научная статья по теме CARRIER ENVELOPE PHASE EFECTS IN PHOTOFRAGMENTATION: ORIENTATION VERSUS ALIGNMENT Физика

Текст научной статьи на тему «CARRIER ENVELOPE PHASE EFECTS IN PHOTOFRAGMENTATION: ORIENTATION VERSUS ALIGNMENT»

ОПТИКА И СПЕКТРОСКОПИЯ, 2011, том 111, № 4, с. 641-651

КОГЕРЕНТНЫЕ ЭФФЕКТЫ В ОПТИЧЕСКИХ И АТОМНО-МОЛЕКУЛЯРНЫХ ПРОЦЕССАХ

УДК 535.14

CARRIER ENVELOPE PHASE EFECTS IN PHOTOFRAGMENTATION: ORIENTATION VERSUS ALIGNMENT

© 2011 M. V. Korolkov***, and K.-M. Weitzel*

*Fachbereich Chemie, Philipps- Universität Marburg, Marburg 35032, Germany ** B. I. Stepanov Institute of Physics, National Academy of Science, Minsk 220072, Belarus E-mail: weitzel@chemie.uni-marburg.de Received April 18, 2011

Abstract—The optically induced fragmentation of deuterium chloride ions (DCl+) has been investigated by means of computer simulation within the Schrödinger wave-function formalism for three lowest 2П electronic states coupled by IR-laser pulse with 34.6 fs duration. We demonstrate that the dependence of dissociation yields as function of the carrier envelope phase (CEP) of few-cycle laser pulses can be fundamentally different (2n or n periodicity) for oriented and aligned ions. To achieve a deep insight in mutual electronic nuclear dynamics we investigate the time dependence of fragmentation yields and vibrational populations as well as the space-time representation of electronic wave function probability dynamics for few selected cases. Ultimately we suggest an approach for distinguishing oriented from aligned molecular ensembles. Furthermore the current concept provides access to directional product ion beams (D+ or/and Cl+) by proper selection of the CEP.

INTRODUCTION

The alignment and orientation of molecules allude to a core topic of chemical reactivity. In this context alignment of molecules implies that the nuclei of a heterogeneous diatomic molecule (e.g. DCl+ see Fig. 1) all lie on one axis with the chlorine atom pointing in one or the other direction. We speak of oriented molecules if the Cl atoms all point into the same direction.

While in thermal systems in general all possible orientations exist in equilibrium, the effectivity of chemical reactions in general depends on the relative orientation of the reacting molecules, except in the case of spherically symmetric molecules. This has stimulated considerable interest in techniques for aligning or orienting molecules. Among the techniques successfully applied so far are the electrostatic hexapole technique [1] and the strong uniform field ("brute force") technique [2]. Alignment and orientation created by these techniques can be probed e.g. by resonance enhanced multiphoton ionization (REMPI) [3]. The latter technique may, however, also serve for the preparation of alignment in the ions produced [4, 5]. Current interest is focused on the role of alignment and orientation in intense laser field [6]. Here, an extensive overview over the field has been given by Stapelfeldt and Seideman [7]. Most recently Holmegaard et al. have demonstrated an unprecedented alignment of jodobenzene by means of a combination of Stark field deflection with laser induced alignment [8]. A concept for orienting molecules of arbitrary symmetry by means of a phase-locked superposition of intense two-color (®, 2®) laser fields has been proposed by Takemoto and Yaman-ouchi [9].

ln the current contribution we wish to shed light on an alternative approach for examining the initial space distribution of ions by means of the dependence of photofragmentation on the carrier envelope phase (CEP) of few cycle laser pulses. We consider two simple models, ensembles of aligned and oriented ions, as an example. The electric laser field, Ey(t), will be described as (Eq. 1)

E ( t) = a ( t) sin (ю t + ф),

(1)

where a(t) is the envelope, ® the laser frequency, t the time and 9 the CEP. In more detail one has to take into account the time dependence of the frequency and eventually also of the CEP.

The importance of the absolute phase of an electric laser field for controlling photochemical dissociation yields was — to our knowledge — first pointed out by Manz and coworkers [10]. The first description of a concept for experimentally measuring the absolute phase of a laser pulse was reported by Corkum and coworkers [11]. Subsequently experimental techniques for locking this CEP [12] and measuring it [13] became available. This progress triggered a tremendous interest in such phase effects [14—16]. A very elegant experimental demonstration of this CEP effect in the dissociative ionization of D2 has been presented by Kling et al [17].

Starting from an investigation of the time dependence of photofragmentation of DCl+ ions [18] we have recently described the relevance of CEP for the branching ratios in the photodissociation of oriented molecules [19]. In this contribution we extend that work by taking into account two opposite orientations

Energy/Eh 0.2

-0.1 -

1

(b)

-

fcn, 3n ^xn, 2n

1 1 1 1 ¿3H i i i i i

R/a

Fig. 1. (a) Illustration of the potential curves and of one of the two orientations of DCl+ considered in this work; (few vibrational eigenfunctions provide the optimal excitation distance from different excited vibrational states ). Note that only highly excited vibrational states within the bound potential provide close to resonance condition for electronic excitation. (b). Dipole moments and transition dipole moments of DCl+ taken from refs. [20, 21].

