Temporal compression of nanosecond laser pulses using coherent control

We present a study of the temporal compression of nanosecond laser pulses resulting from the coherent control peculiarities of the propagation dynamics in a regime of electromagnetically induced transparency. We describe the general theoretical framework and discuss the crucial conditions required in order to experimentally realize such a temporal compression scheme. A proof-of-concept experimental realization of a scheme of this type in a sample of hot sodium vapors is currently being implemented: we describe in detail the experimental setup designed for this purpose.     

On the rigidity of sphericalt-designs that are orbits of finite reflection groups

The concept of rigid sphericalt-designs was introduced by Bannai. He conjectured that there is a functionf(t, d) such that ifX is a sphericalt design in thed-dimensional Euclidean space so that |X|>f(t, d), theX is non-rigid. Furthermore, he asked to find examples of rigid but not tight sperical designs. In the present article we shall investigate the case whenX is an orbit of a finite reflection group and prove thatX is rigid iff tight for the groupsA _n ,B _n ,C _n ,D _n ,E ₆,E ₇,F ₄,I ₃.Research was partially supported by Hungarian National Research fund Grant No. 4267.     

High-order harmonic generation with a strong laser field and an attosecond-pulse train: The Dirac-Delta comb and monochromatic limits

In recent publications, it has been shown that high-order harmonic generation can be manipulated by employing a time delayed attosecond-pulse train superposed to a strong, near-infrared laser field. It is an open question, however, which is the most adequate way to approximate the attosecond-pulse train in a semianalytic framework. Employing the strong-field approximation and saddle-point methods, we make a detailed assessment of the spectra obtained by modeling the attosecond-pulse train by either a monochromatic wave or a Dirac-Delta comb. These are the two extreme limits of a real train, which is composed by a finite set of harmonics. Specifically, in the monochromatic limit, we find the downhill and uphill sets of orbits reported in the literature, and analyze their influence on the high-harmonic spectra. We show that, in principle, the downhill trajectories lead to stronger harmonics, and pronounced enhancements in the low plateau region. These features are analyzed in terms of quantum interference effects between pairs of quantum orbits, and compared to those obtained in the Dirac-Delta limit.     

A novel blue fluorescent chemosensor for metal cations and protons,based on 1,8‐naphthalimide and its copolymer with styrene

A new blue emitting 2‐allyl‐6‐(2‐dimethylaminoethyloxy)‐benzo[de]isoquinoline‐1,3‐dione, bearing an allylic group has been designed and synthesized. Bulk radical copolymerization has been carried out in order to prepare a fluorescent copolymer, based on styrene. The main photophysical characteristics of the monomeric and polymeric fluorophores have been investigated both in the absence and presence of metal cations and protons. It has been found that the monomeric naphthalimide can be used as a sensor for protons and Zn²⁺, Ni²⁺, Ce³⁺, Cu²⁺, Co²⁺, Ag⁺ cations. The polymeric fluorophore has been shown to be a selective chemosensor for Cu²⁺ cations. Copyright © 2006 John Wiley & Sons, Ltd.     

Controlling the propagation of broadband light pulses by Electromagnetically Induced Transparency

We present an experimental and theoretical investigation, performed on hot sodium atoms in a ladder scheme, showing the control of the absorption and of the propagation velocity of a probe light pulse with a spectral bandwidth as large as 1.8 GHz. The predictions of the theoretical model compare favorably with the experimental results.     

Attosecond electron wave packet dynamics in strong laser fields

We use a train of sub-200 attosecond extreme ultraviolet (XUV) pulses with energies just above the ionization threshold in argon to create a train of temporally localized electron wave packets. We study the energy transfer from a strong infrared (IR) laser field to the ionized electrons as a function of the delay between the XUV and IR fields. When the wave packets are born at the zero crossings of the IR field, a significant amount of energy (approximately 20 eV) is transferred from the field to the electrons. This results in dramatically enhanced above-threshold ionization in conditions where the IR field alone does not induce any significant ionization. Because both the energy and duration of the wave packets can be varied independently of the IR laser, they are valuable tools for studying and controlling strong-field processes.     

High harmonic XUV spectral phase interferometry for direct electric-field reconstruction

We demonstrate the first experimental complete temporal characterization of high-harmonic XUV pulses by spectral phase interferometry, with an all-optical setup. This method allows us to perform single-shot measurements of the harmonic temporal profile and phase, revealing a remarkable shot-to-shot stability. We characterize harmonics generated in argon by a 50 fs 800 nm laser pulse. The 11th harmonic is found to be 22 fs long with a negative chirp rate of -4.8 x 10(27) s(-2). This duration can be reduced to 13 fs by modulating the polarization of the generating laser. The technique is easy to implement and could be routinely used in femtosecond XUV pump-probe experiments with harmonics.     

Über die Verteilung der quadratischen Reste

Ohne Zusammenfassung     

Forbidden Configurations and Product Constructions

A simple matrix is a (0,1)-matrix with no repeated columns. For a (0,1)-matrix F, we say that a (0,1)-matrix A has F as a configuration if there is a submatrix of A which is a row and column permutation of F (trace is the set system version of a configuration). Let \({\|A\|}\) denote the number of columns of A. We define \({{\rm forb}(m, F) = {\rm max}\{\|A\| \,:\, A}\) is m-rowed simple matrix and has no configuration F. We extend this to a family \({\mathcal{F} = \{F_1, F_2, \ldots , F_t\}}\) and define \({{\rm forb}(m, \mathcal{F}) = {\rm max}\{\|A\| \,:\, A}\) is m-rowed simple matrix and has no configuration \({F \in \mathcal{F}\}}\) . We consider products of matrices. Given an m ₁ × n ₁ matrix A and an m ₂ × n ₂ matrix B, we define the product A × B as the (m ₁ + m ₂) × n ₁ n ₂ matrix whose columns consist of all possible combinations obtained from placing a column of A on top of a column of B. Let I _k denote the k × k identity matrix, let \({I_k^{c}}\) denote the (0,1)-complement of I _k and let T _k denote the k × k upper triangular (0,1)-matrix with a 1 in position i, j if and only if i ≤ j. We show forb(m, {I ₂ × I ₂, T ₂ × T ₂}) is \({\Theta(m^{3/2})}\) while obtaining a linear bound when forbidding all 2-fold products of all 2 × 2 (0,1)-simple matrices. For two matrices F, P, where P is m-rowed, let \({f(F, P) = {\rm max}_{A} \{\|A\| \,:\,A}\) is m-rowed submatrix of P with no configuration F}. We establish f(I ₂ × I ₂, I _m/2 × I _m/2) is \({\Theta(m^{3/2})}\) whereas f(I ₂ × T ₂, I _m/2 × T _m/2) and f(T ₂ × T ₂, T _m/2 × T _m/2) are both \({\Theta(m)}\) . Additional results are obtained. One of the results requires extensive use of a computer program. We use the results on patterns due to Marcus and Tardos and generalizations due to Klazar and Marcus, Balogh, Bollobás and Morris.