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Journal of Physics B Atomic Molecular and Optical Physics

The propagation of a strong x-ray pulse followed by pulse slowdown and compression, amplified spontaneous emission and lasing without inversion

Yuping Sun, Ji‐Cai Liu, Faris Gel’mukhanov

Published Oct 7, 2009• 8 citations
Publisher

Abstract

We study self-seeded stimulated resonant x-ray Raman scattering and show a 20-fold compression of the strong XFEL pulse propagating through the resonant medium of atomic argon with the frequency (244.3 eV) tuned to the 2p 3/2 –4s resonance. The strong x-ray pulse inverts the medium and produces an extensive ringing tail which widens the power spectrum. Newly created seed field triggers the Stokes channel 3s–2p 3/2 of amplified spontaneous emission. The population inversions are quenched for longer propagation distances where lasing without inversion enhances the Stokes component. The pump pulse also generates weaker Stokes and anti-Stokes fields caused by four-wave mixing. The group velocity is decreased up to 78% of the speed of light in vacuum.

DOI
10.1088/0953-4075/42/20/201001

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We study self-seeded stimulated resonant x-ray Raman scattering and show a 20-fold compression of the strong XFEL pulse propagating through the resonant medium of atomic argon with the frequency (244.3 eV) tuned to the 2p 3/2 –4s resonance. The strong x-ray pulse inverts the medium and produces an extensive ringing tail which widens the power spectrum. Newly created seed field triggers the Stokes channel 3s–2p 3/2 of amplified spontaneous emission. The population inversions are quenched for longer propagation distances where lasing without inversion enhances the Stokes component. The pump pulse also generates weaker Stokes and anti-Stokes fields caused by four-wave mixing. The group velocity is decreased up to 78% of the speed of light in vacuum.
We study the compression of strong x-ray pulses from x-ray free-electron lasers (XFELs) propagating through the resonant medium of atomic argon. The simulations are based on the three-level model with the frequency of the incident x-ray pulse tuned in the $2{p}_{3/2}\text{\ensuremath{-}}4s$ resonance. The pulse propagation is accompanied by the self-seeded stimulated resonant Raman scattering (SRRS). The SRRS starts from two channels of amplified spontaneous emission (ASE), $4s\text{\ensuremath{-}}2{p}_{3/2}$ and $3s\text{\ensuremath{-}}2{p}_{3/2}$, which form the extensive ringing pattern and widen the power spectrum. The produced seed field triggers the Stokes ASE channel $3s\text{\ensuremath{-}}2{p}_{3/2}$. The population inversion is quenched for longer propagation distances where the ASE is followed by the lasing without inversion (LWI), which amplifies the Stokes component. Both ASE and LWI reshape the input pulse: The compressed front part of the pulse (up to 100 as) is followed by the long tail of the ringing and beating between the pump and Stokes frequencies. The pump pulse also generates weaker Stokes and anti-Stokes fields caused by four-wave mixing. These four spectral bands have fine structures caused by the dynamical Stark effect. A slowdown of the XFEL pulse up to 78% of the speed of light in vacuum is found because of a large nonlinear refractive index.
We find that intense short pulses of XUV radiation can be produced by cooperative spontaneous emission from visible or IR laser pulses driving atoms or ions. The process depends on the generation and utilization of atomic coherence as is the case in lasing without inversion. However, the radiation process is not stimulated emission, but is rather cooperative spontaneous emission in the sense of Dicke. More precisely, the many atom mathematics of superradiance has much in common with coherent anti-Stokes Raman scattering. The generation of Raman coherence is considered from the perspectives of multi-photon excitation and breaking of adiabaticity. In particular, we find that the advent of an ultrashort (e.g. single cycle) pulse rewards rethinking of conventional (nanosecond) nonlinear optics with new insights.
The spectrum of resonance fluorescence is calculated for a two-level system excited by an intense, ultrashort x-ray pulse made available, for instance, by free-electron lasers such as the Linac Coherent Light Source. We allow for inner-shell hole decay widths and destruction of the system by further photoionization. This two-level description is employed to model neon cations strongly driven by x rays tuned to the $1s2{p}^{\ensuremath{-}1}\ensuremath{\rightarrow}1{s}^{\ensuremath{-}1}2p$ transition at 848eV848\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{eV}848eV; the x rays induce Rabi oscillations which are so fast that they compete with Ne 1s1s1s-hole decay. We predict resonance fluorescence spectra for two different scenarios: first, chaotic pulses based on the self-amplified spontaneous emission principle, like those presently generated at x-ray free-electron-laser facilities and, second, Gaussian pulses which will become available in the foreseeable future with self-seeding techniques. As an example of the exciting opportunities derived from the use of seeding methods, we predict, in spite of the above obstacles, the possibility to distinguish at x-ray frequencies a clear signature of Rabi flopping in the spectrum of resonance fluorescence.
The regular structure in frequency broadening spectrum of the self-trapped laser and Raman radiations is produced by the phase-modulation of light waves propagating in the filament with intensity-dependent index of refraction. A quantum-mechanical calculation of double quantum transition in a three-level system is shown to explain the process of self-modulation and the production of picosecond pulses in the Raman process. Coherent coupling of the laser and the Stokes waves produces mutual modulation of large amplitude, if the optical field is strong and the vibrational relaxation time is long. Numerical evaluation for CS2 gives a modulation frequency of about 1011 Hz, when an optical power of 10 kW is trapped in a filament of 2 µm radius. Besides, the effect of self-modulation on the spatial distribution of anti-Stokes emission along the filament is discussed and shown to agree with the experimental results observed by Stoicheff and his co-workers.
We study the propagation dynamics of weak Raman sideband fields in a far-off-resonance Raman medium driven by a strong coupling field. We show that the interaction of the system with the strong field, under the conditions of high density, narrow Raman-transition width, and small two-photon detuning, results ina slow group velocity and a substantial enhancement of the injected anti-Stokes sideband field as well as an efficient generation of a Stokes sideband field. We find that the effective group velocity is the same for the two weak fields and is proportional to the field frequency difference instead of the frequency of the corresponding field. We also discuss the condition for exponential growth of the two sideband fields in the medium. We perform numerical calculations for solid hydrogen, a realistic system where the requirements for high density and small Raman width can be met. We demonstrate that the group velocity can be slowed down by several orders, and that the slow light plays a key role for the stimulated Raman scattering process in solid hydrogen.PACS Nos.: 42.50Gy, 42.50Hz, 42.65Ky, 42.79Nv