Field-free alignment of N2, O2, CO, CO2, CS2, and C2H4 molecules was experimentally achieved at room temperature by using 800 nm, 110 fs laser pulses at an intensity of 6×1013 W/cm2. An enhanced degree of alignment was also demonstrated by using two pulses with appropriate separation times. These results indicate that multi-pulse alignment is a feasible approach to provide macroscopic ensembles of highly aligned molecules for practical applications.
©2006 Optical Society of America
The femtosecond laser is becoming more powerful as a tool to manipulate the behaviors of molecules . When the laser intensity is below the ionization threshold of molecules, the laser-molecule interaction tends to align the molecules with the most polarizable axis along the laser polarization vector . If the laser pulse duration is longer than the rotational period of a molecule, the free rotor is transformed into a pendular state that the molecule liberates around the polarization vector. When the laser is turned off, the liberator adiabatically returns to the isotropic free rotator from which it originates. If the laser pulse duration is shorter than the molecular rotational period, the laser-molecule interaction gives the molecule a rapid “kick” to align the molecular axis with the laser field vector. After the laser is deactivated, the transient alignment can periodically be revived as long as the coherence of the rotational wave packet is preserved. Therefore, the former is also called adiabatic alignment and the latter field-free alignment. Even though both adiabatic alignment and field-free alignment can produce macroscopic ensembles of highly aligned molecules, field-free alignment has the obvious advantage of not interfering with subsequent applications. A variety of new and exciting applications of field-free aligned molecules are currently emerging. For example, Litvinyuk et al.  measured strong field laser ionization of aligned N2 molecules and directly obtained the angle dependent ionization rate of N2 molecules by intense femtosecond laser field. Itatani et al.  accomplished a tomographic reconstruction of the highest occupied molecular orbit of nitrogen by using high harmonic generation from intense femtosecond laser pulses and aligned molecules. Recently, Kanai et al  observed the quantum interference during high-order harmonic generation from aligned molecules and demonstrated that aligned molecules could serve as an ideal quantum system to investigate the quantum phenomena associated with molecular symmetries.
One-dimensional field-free alignment of molecules has been successfully addressed by the rotational wave packet theory, in which a rotational wave packet with an aligned multi-J hybrid is formed when molecules are irradiated by a strong laser pulse [6–9]. Following the short pulse, the molecules will evolve subject to the field-free Hamiltonian and move through a moment of collective alignment. Then they continue to rotate and the wave packet is dephased. But through a full rotational period, they move through the collective alignment moment again. The degree of alignment of a rotational wave packet is given by the average of 〈cos2θ〉, where θ is the angle between the molecular axis and the polarization vector of the laser field. 〈cos2θ〉=1/3 represents an isotropic angular distribution evenly distributed across all θ. If 〈cos2θ〉>1/3, the molecule is predominantly aligned along the laser polarization. If 〈cos2θ〉<1/3, the molecule is concentrated orthogonal to the laser polarization and labeled as an antialignment molecule. The current theoretical work focuses on exploring the three-dimensional alignment of molecules  and novel applications of aligned molecules [11–13]. In contrast with the rapid progress in theoretical research, the experimental research is progressing extremely slowly due to the difficulty in obtaining highly field-free aligned molecules in the laboratory. Now, researchers have developed two typical methods to experimentally measure the alignment degree of molecules. The first one is realized by breaking apart aligned molecules through multielectron dissociative ionization  or dissociation followed by ionization of the fragments . The alignment degree is thus deduced from the angular distribution of the ionized fragments. The disadvantage of this method is that the probe laser is so strong that it destroys the aligned molecules. The second method is the weak field polarization spectroscopy technique based on the birefringence caused by aligned molecules [16–19]. The advantage of this method is that the probe laser is so weak that it neither affects the alignment degree nor destroys the aligned molecules.
