color laser pulse with the higher frequency being resonant with an excitation of the target atom revealed a significant enhancement of photoionization as well as high-order harmonic generation [K. Ishikawa, Phy. Rev. Lett. 91, 043002 (2003)]. We investigate the problem in the framework a fully quantum-mechanical pulse propagation algorithm and perform calculations for rare gases in the single-active-electron approximation. The enhancement of harmonic output compared to the corresponding one-color pulse remains intact for short propagation lengths, promising the feasibility of experimental realization. We also study weak second colors resonant via a two-photon transition where significant enhancements in harmonic yields can be observed as well.

Received 12 April 2006

DOI:https://doi.org/10.1103/PhysRevA.74.053412

Authors & Affiliations

K. Schiessl¹, E. Persson¹, A. Scrinzi², and J. Burgdörfer¹

¹Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Vienna, Austria
²Photonics Institute, Vienna University of Technology, Gußhausstraße 25-29, A-1040 Vienna, Austria

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Vol. 74, Iss. 5 — November 2006

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Figure 1
(Color online) (a) Ionization probability for hydrogen versus $ω_{2}$ for pulse parameters $τ_{p} = 10 fs$ , $λ_{1} = 850 nm$ , $I_{2} = 3.2 \times 10^{10} W ∕ {cm}^{2}$ , and various values of the intensity $I_{1}$ . The arrow marks the position of the zero-field $1 s − 2 p$ resonance. (b) Same as (a) but now $ω_{2}$ is kept constant at $ω_{2} = 7 ω_{1} = 0.375 a.u.$ , while $I_{1}$ varies. The dotted curve is the ionization probability out of the ground state calculated by the quasistatic Ammosov-Delone-Krainov (ADK) rate [29] for the strong color $I_{1}$ alone. (c) Power spectra for the same pulse parameters as in (b) and $I_{1} = 2 \times 10^{13} W ∕ {cm}^{2}$ . (d) Power spectra for the same pulse parameters as in (b) and $I_{1} = 8 \times 10^{13} W ∕ {cm}^{2}$ . For $I_{1} \approx 8 \times 10^{13} W ∕ {cm}^{2}$ , the difference between a one- and two-color pulse becomes negligible.Reuse & Permissions
Figure 2
(a) Ionization probability for xenon for pulse parameters $τ_{p} = 10 fs$ , $I_{1} = 2 \times 10^{13} W ∕ {cm}^{2}$ , $λ_{1} = 1064 nm$ , and $I_{2} = 3.2 \times 10^{10} W ∕ {cm}^{2}$ . The arrow at $ω = 0.318 a.u.$ marks the position of the zero-field $5 p − 6 s$ resonance. The resonant structure is most pronounced for intermediate $I_{1}$ . Here the resonance is already broadened, and begins to be washed out at even higher intensities (not shown). The arrow at $ω = 0.26 a.u.$ marks the choice for $ω_{2}$ in (b) Power spectra for one- and two-color pulses with same parameters as in (a) and $ω_{2} = 0.26 a.u.$ Reuse & Permissions
Figure 3
(a) Harmonic spectra after $0.5 mm$ of propagation in a gas of xenon atoms at $0.1 atm$ . One- and two-color pulses with $τ_{p} = 10 fs$ , $I_{1} = 2 \times 10^{13} W ∕ {cm}^{2}$ , $λ_{1} = 2100 nm$ and $I_{2} = 3.2 \times 10^{10} W ∕ {cm}^{2}$ , $λ_{2} = 177 nm$ respectively. (b) Yield of the 43rd harmonic H43 and of the second color versus propagation distance. The attenuation of H43 in the case of two-color driving is mainly because of absorption. The second color itself is first attenuated and begins to grow again later.Reuse & Permissions
Figure 4
Harmonic spectra for one- and two-color pulses after $0.5 mm$ of propagation in a gas with a pressure of $0.2 atm$ . (a) Spectra for helium atoms; the parameters of the incident pulses are $τ_{p} = 12 fs$ , $I_{1} = 1 \times 10^{14} W ∕ {cm}^{2}$ , $λ_{1} = 780 nm$ , and $I_{H 13} = 3.2 \times 10^{12} W ∕ {cm}^{2}$ , respectively. (b) Spectra for argon atoms; pulse parameters are $τ_{p} = 10 fs$ , $I_{1} = 2 \times 10^{13} W ∕ {cm}^{2}$ , $λ_{1} = 790 nm$ , and $I_{H 7} = 5 \times 10^{10} W ∕ {cm}^{2}$ . (c) Selected harmonic yields versus propagation distance; pulse parameters same as in (a). A large enhancement for H29 for the propagation length presented can be observed, while the resonant second color is attenuated. (d) Same parameters as in (b). First, the enhancement of H13 is large, while later it decreases mainly due to absorption. The straight dark line denotes the nominal absorption of H13 radiation in a gas of argon atoms [30].Reuse & Permissions
Figure 5
(a) Harmonic spectra after $0.5 mm$ of propagation in a gas of xenon atoms at $0.1 atm$ . One- and two-color pulse with $τ_{p} = 10 fs$ , $I_{1} = 2 \times 10^{13} W ∕ {cm}^{2}$ , $λ_{1} = 2100 nm$ and $I_{2} = 1.3 \times 10^{11} W ∕ {cm}^{2}$ , ${\bar{λ}}_{2} = 2 λ_{2} = 354 nm$ . (b) Harmonic yield for H43. The pulse parameters are the same as in Fig. 3 if not otherwise stated. A two-color pulse with wavelength-doubled second color ${\bar{λ}}_{2}$ performs about as well as a two-color pulse with $λ_{2} = {\bar{λ}}_{2} ∕ 2$ , provided that the intensity $I_{2}$ is increased.Reuse & Permissions

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