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Journal of Physics B Atomic Molecular and Optical Physics

Single-pulse characteristics of the Xe(L) amplifier on the Xe35+(3d→2p) transition array at λ cong 2.86 Å

Alex B Borisov, Xiangyang Song, Ping Zhang, John C McCorkindale, Shahab F Khan, Richard DeJonghe, Sankar Poopalasingam, Ji Zhao, Keith Boyer, C. K. Rhodes

Published Aug 14, 2006• 13 citations
Publisher

Abstract

The triple comparison of (1) single-pulse spectral data, recorded with a CCD-equipped von Hámos spectrometer both axially and transversely; (2) axially measured time-integrated spectra registered on a film and (3) single-pulse x-ray images of the morphology of the self-trapped plasma channel, recorded simultaneously with the single-pulse spectra, establishes several leading characteristics of the saturated amplification observed on the Xe 35+ transition array at λ ≅ 2.86 Å. The chief findings are (α) absolute positive correlation of amplification with the formation of a plasma channel, (β) a perfect spectral match of the amplified transitions in the comparison of axially recorded single-pulse and time-integrated film data and (γ) exact spectral correspondence of both the axially registered single-pulse and time-integrated film data with single-pulse transversely measured spectra exhibiting deep spectral hole burning at the position of the Xe 35+ array.