In this article, we report the results of our experiment on the field-free alignment of diatomic molecules (N2, O2, CO) and polyatomic molecules (CO2, CS2, C2H4) at room temperature under irradiation of femtosecond laser pulses. We also demonstrated experimentally that the alignment degree could be enhanced by using two pulses with delayed separation times. These results provide a feasible approach to prepare field-free highly aligned molecules in the laboratory for practical applications.
2. Experimental setup
Figure 1 shows the experimental setup for measuring field-free alignment of molecules. The laser system consisted of a chirped pulse amplified Ti:sapphire system operating at 800 nm and at a repetition rate of 10 Hz. The 110 fs output pulse was split into two parts to provide a strong energy pump beam and a weak energy probe beam both linearly polarized at 45° with respect to each other. For double-pulse alignment of molecules, the strong pump laser was split into another two aligning pulses with equal intensity. The relative time separation between the laser pulses was precisely adjusted by an optical translational stage controlled by a stepping motor. Both the pump beam and the probe beam were focused with a 30 cm focal length lens into a 20 cm long gas cell at a small angle. The gas cell was filled with different gases at room temperature and at one atmospheric pressure except that CS2 was under its saturated vapor pressure of room temperature. The field-free aligned molecules induced by the short pump laser caused birefringence and depolarized the probe laser. After the cell, the depolarization of the probe laser, which represents the alignment degree, was analyzed with a polarizer set at 90° with respect to its initial polarization detection. In order to eliminate laser fluctuation, a reference laser was introduced. The alignment signals and the reference laser signals were detected by two photoelectric cells and transferred into a computer via a four-channel A/D converter for analysis.
3. Results and discussion
Figure 2 shows the alignment signal for diatomic molecules (a) N2, (b) O2, and (c) CO irradiated by 800 nm, 110 fs pulses at an intensity of 6×1013 W/cm2. The classical rotational period Tr of molecules is determined by the equation Tr=1/(2 B0 c), where B0 is the rotational constant in the ground vibronic state and c is the speed of the light. For N2, O2 and CO, B0 is 2.010, 1.4456, 1.9772 cm-1, respectively . The corresponding rotational period Tr is therefore 8.3 ps for N2, 11.6 ps for O2 and 8.5 ps for CO. It is clear from Fig. 1 that the alignment signal is fully revived every molecular rotational period. However, there are also moments of strong alignment that occur at smaller intervals. The difference at quarter full revival for N2, O2 and CO can be explained by the different nuclear spin weights of the even and odd J states in the initial distribution.
Figure 3 shows the alignment signal for polyatomic molecules (a) CO2, (b) CS2, and (c) C2H4 irradiated by 800 nm, 110 fs pulses at an intensity of 6×1013 W/cm2. The classical rotational period Tr is 42.7 ps for CO2, 152.6 ps for CS2 and 9.3 ps for C2H4 . It can clearly be seen that the alignment signal repeats every molecular rotational period. Note that although CO2 molecules are not actually homonuclear diatomic molecules, the two O atoms are indistinguishable. Hence symmetrization of the wave function with respect to these two particles requires that only even J states are populated. Since only a single localized wave packet exists, strong net alignment and antialignment is observed near the time of a quarter revival. For the same reason, the net alignment and antialignment is also observed near the time of a quarter revival for CS2. In a recent theoretical study, Torres et al . explicitly calculated the angular distribution of the CS2 ensemble as it evolves through a rotational revival. They found that the ensemble displays a rich variety of butterfly-shaped distributions, always presenting some degree of order between the aligned and antialigned distributions. Unlike the linear molecules, complex revival signals were observed for C2H4 because of its asymmetric planar structure. Our experimental observation of C2H4 agreed with the theoretical calculation carried out by Underwood et al., who also proposed a theoretical scheme to realize three-dimensional field-free alignment of C2H4 by using two orthogonally polarized, time-separated laser pulses .
