Researchers at Skoltech (VEB.RF group), together with a colleague from the Shanghai Institute of Optics and Fine Mechanics of the Chinese Academy of Sciences, working within the joint SIOM–Skoltech laboratory, have determined how to select the thickness and density of a plasma target so that a pulse passing through it retains its attosecond duration and high intensity. The results will help improve the design of plasma-based sources of ultraviolet and X-ray radiation used to study ultrafast processes in matter. The work is published in Applied Physics Letters (Q1, Nature Index).

An attosecond is 10⁻¹⁸ of a second. Pulses of this duration can be compared to an ultrafast camera flash: they make it possible to effectively “freeze” the motion of electrons and investigate processes that cannot be resolved using longer pulses. This is important for studying atoms, molecules, solids, and new materials.

One promising method for generating intense attosecond radiation is based on the interaction of a high-power laser pulse with dense plasma. Thin electron bunches form near the plasma surface and emit short flashes in the ultraviolet and X-ray ranges.

However, the same plasma involved in generating the pulse can also “blur” it. Different frequency components of the radiation travel through the medium at different speeds. As a result, the pulse stretches in time, its frequency structure changes, and its peak intensity decreases. The denser the plasma and the thicker the target, the more dispersion accumulates. At a certain point, the pulse ceases to be attosecond and can no longer be used to observe the fastest electronic processes.

To determine this limit, the researchers performed one- and two-dimensional particle-in-cell simulations on Skoltech’s Zhores supercomputer. The calculations were compared with a spectral model of wave propagation and a simplified analytical description.

As a result, the authors derived compact relationships linking pulse stretching to plasma density and thickness, as well as to the characteristic frequency of attosecond radiation. Based on these relationships, they formulated a criterion for accumulated dispersion that shows which target parameters preserve the attosecond structure of the pulse and which cause it to break down.

“An attosecond pulse can be compared to a very short flash needed to obtain a sharp image of an ultrafast process. When it passes through plasma that is too thick or too dense, the flash stretches and the ‘image’ loses sharpness. We have obtained a practical criterion that makes it possible to determine the permissible target parameters in advance and avoid a large number of computationally intensive trial-and-error simulations,” said Elizaveta Lipkova, the paper’s first author, a junior research engineer at the Skoltech AI Center’s Artificial Intelligence & Supercomputing Laboratory.

The paper also presents a map that can be used to determine the maximum target thickness permissible in attosecond experiments for a given plasma density. This diagram will help researchers select experimental parameters in advance and assess whether the pulse will retain the required duration after passing through the plasma.

The findings provide practical guidelines for developing more efficient plasma-based sources of attosecond ultraviolet and X-ray radiation, as well as components for attosecond optics. In the future, such systems could be used to investigate electron motion, chemical reactions, and material properties on extremely short timescales.

The authors of the paper are Elizaveta Lipkova, Junior Research Engineer at the Artificial Intelligence and Supercomputing Laboratory of the Skoltech AI Center; Dmitry Dylov, Professor and Head of the Computational Imaging Laboratory at the Skoltech AI Center; Sergey Rykovanov, Associate Professor and Head of the Artificial Intelligence and Supercomputing Laboratory at the Skoltech AI Center; and Jingwei Wang, Professor at the Shanghai Institute of Optics and Fine Mechanics of the Chinese Academy of Sciences.