For the purpose of preparing a sample of aligned and oriented molecules in the laser-field-free condition, we developed a plasma shutter, which enables laser pulses with 100-mJ-class, 10-ns pulse durations to be rapidly turned off within ∼150 fs. Inthis work, the residual field intensity after the rapid turn off is carefully examined by applying the shaped laser pulse to OCS molecules in the rotational ground state. Based on the comparison between the observation of alignment revivals of the OCS molecules and the results of numerical simulations, we demonstrate that the residual field intensity is actually negligible (below 0.4% of the peak intensity) and, if any, does not influence the alignment and orientation dynamics at all.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Nonresonant, moderately strong ( W/cm) laser field can control rotational motions of molecules without disturbing the internal electron dynamics of the molecules [1, 2]. Therefore, the laser-field-based techniques for controlling rotational motions of molecules have been widely used for experimental studies relevant for anisotropic structures of molecules [3–7].
In the adiabatic regime, where the width of the laser pulse is much longer than the rotational period of a molecule, the initial field-free state of the molecule evolves into the corresponding field-dressed pendular state. In this regime, the molecular axis is confined along the laser polarization in the presence of the laser field . In contrast, an ultrashort laser pulse can impulsively excite the initial rotational states into a broadly excited rotational superposition. The interference of the excited states causes periodic revivals of the molecular alignment after the laser pulse has passed [8–13].
As a special case, a plasma shutter technique was used to rapidly turn off the laser pulse with a slow turn on and to prepare a sample of well-oriented molecules in the laser-field-free condition. By the rapid turn off, the field-dressed pendular state created by the slow turn on is projected into the laser-field-free states. Then, due to the interference of the rotational states, laser-field-free molecular alignment [14, 15] or orientation [16–18] repeats periodically. It has been pointed out that the considerably long turn on of the laser field is especially important for achieving stronger molecular orientation [16–19]. Thus, the plasma shutter technique is very useful for achieving molecular orientation in the laser-field-free condition. In addition, a laser pulse with a slow turn on and a rapid turn off, which can be shaped by the plasma shutter technique, has attracted researchers’ attention to the formation of ultracold molecules via photo association [20, 21].
Some researchers are very much interested in the residual field component after the rapid turn off of the intense nanosecond laser pulse . In the previous studies in which the plasma shutter was used [15, 16], for characterizing the temporal shapes of the rapidly turned-off laser pulses, the cross-correlation measurement was used. In fact, the result of the cross-correlation measurement serves to confirm how fast the nanosecond (ns) pump pulse can be turned off and the intensity of the shaped ns pulse does not start to increase at least during the measurement.
However, the residual field intensity observed by the cross-correlation measurement is not the same as that in the laser-molecule interaction region of the molecular alignment and orientation experiments. Our numerical simulations, which are described in the Appendix, show that the residual field intensity observed by the cross-correlation measurement comes from the contribution of the very peripheral part of the section of the ns pulse, where the electron density in the formed plasma is lower than that in the central part of the plasma. However, such a peripheral part of the ns pulse cannot be well focused in the laser-molecule interaction region because of the defocusing effect after the plasma formation.
In this work, we provide a direct piece of evidence that the residual field intensity is negligible based on the comparison between our recent experimental observation and the theoretical calculations, though the cross-correlation measurement, which was done with a loose focusing condition, estimated the residual field as around 5% of the peak intensity . We estimate the residual field intensity by observing the temporal evolution of molecular alignment exhibited after the rapid turn off. As it is shown by our numerical simulations, the residual field, if any, affects the rotational dynamics of molecules. Specifically, it delays the revival times of the molecular alignment. In our experiment with OCS molecules as a sample, a full revival time of the alignment is observed at (82.3 ± 0.5 ps), which matches well with the rotational period of OCS molecule (82.2 ps). From the agreement, we conclude that the intensity of the residual field is much lower than the cross-correlation result at least by more than one order of magnitude.
A plasma shutter technique was first demonstrated for the rapid turn off of 1.3-mJ-class, 150-ps laser pulses so that aligned N molecules were prepared in the laser-field-free condition [14, 15]. In order to apply the technique to 100-mJ-class, 10-ns laser pulses, we need to carefully optimize the experimental condition . The experimental setup is shown in Fig. 1. A ns fundamental (ω) pulse from an injection-seeded Nd:YAG laser (Spectra-Physics, LAB-130-10) and its second harmonic (2ω) pulse are collinearly focused by a 700-mm-focal-length lens (L1) onto a 50-μm-thick ethylene glycol jet sheet with a portion of femtosecond (fs) laser pulse from a Ti:sapphire laser amplification system (Spectra-Physics, Spitfire Ace) . At the jet sheet, the two-color ns pulses are loosely focused in order to avoid the formation of the plasma by themselves, which is of crucial importance to apply the plasma shutter to 100-mJ-class laser pulses. Specifically, the jet sheet is located 2.5 mm before the best focus of the two-color ns pulses. The 1/e beam radii of the ω and 2ω pulses at the jet sheet are estimated as ∼44 μm and ∼29 μm, respectively. On the other hand, the intensity of the fs laser pulse on the jet sheet must be well above the threshold of the plasma formation. At the same time, the 1/e beam radius (∼50 μm) of the fs pulse is adjusted to be larger than those of the ns pulses, which is done by using a telescope (T1).