In Fig. 3, it is obvious that the alignment signal does not return to a background signal with the probe laser preceding the aligned laser, especially for CS2. The increased background signal results from the permanent alignment of the molecules,  in which the laser-molecule interaction spreads each initial angular momentum state to higher J states but does not change the M. Thus, rather than being uniformly distributed, the angular momentum vectors of each J state in the wavepacket are preferentially oriented perpendicular to the aligning pulse polarization. Due to the relaxation of the rotational population, the permanent alignment will decay monotonically under field-free conditions towards its thermal equilibrium.
For real applications, it is important to ensure that a higher degree of alignment can be obtained under field-free conditions. Theoretical investigation has indicated that the degree of alignment could be improved by minimizing the rotational temperature of the molecules or by increasing the laser intensity . For practical application, minimizing the rotational temperature is not a good general approach. Therefore, we studied the field-free alignment of molecules by varying the laser intensity. As an example, Fig. 4 shows the laser intensity dependence of the field-free alignment of CS2 with the pump laser intensity ranging from 17 to 64 TW/cm2. The results show that the degree of alignment can be improved by increasing the laser intensity. The permanent alignment is obviously enhanced as the laser intensity increases because the stronger aligned laser excites CS2 molecules to higher J states from the initial values and then induces an enhanced permanent alignment during and after the interaction.
However, the maximum degree of alignment thus obtained is limited by ionization of the molecules in the laser field. In order to obtain highly aligned molecules without destroying the molecules, some theorists have proposed the multi-pulse method, in which alignment is created with an initial pulse, and then the distribution is brought to a higher degree of alignment with subsequent pulses [22–24]. Thus the multi-pulse method is not constrained by the maximum intensity limit for single laser pulses and highly aligned molecules can be obtained without destroying the molecules.
An experiment was also conducted to investigate the enhanced field-free alignment of CS2 by means of a two-pulse laser. In this experiment, the aligning laser was divided into two beams with equal intensities of 2×1013 W/cm2. Figure 5 shows the timing for the two aligning laser pulses and the probe laser pulse. The first aligning laser pulse prepares a rotational wave packet at time zero and the second aligning laser pulse modifies this rotational wave packet at Tr/4. The probe laser pulse measures the alignment degree of molecules at 3Tr/4. When the first aligning laser worked alone, the probe laser measured the alignment signal at 3Tr/4, which is represented by the red line in Fig. 5. When the second aligning laser worked alone, the probe laser measured the alignment signal at Tr/2, which is represented by green line in Fig. 5. Depending on the delay time between the first and the second aligning laser pulses, the field-free alignment can be constructive or destructive. With a proper adjustment of the delay between the two aligning laser pulses, an obvious enhanced alignment signal was observed in the probe region, as well as the permanent alignment, which is represented by the black line in Fig. 5. The optimal delay of the second aligning laser pulses is typically located before the maximum alignment during a strong revival after the first aligning laser pulse. With this timing, the second aligning laser pulse catches the molecules as they are approaching the alignment peak and pushes them a bit more toward an even stronger degree of alignment. The region of increased alignment will appear in subsequent full revivals from this point. Thus, a sequence of several properly timed pulses overcomes the maximum intensity limit imposed by ionization for single-pulse alignment and leads to highly field-free aligned molecules. Therefore, multi-pulse alignment provides a promising approach for creating macroscopic ensembles of highly aligned molecules needed for various practical applications.
In summary, we have realized the field-free alignment of N2, O2, CO, CO2, CS2, and C2H4 molecules at room temperature using strong femtosecond laser pulses. We also demonstrated that the degree of alignment could be improved by using a two-pulse scheme with appropriate separation times. These results indicate that multi-pulse alignment is a feasible approach to obtain macroscopic ensembles of highly aligned molecules in the laboratory. We believe our results will promote the practical applications of field-free aligned molecules.
This work was supported by the National Natural Science Foundation of China under grant Nos. 10534010, 60378012 and 10521002.
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