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Ultrashort ultraviolet pulses at 267 nm were generated through four-wave mixing processes in dual-color femtosecond filaments. The generated ultrashort ultraviolet pulses experienced intensity modulation due to molecular-alignment-induced spatial (de)focusing effects, and the output beam profiles were shown to vary observably at different molecular alignment revivals, facilitating all-optical field-free and ultrafast spatial shaping and profile optimization of the ultraviolet pulses.
© 2013 Optical Society of America
1. Introduction
Much effort has been devoted to efficient generation of intense ultra-short ultraviolet pulses via nonlinear frequency conversion processes in solid or gaseous media. The attainable ultraviolet (UV) wavelengths and conversion efficiencies in solid media were typically limited by the UV transparent windows and material dispersions, while standard gaseous media possessed quite low conversion efficiencies as a result of their intrinsic low optical nonlinearities. In order to improve nonlinear frequency conversion efficiency, several methods have been proposed such as the use of a gas jet to increase the gas density [1,2], micro-structured hollow fibers to modulate phase matching [3] along appropriately extended nonlinear interaction lengths [4–7], interaction of fundamental-wave (FW) and its second harmonic (SH) filaments in hollow fibers filled with some noble gases to simultaneously compress the co-propagating pulses [8], and non-collinear interaction of synchronously overlapped filaments to create photonic-crystal like plasma gratings via wavelength-scale plasma density modulation [9]. On the other hand, reliable UV pulse modulation and particularly all-optical field-free control of UV pulse generation are desired in various applications. Nevertheless, currently available optical modulators are inefficient in the UV region. It is also quite difficult to modulate nonlinear frequency conversion processes in gaseous media, while direct modulation of the FW driving pulses may outcome efficient UV pulse modulation but it needs special design to maintain the optical modulation in the nonlinear frequency conversion processes.
It is well-known that femtosecond filament could be controlled on the basis of revivable transient birefringence induced by field-free molecular pre-alignment [10,11], from which robust modulation of terahertz generation was achieved through dynamic phase-delay change of co-propagating FW and SH dual-color pulse filaments [12]. In this paper, we demonstrated that molecular pre-alignment excited by pump pulses could be used to control four-wave mixing (FWM) processes in intense FW and SH dual-color filaments, generating UV pulses at 267 nm with intensity modulated as a function of the pump pulse delay. In addition, the UV pulse beam profile was modified due to the alignment-induced spatial (de)focusing effects.
2. Experimental setup
The experimental setup is shown in Fig. 1. The 800-nm femtosecond laser pulses with the pulse duration of 35 fs and repetition rate of 1 kHz was split by a 1:3 beam splitter. The weak pulse was used to pre-align nitrogen and oxygen molecules in air (M-pulse), while the strong pulse was frequency-doubled by using a 200-μm-thick 29.2°-cut type-I β-BBO crystal and focused with a lens of f = 60 cm to generate FW-SH dual-color filament of 2 cm long. The M-pulse energy could be tuned from 0.2 to 0.4 mJ by using a half-wave plate (HWP-1) and Brewster plate. Another half-wave plate (HWP-2) was used to adjust the relative polarization between the M-pulse and dual-color pulses. A motorized translation was placed in the M-pulse arm to adjust the time delay between M-pulse and dual-color pulses. Negative time delays accounted for the M-pulse delayed behind the dual-color pulse. The M-pulse was focused with a lens of f = 50 cm and its focus was spatially overlapped with that of the dual-color pulse. A 3-mm-thick α-BBO crystal was placed in the dual-color pulse arm after the β-BBO crystal to compensate for the dual-color temporal walk-off, and a dual-wave plate was used to parallelize the FW and SH polarizations. The FW and SH pulse energies were 0.50 and 0.13 mJ, respectively. A prism was used to separate the generated 267 nm pulse from the dual-color pulses after the filaments. The intensity change of the generated UV pulse with the molecular pre-alignment signal was detected with the same method as in [13,14]. The UV pulse beam profile was recorded by a UV-enhanced camera to show its modulation by the molecular pre-alignment.
Fig. 1 Experimental setup. The M-pulse used to excite the molecular alignment was tuned from 0.2 to 0.4 mJ by using HWP-1 and Brewster plate. HWP-2 was placed to adjust the relative polarization between the M-pulse and dual-color pulse. The focal lengths of the L1 and L2 were 60 and 50 cm, respectively. β-BBO crystal made a dual-color pulse with orthogonal polarization. The thickness of the α-BBO was 3 mm. DWP was a dual-wave plate: half-wave plate for FW and full-wave plate for the SH. The prism was used to distinguish the UV pulse from the dual-color pulse after the filament. The change of the UV pulse intensity as the function of the M-pulse time delay was detected by a spatial (de)focusing method.