The relative delay between the two-color ns pulse and the fs pulse is adjusted so that the first half of the two-color ns pulse passes through the jet sheet, while the second half is absorbed by the plasma formed by the fs pulse. The divergence of the two-color shaped ns pulse is collimated by another 700-mm-focal-length lens (L2). Then, the shaped two-color ns laser pulse, combined with another portion of fs laser pulse, are sent either to a setup for the cross-correlation measurement or to a vacuum chamber for observing the molecular alignment.
2.1.1. Cross-correlation measurement
In the cross-correlation measurement, the temporal profile of the rapidly turned-off laser pulse is characterized by measuring the sum-frequency signals between the shaped ω pulse and the portion of the fs pulse as a function of the delay time between the two pulses (pump and probe). For efficiently generating the sum-frequency signal, the two pulses are focused to a BBO crystal by a 1000-mm-focal-length lens. The BBO crystal is located at 250 mm before the focal point in order to avoid the damage. The beam shape and the focusing characteristic of the ω laser pulse with and without the plasma absorption are numerically investigated in the Appendix. The profile of the unshaped ω pulse (Fig. 2(a)) shows the slow turn on with 4.5 ns by HWHM . The rising time of the 2ω pulse was estimated as 3.0 ns by observing it with a fast photodiode. Figures 2(b) and 2(c) show the temporal profiles of the shaped ω pulse at around the rapid turn off measured with different temporal resolutions. The pulse energies of the ω and 2ω pulses, before the shaping, are 25mJ and 18 mJ, respectively , and the corresponding peak intensities in the laser-molecule interaction region in the vacuum chamber are estimated as and W/cm for the ω and pulses, respectively.
Figure 2(b) shows that the falling time of the ω pulse is about 150 fs, which ensures the nonadiabatic turn off. Figure 2(c) shows that the second half of the shaped ω pulse does not start to increase at least up to 100 ps, where the remaining residual field intensity is estimated as 4∼6% of the peak intensity. We note that the residual field intensity observed by the cross-correlation measurement with a loose focusing condition is not the same as that in the laser-molecule interaction region of the molecular alignment experiment with a tight focusing condition as discussed in section 3 and in the Appendix.
2.1.2. Observation of the molecular alignment dynamics
The experimental setup for observing the molecular alignment, which has been detailed in [26, 27], is used. In the present work, an ensemble of OCS molecules buffered with 50-atm He is deflected by a home-built molecular deflector with the applied a voltage of 8 kV. Based on the comparison between the observed intensity profile of the deflected OCS molecular beam and the numerical simulation, we estimate that more than 92% of the selected OCS molecules are in the rotational ground state. The shaped two-color pump pulse and the fs probe pulse are collinearly focused by a 300-mm-focal-length lens into the molecular ensemble. The shaped two-color pump pulse is polarized parallel to the detector plane, whereas the fs probe pulse is polarized vertical to that. Fragment ions produced by the Coulomb explosion with the intense fs probe pulse are observed. Here the produced S ions are detected by the velocity map imaging (VMI) method. From the 2D-projected emission angles () of S ions, the degree of alignment is obtained. We observe the degree of alignment as a function of the delay between the shaped two-color pump pulse and the fs probe pulse.
2.2. Numerical simulation of molecular alignment
We numerically calculate the alignment dynamics of OCS molecules by solving the time-dependent Schrödinger equation with the Hamiltonian first given in Ref. . The details of the numerical method are given in Ref. . The rotational constant of OCS is [29 30], which corresponds to the rotational period of 82.2 ps. The temporal profile of the shaped two-color pump pulse is determined by the experimental observation (see Figs. 2(a) for the rising part and 2(b) for the falling part). From the time-dependent rotational wave packet, the degree of alignment is calculated. We assume that the OCS molecules are in the rotational ground state, which is necessary to reproduce our experimental result as it is noted in the next section. The focal volume effect of the laser pulses is not taken into account. Instead of that, the peak intensities of the ns pump pulses (ω and 2ω) are scaled by a factor of 0.3 (in Fig. 3) in order to reproduce the experimental observation.
