Laser pulses, picosecond

Hydrogen transfer in excited electronic states is being intensively studied with time-resolved spectroscopy. A typical scheme of electronic terms is shown in fig. 46. A vertical optical transition, induced by a picosecond laser pulse, populates the initial well of the excited Si state. The reverse optical transition, observed as the fluorescence band Fj, is accompanied by proton transfer to the second well with lower energy. This transfer is registered as the appearance of another fluorescence band, F2, with a large anti-Stokes shift. The rate constant is inferred from the time dependence of the relative intensities of these bands in dual fluorescence. The experimental data obtained by this method have been reviewed by Barbara et al. [1989]. We only quote the example of hydrogen transfer in the excited state of... 

Noguchi, H., Okada, T, Onda, K., Kano, S. S., Wada, A. and Domen, K. (2003) Time-resolved SFG study of formate on a Ni(lll) surface under irradiation of picosecond laser pulses. Surf. Sci., 528, 183-188. 

An approximate method, described in detail in Ref. (15), was applied to simulate a complementary pump-probe experiment performed with picosecond laser pulses. In this method the interaction with the probe laser pulse is approximated. A complete three-dimensional ab initio simulation, as carried out for the femtosecond experiment, is hardly possible for the picosecond experiment with the computers available today. The free laser pulse parameters were taken from the picosecond experiment duration AffWhm = 1.5 ps, intensity I = 300 MW/cm2, and central wavenumber v = O.QTiEh/h = 16021 cm 1. The dynamics induced by such a laser pulse are illustrated by... 

The 3d ab initio simulations [4] for Na3 are based, in a similar way, on three ab initio potential-energy surfaces for Na3(X), Na3(B), and Na3(X), with 3d ab initio dipole coupling between Na3(X) and Na3(B) evaluated by V. Bonacic-Koutecky et al. [5] plus Condon-type coupling between Na3(B) and Na3(X). Additional potential-energy surfaces interfere at the conical intersections of the pseudo-Jahn-Teller distorted Na3(B) state (see Ref. 6), but we have tested carefully [4] that these interferences are negligible in the frequency domains of the experimental femtosecond/picosecond laser pulse experiments [7] as well as in the continuous-wave experiments [8]. 

Very recently, Jakubetz et al. have extended the applications of our variant of Rabitz s theory of optimal control by IR femtosecond/picosecond laser pulses [31 from vibrational transitions to isomerizations, specifically for the HCN = CNH reaction [4],... 

The original theory of individual state-selective vibrational transitions induced by IR femtosecond/picosecond laser pulses has been developed by Paramonov and Savva et al. for single laser pulses [13] (see also Ref. 23) followed by more general extensions to series of IR femtosecond/picosecond laser pulses in Refs. 14 and 24. For illustration, let us consider two simple, one-dimensional model systems that are assumed to be decoupled from any... 

The OH and SBV potential-energy surfaces V(q) versus bond or reaction coordinates q, together with the vibrational levels Ev and eigenfunctions 4>v(q), are shown in Figs. 1 and 2, respectively. Our first task will be to design optimal IR femtosecond/picosecond laser pulses for vibrational transitions,... 

Figure 1. Morse potential V(q), vibrational levels Ev, and wave functions < (q) for the model OH (adapted from Ref. 14). The arrows indicate various selective vibrational transitions as well as above-threshold dissociations (ATDs) induced by IR femtosecond/picosecond laser pulses, as discussed in Sections III.A-III.D see Figs. 3-5. Horizontal bars on the arrows mark multiple photon energies ha of the laser pulses cf. Table 1. The resulting ATD spectrum is illustrated by the insert above threshold.

Figure 2. Double-well potential V(q) with corresponding vibrational levels Ev and wave functions v(q) for the model 2,6-dicyanoethylmethylsemibullvalene (SBV) (adapted from Ref. 26). The reaction coordinate q indicates the Cope rearrangement of the model SBV from the reactant (R) isomer versus the transition state 1 to the product (P) isomer. Vertical arrows indicate the laser control of the isomerization R - — P by two IR femtosecond/picosecond laser pulses cf. Fig. 6 and Table I.

These selective transitions (1), (7), and (9) may be achieved by proper optimization of the parameters eo and w, as described elsewhere [13, 18, 21]. Extensions to IR femtosecond/picosecond laser-pulse-induced dissociation or predissociation have been derived in Ref. 16, using either the direct or the indirect solutions of the Schrodinger equation (2) the latter requires extensions of the expansion (5) from bound to continuum states [16,31]. (The consistent derivation in Ref. 16 is based on S. Fliigge in Ref. 31). The same techniques can also be used for IR femtosecond/picosecond laser-pulse-induced isomerization as well as for more complex systems that are two dimensional, three dimensional, and so on, at the expense of increasing numerical efforts due to the higher dimensionality grid representations of the wavepackets f/(t) or the corresponding expansions (5) (see, e.g., Refs. 18, 20, and 21). 

