Attosecond-pulse formation in the water-window range by an optically dressed hydrogen-like plasma-based C5+ x-ray laser

Abstract

In this paper, we present the analytical theory of attosecond pulse formation via optical modulation of an active medium of the hydrogen-like C 5+ plasma-based X-ray laser at 3.4 nm wavelength in the "water window" range, taking into account a variation of the population inversion caused by radiative decay of the upper lasing states. We derive an analytical solution for the X-ray field amplified by an X-ray laser with time-dependent population inversion, which is simultaneously irradiated by a strong optical laser field, and use it to find the optimal conditions for the attosecond pulse formation from a narrowband seeding X-ray field. We show that the shape of pulses can be improved at the cost of reduced pulse peak intensity (i) via external attenuation of the resonant spectral component of the amplified X-ray field or (ii) by using a resonantly absorbing medium (the active medium of the X-ray laser after the change of sign of the population inversion) for the pulse formation. The results of the analytical theory are in a good agreement with the numerical solutions of the Maxwell-Bloch equations which account for the nonlinearity, as well as the amplified spontaneous emission, of the active medium. Both analytically and numerically we show the possibility to produce a train of attosecond pulses with sub-200 as duration and the peak intensity exceeding 10 12 W/cm 2 at the carrier wavelength 3.4 nm in the "water window" range, which makes them attractive for the biological and medical applications.

Temporal and spectral control of the X-ray pulses in a resonant medium with a modulated transition frequency

“…It is worth noting that the considered technique of the atomic transition frequency modulation is rather general. In particular, as shown in our recent works [17][18][19] , it can be used also for generation of the attosecond extreme ultraviolet and x-ray pulses or amplification of the attosecond pulses produced via HHG in the active medium of a plasma-based x-ray laser modulated by a strong infrared laser 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

“…In the case of C 5+ ions, this condition limits the intensity of the modulating field 2 . In this case, both the shifts of the resonance energy levels due to the quadratic Stark effect and the ionization rate turn out to be much smaller than the frequency of the modulating field of the visible or near/mid-IR range, which allows one to take into account their effect as time-independent additions to the energy and decay rate of the corresponding states [22,25,26]. In addition, in this case, the corrections to the Stark effect of the third and higher orders turn out to be negligible.…”

“…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:…”

“…where n (0) tr is the initial population difference at the transitions |i → |1 , i = {2,3,4,5}. At the same time, the initial values of the coherences on inverted transitions |i → |1 , i = {2,3,4,5} are random functions of the longitudinal coordinate x, which makes it possible to take into account the amplified spontaneous emission of the active medium [22,[27][28][29][30], while the initial values of the coherences on the other transitions are equal to zero:…”

“…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].…”