3. Results and discussions
Figure 3(a) shows the temporal evolution of the degree of alignment as a function of the delay time between the shaped two-color pump pulse and the fs probe pulse. The temporal evolution of the ωpulse, characterized by the cross-correlation measurement, is also shown as a blue solid line. The observed maximum degree of alignment is . In our measurement, the self-breakdown of the focused ns pulse occasionally takes place due to the floating dusts in the beam path near the plasma shutter. In addition, when the plasma shutter is operating, vapor and/or small particles are produced from ethylene glycol, which increases the frequency of the self-breakdown events. Thus, the observation after the rapid turn off includes the data measured without the ns pulses. Due to such occasional misfires of the ns pump pulse, after the rapid turn off, the degree of alignment is . We note, however, that such occasional misfires do not influence the observed clear revival structures of the degree of alignment. In fact, the degree of alignment right before the rapid turn off revives at least three times within the delay time up to 100 ps.
We also show the results of numerical calculations to analyze our experimental observation. We calculate the alignment dynamics of OCS molecules in the initial ground state. As mentioned above, the peak intensities of the shaped laser pulses are scaled by a factor of 0.3 in order to reproduce the experimental observation. The intensity ratios of the residual field are set at 0, 4, and 8% in Figs. 3(b)-3(d), respectively. The simulations reproduce the experimentally observed clear revival structures. The observed simple revival structures can be generated only from the interference between the two lowest-lying rotational states, |0,0⟩ and |2,0⟩,meaning that the sample molecules are in the initial rotational ground state |0,0⟩ and, at the same time, the applied laser intensity is sufficiently low. If other rotational states except for |0,0⟩ and |2,0⟩ are noticeably populated, the revival structures become more complex.
We fit the peak around 82.2 ps with a Lorentzian function. As it is well studied [8–13], regardless of the rotational state and the applied laser intensity, the revival structure shows a full revival at the rotational period of the molecule, 82.2 ps for an OCS molecule, which is marked with a blue dotted line in Fig. 3. The numerical results clearly show that the residual field, if any, delays the full revival time of the alignment. In the experiment, although the cross-correlation result estimates the residual field as 4 - 6%, the measured full revival time does not show a recognizable delay. This is a direct piece of evidence that the residual field in the molecular alignment experiment is negligible and is different from that observed by the cross-correlation measurement.
Figure 4 shows the effective full revival time as a function of the residual field ratio for different peak intensities of the ns pulses. The experimentally observed delay of the full alignment is shown by the green symbol with error bars. We emphasize that the error bars have the similar physical meaning to the standard deviations associated with the Gaussian fitting, meaning that the error bars themselves have the probability distributions peaked at the centers of the error bars. The other symbols are from the numerical calculations. By comparing the results, the residual field intensity is estimated to be below 0.4% of the peak intensity, which is much lower than the result of the cross-correlation measurement at least by more than one order of magnitude. Our conclusion is reinforced by the numerical simulations about the residual field intensity, which is given in the Appendix.
4. Summary and outlook
We develop a plasma shutter technique applicable to 100-mJ-class, 10-ns laser pulses. The rapidly turned off ns pulses by the plasma shutter technique are applied to the laser-field-free alignment experiment. The ground state OCS molecules irradiated by the rapidly turned off pulses exhibit clear revivals of alignment. The result is compared with our numerical calculations based on the time-dependent Schrödinger equation. The numerical results show that the residual field, if any, noticeably delays the full revival time of the molecular alignment. In the experiment, the full revival time agrees well with the rotational period of an OCS molecule in the field-free condition, which ensures that the residual field is actually negligible.
The performance of our plasma shutter is summarized as follows: (1) The falling time is ∼150 fs. (2) After the rapid turn off of the laser pulse, it does not start to increase at least up to ∼100 ps. (3) The residual field component after the rapid turn off is below 0.4% of the peak intensity. This estimation is limited by the accuracy in the determination of the experimentally observed rotational period of OCS molecules in the rotational ground state. We emphasize that the residual field component is actually negligible and does not influence the alignment dynamics after the rapid turn off at all.
The laser pulse with a slow turn on and a rapid turn off provides a powerful method for laser-field-free molecular alignment and orientation. Our pulse-shaping technique based on the plasma shutter can be applied to future experimental studies on the control of spatial directions of molecules.
5. Appendix Simulations for propagation of the laser beam through the optical setup
In this Appendix, we calculate propagation of the ω laser beam in order to estimate the intensity of the focused beam at the laser-matter interaction region numerically. Atomic units are used unless otherwise stated.
We use the cylindrical coordinates, where a space vector is represented by . z is the on-axis spatial coordinate along the propagation of the beam. r is the transverse radial coordinate. Considering a continuous wave laser, the laser field is associated with the beam shape by . The free propagation of a diverged or focused beam from a position to another one is calculated by the Huygens-Fresnel diffraction integral , which is expressed as
Beam focusing or collimation by a lens with the focal length f is numerically considered by multiplying an r-dependent term to the beam shape . Here ,where is the optical path difference illustrated in Fig. 5(e).