Extensions from the preceding ideal, isolated systems to others that are coupled to an environment are quite demanding and nontrivial [32] because the IR femtosecond/picosecond laser pulse has to achieve the selective vibrational transition (9) in competition against nonselective processes such as dissipation. For simulations, we employ the equation of motion for the reduced-density operator... 

The results are shown in Fig. 3 and Table I. Apparently, optimal IR femtosecond/picosecond laser pulses with durations tp = 500 fs may induce nearly perfect transitions (12), (13) in the model OH. Similar examples are documented in Refs. 13, 18, and 23. A detailed discussion of the derivation of the optimal laser parameters, depending on the vibrational level Ev and the transition dipole matrix elements nvw, is also given in Refs. 13, 18, and 23. Suffice it here to say that in many (but not all) cases the optimal frequency is close (but not identical) to the resonance frequency,... 

Figure 3. Selective vibrational transitions OH(l>, = 0) - OH(ty = 5) and OH(u, = 5)->-OH(iy = 10) induced by two individual IR femtosecond/picosecond laser pulses. The electric fields c(i) and the population dynamics Pv(t) are shown in panels (a) and (b), respectively. Sequential combination of the two individual laser pulses yields the overall transition OH(u = 0) - OH(u = 5) - OH(u/ = 10) cf. Fig. 1 and Table I. For the isolated system, the population of the target state Pv= fo(t) is constant after the series of IR femtosecond/picosecond laser pulses, i > 1 ps.

Combination of several individual vibrational transition (Section III.A) yields a selective sequence of vibrational transitions induced by series of IR femtosecond/picosecond laser pulses. For example, the two individual transitions (12), (13) may be combined to the sequence... 

Figure 5. Series of IR femtosecond/picosecond laser pulses for the sequence of transitions OH(u = 10)- OH(u = 15) - 0 + H for the isolated model OH cf. Fig. 1 and Table I. The notations are as in Fig. 3 populations Pwen(t) = Xoio Po( ) and PCOnt(t) = lPweiKO indicate the total populations of bound and continuum states embedded in the potential well and above the dissociation threshold, respectively. The resulting spectrum of ATD is shown in Fig. 1.

Figure 6. Series of IR femtosecond/picosecond laser pulses for the sequence of vibrational transitions SBV(u = 0) - SBV(u = 6) - SBV(t> = 1) for laser control of the Cope rearrangement of the model substituted semibullvalene (SBV) shown in Fig. 2 (adapted from Ref. 26). The notations are as in Fig. 3. The electric field is scaled by the scaling factor / of the effective charge associated with the dipole function jt =/ e q.

Figure 1. Testing the Keldish limit [1, 2] to ionization by intense infrared femtosecond/picosecond laser pulses used for control of chemical reactions [3, 4], (a) Electronic ground state embedded in a typical model potential curve with the ionization potential Es = 12.9 eV. (b) Intense ( o = 35.5 GV/m"1, Iq = 3.3 x 1014 W/cm2), ultra-short (tp = 0.5 ps), infrared (l/X = 3784 cm" ) laser pulse, (c) Expectation value for the position of the election, which is driven by the laser held shown in panel (b) [compare with ro = 122 A, Eq. (3)]. (d) Electron energy. These model calculations demonstrate that even very intense (/ > /Keldish) ultrashort 1R laser pulses may not cause ionization that is, the simple estimates (1)—<4) [1, 2] are not applicable.

The experiments described above used nanosecond laser pulses, which are much longer than the rotational period of the molecules. At the termination of the pulse, the pendular state that is formed relaxes adiabatically to a free-rotor eigenstate. If instead picosecond laser pulses are used, a rotational wave packet is formed by successive absorption and re-emission of photons during the laser pulse. Such wave packets are expected to display periodic recurrences of the alignment after the end of the pulse. 

Let us mention the rotational beats which have recently been observed (with a trans-stilbene molecule in a gasodynamic jet) and interpreted by Felker and Zewail [54, 145]. The essence of this interesting phenomenon may be described in a simplified way as follows. Let a picosecond laser pulse be capable of coherently exciting from some rotational state J f of a... 

For DFWM and Z-scan with picosecond laser pulses molecular vibrations (or optical phonons in crystals) and reorientation of small molecules can add contributions to the electronic nonlinearity. For longer laser pulses even large molecules can orient and also thermal contributions can occur. 

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