DOI
10.1088/0953-4075/39/17/l01

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The triple comparison of (1) single-pulse spectral data, recorded with a CCD-equipped von Hámos spectrometer both axially and transversely; (2) axially measured time-integrated spectra registered on a film and (3) single-pulse x-ray images of the morphology of the self-trapped plasma channel, recorded simultaneously with the single-pulse spectra, establishes several leading characteristics of the saturated amplification observed on the Xe 35+ transition array at λ ≅ 2.86 Å. The chief findings are (α) absolute positive correlation of amplification with the formation of a plasma channel, (β) a perfect spectral match of the amplified transitions in the comparison of axially recorded single-pulse and time-integrated film data and (γ) exact spectral correspondence of both the axially registered single-pulse and time-integrated film data with single-pulse transversely measured spectra exhibiting deep spectral hole burning at the position of the Xe 35+ array.
The amplification of ultrashort extreme-ultraviolet (XUV) pulses in argon in high-order harmonic generation processes is studied by using the time-dependent Schr\"odinger equation in the spin-free one-active-electron and single-atom approximation. We consider a neutral argon atom initially in the valence 3p state and a sufficiently intense two-cycle driving infrared (IR) pulse for the atom to be mainly ionized after the first laser cycle. The correlated dynamics and transitions from the valence 3p to a virtual subvalence 3s state and in the ionized regions are examined by synchronizing a 1.5-fs XUV pulse to the IR pulse. The calculated single-atom gain spectrum (26--45 eV) agrees with recent experimental measurements. We discuss different channels that can be present in the gain process as a function of pulse parameters and through an analysis of the dynamics of the populations in terms of field-free eigenstates. When the XUV pulse is considered at the end of the driving IR field the amplification is due to contributions of stimulated recombination from excited Rydberg and low energy continuum states to the 3s and 3p states of argon. In regions where the IR field is intense, high energy and angular momentum states are populated and the medium can interact with the pulses through bound and continuum states involving parametric transitions, which is further confirmed by studying classical electron trajectories. We discuss how these parametric interactions might be suitable for amplification of photon energies far from the ionization threshold as observed in the experiments.
The Xe(L) system at ? ~ 2.9 ? uniformly exhibits all of the canonical attributes of a strongly saturated amplifier on the full ensemble of single-vacancy Xeq+ transition arrays (q = 31, 32, 34, 35, 36) that exhibit gain. The key observables are (1) sharp spectral narrowing, (2) the detection of a narrow directed beam (??x200 ?rad), (3) an increase in the amplitude of the emission and the development of an intense output (?106 enhancement) and (4) the observation of deep spectral hole-burning on the inhomogeneously broadened spontaneous emission profile. Experimentally determined by two methods, (a) line narrowing and (b) signal enhancement, the observations for several single-vacancy 3d?2p transitions indicate a range of values for the effective small signal (linear) gain constant given by go25?100 cm?1. Quantitative analysis shows that this result stands in clear conflict with the corresponding upper bound go40?80 cm?1 that is based on available spectroscopic data and estimated with conventional theory. Overall, the observed values deviate substantially from expectations scaled to the spectral density of the measured Xe(L) spontaneous emission profile; they are systematically too high. The most extreme example is the heavily saturated Xe32+ transition at ? = 2.71 ?, a case that fails to reconcile the lower bound of the measured signal strength with the corresponding theoretically predicted maximal value; the former falls above the latter by a factor exceeding 400 giving an enormous gap. Moreover, although saturation is a prominent characteristic of the amplification at ?2.71 ?, as demonstrated by spectral hole-burning, the theoretical upper bound of go given for this transition is far too small for saturation to be reached. The Xe31+ transition at ?2.93 ? exhibits comparably pronounced anomalous behaviour. This double paradox is resolved with the Ansatz that the amplification is governed principally by the saturated gain gs, not the conventionally described small signal value go. This interpretation is further supported by the observation of deep spectral hole-burning, the signature of strong saturation, that occurs uniformly across the spectrum of the spontaneous emission profile. The effective amplification exhibits an anomalously weak dependence on the spectral density; saturation is the rule, not the exception. A lucid manifestation of the saturation is the recording of spectrally resolved x-ray yields on the Xe31+ array that are sufficiently high to produce gross structural damage to the material in the film plane of the spectrograph. The behaviour of the amplifier can be best described as an explosive supersaturated amplification. The source of this exceptionally strong amplification can be traced to the dynamically enhanced radiative response of the excited Xe hollow atom states located in the clusters that are mode coupled to the plasma waveguide forming the amplifying channel.
The first decay frequency, 1/r i is attributed to the Xe(3P ) ) state. In this case, 1/k i corresponds to the apparent lifetime of the resonant state (1.„ = 3.98 µs) and k51 is the 3-body rate constant of formation of the Xe[0+„ CPO] excimer. The second one, 1/T2 is attributed to the Xe(3P2) state. Then, 1/1(12 corresponds to the lifetime of the metastable state and k52 is the 3-body rate constant of formation of the Xe 1„ (3P2)] excimer. These results are in good agreement with those obtained with 3-photon selective excitation of Xeelp i ) state [3]. In both cases, no 2-body collision rate constant term is found.
The Xe(L) system is an amplifier with fundamentally different dynamic characteristics from all previously developed laser amplifiers; it represents the conceptual ideal through full utilization of the Kramers–Kronig relations that fundamentally couple the dispersive and absorptive components. The dispersive response of the system, through optimal governance of the power compression, rules the amplification and establishes a minimum gain for the amplifier. Accordingly, the amplification requires a minimum value of the dispersion to be surpassed; the corresponding gain follows automatically. As a leading consequence, since this minimum gain is sufficiently high, the key experimental observation is the uniform presence of saturated amplification signaled by strong spectral hole burning on all transitions exhibiting amplification, including double-vacancy lines. This cardinal signature demonstrates that the amplification is legislated by the saturated gain g s , not the corresponding small signal value g 0 . The chief outcome is that explosive dispersion yields perforce explosive amplification and the efficient generation of maximally bright coherent power.
Spatio-temporal holography using persistent spectral hole-burning in dye molecules embedded in plastic films is promising for applications such as femtosecond pulse shaping, data storage or phase conjugation. In addition to the common 2 spatial dimensions of classical holograms, each point in the sample plane can be used to store spectral informations such as the shape of a femtosecond pulse. On each point of the sample, spectral interferences between a reference pulse and an object pulse (for example chirped) are recorded via spectral hole-burning in the absorption band of the dye molecule. As early as 1983, photon echo and time-reversal experiments using persistent spectral hole-burning were performed in porphyrazine styrol solutions at 630 nm [1]. Then several developments, like the reconstruction of the polarization state of object pulses [2], time and space holography [3,4], image holograms using a single pair of femtosecond pulses [5] were demonstrated in different photosensitive media.