The laser beams with () and without () the plasma absorption (PA) are used for two initial conditions in the simulations. At the position zPA, where the plasma absorption takes place, the two beams are related by
Assuming the collisionless free electron plasma, the refractive index is given by
Here Njet is the density of the liquid ethylene glycole, . and IP are the instantaneous field amplitude of the fs laser and ionization potential of the ethylene glycole (10.16 eV), respectively. The ADK model is employed for the ionization rate Γ . The fs laser pulse has 50-μm-1/e beam radius and 35-fs pulse duration by FWHM. The peak intensity of the fs laser pulse is set at in order to reproduce the residual field intensity measured by the cross-correlation measurement.
In Fig. 5(a), a sketch of the optical beam propagation through the plasma shutter is shown. We show the beam shapes of the ω laser as and at several z positions as a function of the position r. At the ethylene glycol jet sheet (), the ω laser without the absorbing plasma has a 44-μm-1/e beam radius as shown in Fig. 5(b) with a black line. The shape of the beam with the plasma absorption is shown by a blue line. The plasma density calculated by Eq. (4) is given in Fig. 5(d) as a function of the position r. As it is shown in Fig. 5(b), the central area of the beam is absorbed because the plasma density is higher than the critical one in the area.
Due to the under-critical-density plasma, the remaining peripheral part of the ω beam also experiences a phase variation over the transverse position r (see Fig. 5(c)), which causes a slight defocusing of the beam. The phase of the absorbed beam changes very rapidly near the critical density region, which leads to a destructive interference of the beam and the energy of the absorbed beam is further reduced as the beam propagates (compare Figs. 5(b) and 5(f)). We note that the beam without the plasma absorption has a phase distribution given by the Gouy phase near the focus.
The laser beams are propagated to mm by using Eq. (1). The far-field structures of the beams are shown in Fig. 5(f). The beam without the plasma absorption is converted to a Gaussian beam with -mm-1/e radius, which is consistent with our experimental condition. The absorbed beam is converted into a beam with two weak peaks, the inner one being stronger than the outer one. As it is already mentioned, due to a destructive interference, the energy of the beam is reduced than that at .
The phase distributions, i.e., the wavefronts of the beams are quadratic as shown in Fig. 5(g), illustrating the beams with and without the plasma absorption are almost equally diverged. The diverged beams are collimated by a 700-mm-focal-length lens at mm. The collimation is numerically considered by Eq. (2). The wavefronts of the collimated beams are shown in Fig. 5(h), demonstrating the beams are well collimated.
The collimated beams are then, after 1500 mm propagation, focused either by 1000-mm-focal-length lens for the cross-correlation measurement or by 300-mm-focal-length lens for the molecular alignment experiment. In the cross-correlation measurement, the ω pulse and the portion of the fs pulse are focused into a BBO crystal. In order to avoid the damage of the BBO crystal, the crystal is located at 250 mm before the focal point (see Fig. 6(a)). At this position, the beam shapes and the wavefronts are shown in Figs. 6(b) and 6(c), respectively. In such a loosely focused condition, the wavefronts of the two beams are almost equally quadratic. The peak intensity of the absorbed beam is around 5% of that of the beam without the plasma absorption as shown in Fig. 6(b). The residual field intensity measured by the cross-correlation measurement would be 4-6% of the peak intensity, which is consistent with our cross-correlation measurement. Therefore, the cross-correlation measurement serves as a tool, not for measuring the residual field intensity, but for observing the temporal profile of the rapid turn off of a ns laser pulse.
In the molecular alignment experiment, the ω pulse and the fs pulse are focused into the the vacuum chamber by a 300-mm-focal-length lens. We emphasize that, in the molecular alignment experiment, the laser beams are tightly focused to the gas target in order to increase the laser intensity. At the same time, in order to keep the beam size larger than the size of the fs probe beam, the gas target is located at 0.5∼1 mm before the best focal point. The focal point of the fs pulse is well located at the gas target.
Figures 6(e) and 6(f) show the beam shapes and the wavefronts at 0.8 mm before the focal point. The beam without the plasma shutter is well focused with a 1/e-beam radius of ∼ 20 μm. On the other hand, the absorbed beam exhibits the peak at the peripheral part as indicated by the arrow in Fig. 6(e). The peak intensity is estimated as 1.1% of the beam without the plasma absorption. Furthermore, the beam quality is low as can be seen from the wavefront. It is clear that at the position r = 0 the intensity of the absorbed beam is virtually zero. The results of the numerical simulations are consistent with the arguments given in the main text.
Grant-in-Aid for Specially Promoted Research No. 21000003 from MEXT and the Photon Frontier Network Program of MEXT.
We thank Daisuke Takei, Yuta Murotani, and Peiyu Xia for their cooperation in the experiment.
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