3

5

7

9

6

4

2

0

1

3

5

7

9

of a target molecule. We show that this has an important effect on fragmentation ratios. More specifically we show that the difference between initially aligned and oriented ions can be analyzed from the CEP dependence of their fragmentation yields by employing CEP stabilized few-cycle laser pulses. A complementary side aspect pertains to the possibility of forming directional fragment ion beams by proper choice of the CEP.

MODEL AND NUMERICAL APPROACH

For comparison of photodissociation dynamics of aligned versus oriented ions the same numerical approach as in previous publication for oriented ion [19] has been employed in this work. Only the most vital aspects essential to the understanding of the current results will be mentioned below.

The photofragmentation of DCl+ in the near and mid IR is dominated by parallel transitions from the ion ground state (X) to the next two excited n states. The potential curves for the electronic states considered in this work, Vx, V2n, and V3n, are illustrated in Fig. 1a. Consequently we set up the following time dependent Schrodinger equations

ih ^^ = [ T + V - VxE( - (2)

- Mx, 2nEy(2n - MX, 3nEy( t3n,

ih= [T + V2n - M2nEy(t)]W2n -

dt y (3)

- M X, 2 n Ey ( t )Y

X

ih= [T + V - ^nEy(t-

dt (4)

- Vx, 3nEy(t)¥x,

where X2n, (2) 2n, and (3) 2n are the three lowest 2n states of DCl+. T is the kinetic energy operator, and Vj is the potential of the electronic state. vx, V2n and v3n are the dipole moments, vx, 2n, and vx, 3n are the transition dipole moments. Ey(t) is the component of the electric field parallel to the molecule axis due to the laser pulse.

The nuclear wave functions ^/r, t), where j = X, 2n, 3n reflects the electronic state, are represented on an equidistant N-point spatial grid with r = (rx, r2, ..., rn), r1 = 1.5a0, Ar = 0.02a0, for 4096 < N < 32768, where r is the distance between the D and the Cl atom. A combination of the split-operator method [22] and the integral equation method [23, 24] is used for the propagation of the wave functions (given in Eq. 2 to Eq. 4) in time with time steps of At < 1 atomic unit (1 a.u. ~ 0.024 fs). For the ground electronic potential the vibrational eigenfunctions xv(r) have been calculated by the Fourier grid Hamiltonian method [25]. The dissociation yield of the ground electronic state is obtained from the difference Px — Pwe„ between the to-

Weil1

tal population of the electronic state Px = = r))| and the population in the well

Pwell= X.I<Xv(rr))|2 .

The absorbing boundary[26] is used to prevent the artificial reflection of all ¥j(r, t) wave functions at the edge of the grid, where necessary.

The laser pulses were represented by the following function:

Z7 • 2

E0sin

0

L ?1 -I

sin(ю? + ф) for 0 < t < 11,

for t > ?,.

(5)

: 3.5 x 1016 —2 e2 (a.u.). cm

where a is a parameter characterizing the chirp. A value of a = 0 corresponds to no chirp. Plus and minus sign indicate up chirp and down chirp, respectively. In the current work we considered three different chirp values: a = —2, a = 0, and a = +0.2, i.e. the maximum chirp considered corresponds to 20% of the laser bandwidth. Such a chirp can be easily realized in an experiment [27].

We distinguish three different reaction channels in the photofragmentation of DCl+: i) the formation of Cl+(3P) (channel 1, dissociation limit of the ion ground state); ii.) the formation of D+ (channel 2, dissociation limit of the (2) 2n state); and iii.) the formation of Cl+(1^)) (channel 3, dissociation limit of the (3) 2n state [28, 29, 20, 21]. Note that channel I and channel III both lead to Cl+ ions, however, in different electronic states and with different kinetic energy. All calculations of this work refer to molecular ions aligned or oriented along the y axis (see Fig. 1).

RESULTS

In the following we will present the results of photodissociation induced by laser pulses with duration %hm = 36.4 fs in the IR frequency range for ©1 = = 0.0085 Eh (1865 cm-1) and ©2 = 0.0071 Eh (1558 cm-1) with different values of the linear chirp parameter a (see Eq. 6). These two laser frequencies were previously identified to exhibit most interesting dynamics with very high contrast of fragmentation ion ratios [18] and close to the one-photon vibrational resonances for the

ground ©1h « 0 - E% ! = 0.008516Eh « 0.23 eV and excited EVg 6 — E^l 7 < '

: 0.193eV < E;lg= 5 -

where tt is characterizing the width of the laser pulse at the base. Throughout this work tt = 100 fs has been employed. Note, that the full width at half maximum (FWHM) pulse duration for the intensity of a laser pulse given by Eq. 5 is obtained from tFWHM ~ 0.364t?. Intensities discussed throughout t

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