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

Abstract

Coherent intense attosecond X-ray pulses could lead to a fast dynamical imaging of the biological macromolecules and other material nanostructures with a unique combination of a record high temporal and spatial resolution. Plasma based X-rays laser sources are capable to produce high energy X-ray pulses but with relatively long picosecond duration. The sources based on high-harmonic generation (HHG) of a laser field allow to produce much shorter pulses but of lower energy. We suggest two different paths towards intense sub-femtosecond X-ray sources, namely i) via efficient transformation of the picosecond radiation of the X-ray plasma lasers into the trains of sub-femtosecond 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 sufficiently strong infrared or optical field. We propose experimental realization of the suggested technique in the passive/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. I.

Attosecond Pulse Amplification in a Plasma-Based X-Ray Laser Dressed by an Infrared Laser Field

“…But narrow linewidths of X-ray lasers did not allow for joint amplification of several harmonics. However, in the presence of a strong IR field, the frequency of transition of the X-ray laser becomes modulated with the period equal to a half-cycle of the optical field [43]. As shown below, in such a case the active medium amplifies X-ray radiation not only at the resonant frequency, but also at its multiple sidebands separated by twice the frequency of the modulating field.…”

Enhanced Amplification of Attosecond Pulses in a Hydrogen-like Plasma-Based X-ray Laser Modulated by an Infrared Field at the Second Harmonic of Fundamental Frequency

“…21 . As shown in [19,20,22], in this case the propagation of X-ray radiation (6) in a hydrogen-like active medium of a plasma-based X-ray laser is described by the system of Maxwell-Bloch equations in a five-level approximation:…”

“…Expressions (12) also imply the unidirectional propagation of X-ray radiation, which takes place in the absence of reflections from the boundaries of the medium at ε X−ray 1. The explicit form of the equations in the aforementioned approximations is given in [20] and, because of its cumbersomeness, will not be reproduced here.…”

“…Then from (20) it is easy to obtain an algebraic equation for the spectral amplitude ρ(ω) 21 (x, ω) and, then, a solution for coherence ρ 21 (x, τ):…”

“…At the same time, if the plasma dispersion at the frequency of the modulating field is moderate, then a particular high-order harmonic tuned into resonance with any of the induced gain lines of the active medium is not only amplified, but also generates radiation at combination frequencies spaced from the seed frequency by even multiple of the modulating field frequency. Under certain conditions, the generated Raman spectral components turn out to be in phase with the radiation of the amplified harmonic, which leads to the formation of a train of subfemtosecond pulses [20][21][22]. If several harmonics are present in the incident field, and they are spaced from each other by an even multiple of the modulating field frequency, then in a plasma medium with a low free-electron concentration, the amplified harmonics are scattered into each other, which opens up the possibility to control their amplitudes and phases via interference of the amplified incident and generated scattered fields [23].…”