Formation and amplification of subfemtosecond x-ray pulses in a plasma medium of hydrogenlike ions with a modulated resonant transition

Coherent intense attosecond x-ray pulses could lead to a fast dynamical imaging of biological macromolecules and other material nanostructures with a unique combination of a record high temporal and spatial resolution. Plasma-based x-ray laser sources are capable of producing high-energy x-ray pulses but with relatively long picosecond duration. The sources based on high-harmonic generation (HHG) of a laser field allow one to produce much shorter pulses but of lower energy. We suggest two different paths towards intense subfemtosecond x-ray sources: (i) via efficient transformation of the picosecond radiation of the x-ray plasma lasers into the trains of subfemtosecond pulses in a resonantly absorbing medium, and (ii) via amplification of HHG radiation in the active medium of the x-ray plasma lasers. We show that essentially the same technique can be used for realization of both paths. This technique is a modulation of the parameters of the resonant transition (accordingly in absorbing or amplifying medium) produced under the action of a sufficiently strong infrared or optical field. We propose experimental realization of the suggested technique in the passive and/or active media of (i) Li iii ions modulated by the mid-IR laser field and (ii) C vi ions modulated by the optical laser radiation.

Figure 1

Energy levels of the ground and first excited state of the hydrogen-like-ion dressed by an IR or optical field.

Figure 2

Time dependence of x-ray radiation intensity: (a) incident x-ray field, (b) output field, and (c) the same as (b) but showing only a small part of the whole envelope. The parameters of the Li iii plasma, an IR field, and an incident XUV field are provided in the text of the paper.

Figure 3

Time dependence of x-ray radiation intensity: (a) incident x-ray field, (b) output field, and (c) the same as (b) but showing only a small part of the whole envelope. The parameters of the C vi plasma, as well as optical and incident XUV fields, are provided in the text of the paper.

Figure 4

Time dependence of an x-ray radiation intensity: (a) incident x-ray field, (b) output field, and (c) the same as (b) but showing only a small part of the whole envelope. The parameters of the inverted Li iii plasma, an IR field, and an incident XUV field are provided in the text of the paper. An abrupt decrease in amplification at about 350 fs duration is due to the shortness of a seed pulse duration compared to the gain duration.

Figure 5

Time dependence of an x-ray radiation intensity: (a) incident x-ray field, (b) output field, and (c) the same as (b) but showing only a small part of the whole envelope. The parameters of the inverted C vi plasma, optical field, and an incident XUV field are provided in the text of the paper. An abrupt decrease in amplification at about 250 fs duration is due to the shortness of a seed pulse duration compared to the gain duration.

Figure 6

Time dependence of intensities of $z$-polarized (a), (c) and $y$-polarized (b), (d) components of x-ray radiation after propagation through 1.25 mm of inverted Li iii plasma. The parameters of the plasma, IR field, and envelope of the incident field are the same as in Fig. 4. (a) and (b) correspond to $I_y(x=0)={10}^3\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$, (c) and (d) correspond to $I_y(x=0)={10}^6\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$.