3. Experimental results
As a result of dynamic balance of plasma defocusing and Kerr focusing, filaments formed in air were quite sensitive to the nonlinear properties of air molecules. Accordingly, filamentary dynamics, such as the filament length, field intensity, and plasma density, were affected by the M-pulse excitation [15–17]. Molecular pre-alignment induced focusing or defocusing for pulses propagating after the M-pulse, presenting an additional effect that jointly interacted with Kerr focusing, plasma defocusing, and beam diffraction. The change of the refractive index induced by pre-aligned molecules could be described by
where ρ0 is the initial molecular number density, α is the molecular polarizability difference, and n0 denotes the linear refractive index without molecular alignment revival. The statistic metric <<cos2θ (r,t)>> quantified the molecular alignment, which distinguished parallel, perpendicular and random molecular alignment revivals. The parallel (perpendicular) molecular alignment revival, with molecular axis oriented parallel (perpendicularly) to the field polarization of the followed dual-color pulse, induced positive (negative) change of the refractive index. As molecular alignment was excited by Gaussian beams, more molecules were aligned in the beam center. Accordingly, molecular pre-alignment induced spatial focusing (defocusing) at parallel (perpendicular) molecular alignment revivals. As a result, the dual-color pulse peak intensity increased (decreased) at the parallel (perpendicular) molecular alignment revivals. In our experiments, the significant contribution to the generation of the UV pulse was the FWM process 2ω + 2ω−ω = 3ω instead of third-harmonic generation ω + ω + ω = 3ω, which was testified by blocking the SH wave pulse in the filament as reported in [18]. The frequency conversion efficiency mainly depends on the nonlinear coefficient χ(3) and the phase matching conditions. The phase matching condition holds on in a long propagation distance due to the nonlinear phase locking effect in filaments. Meanwhile, molecular pre-alignment induced a negligible change of phase mismatching [18]. Hence, the dual-color pulse intensity modulation induced by molecular pre-alignment played an important role at the conversion efficiency of the FWM process.In the experiment, the energy of the UV pulse was about 10μJ as produced by the FWM process without any effect of the molecular alignment. At first, we adjusted the M-pulse polarization parallel to that of the dual-color pulse by using HWP-2 as shown in Fig. 1. The generated UV pulse intensity experienced revivable modulations as a function of the M-pulse time delay as shown in Fig. 2, which exhibited thesame trends as the statistic metric of molecular alignment detected under the circumstance of parallel polarized pump and probe pulses. The focusing effect induced by the parallel molecular alignment revival further focused the FW and SH pulses and increased the dual-color pulse intensity. The FWM process in the dual-color pulse filament was improved. The UV pulse intensity increased at the parallel molecular alignment revival, which was in excellent agreement with the increase of the dual-color pulse intensity derived from the molecular alignment induced focusing effect. In comparison, the UV pulse intensity decreased due to alignment-induced defocusing effect while the molecular axis was oriented perpendicularly to the dual-color pulse field polarization as shown in Fig. 2(b). And then, we rotated the M-pulse polarization perpendicularly to that of the dual-color pulses. The intensity modulation of the UV pulse was also observed as a function of the perpendicularly polarized M-pulse time delay, which showed similar time-dependence as the molecular alignment signal detected under the circumstance of perpendicularly polarized pump and probe pulses.
Fig. 2 (a) Calculated molecular alignment metric <<cos2θ>> of air versus time delay as the M-pulse polarization was parallel to that of the probe pulse. (b) Measured change of the UV pulse intensity along with the molecular alignment signal with the M-pulse polarization parallel to that of the dual-color pulse.
The generated UV pulse beam profiles were also recorded at different molecular alignment revivals. With Gaussian distribution of the laser pulse beam profile, the central part of the dual-color pulse was further affected than its periphery. Figure 4 shows that the central part of the generated UV pulse beam profile was spatially focused (defocused) at parallel (perpendicular) molecular alignment revivals. The full revival for N2 and 3/4 revival for O2 are reported in Fig. 3. Graph (a) in Fig. 4 displayed the image of the UV pulse beam profile at random molecular alignment corresponding to point (a) in Fig. 3. As displayed in Fig. 4, the central part of the generated UV pulse was defocused in graphs (b) and (d), while the UV pulse beam diameter were enlarged as the perpendicular molecular alignment revival balanced the spatial focusing from convex lens and high-intensity pulse self-focusing with the (b) and (d) showing the perpendicular molecular alignment in Fig. 3. The generated UV pulse shown in (c) of Fig. 4 indicated that the pulse was further focused at parallel molecular alignment revivals.
Fig. 3 The variation of the measured UV pulse intensity contained in the central part at whole revival for N2 and 3/4 revival for O2 (The revival periods for N2 and O2 are 8.3 and 11.6 ps, respectively). This alignment-induced variation was obtained by subtracting the constant UV pulse energy under circumstance of random molecular alignment. Positive (negative) signals corresponded to the case of parallel (perpendicular) molecular alignment.
Fig. 4 The UV pulse beam profiles at different molecular alignment revivals with the M-pulse energy 0.3mJ. The beam intensity was strengthened under focusing effect in (c) and decreased in (b) and (d) due to defocusing effect. Image in (a) presented the pulse beam at random molecular alignment.
In addition, the whole beam spot diameter was smaller than that at random alignment. The intensity distributions of the UV pulse beam were also presented in Fig. 4. Figure 4(a) exhibited the UV pulse intensity distribution as the dual-color pulse experienced therandom molecular alignment. The depression of the central UV pulse intensity in Figs. 4(b) and 4(d) was consistent with the defocusing effect induced by perpendicular molecular alignment revivals. Interestingly, the UV pulse intensity achieved significant enhancement, and an ideal UV Gaussian beam emerged while the dual-color pulse experienced parallel molecular alignment revival excited by a Gaussian M-pulse beam, as shown in Fig. 4(c). The amount of the energy of the UV pulse was contained at the centre of the beam while the molecular alignment revival was at the maximum. And the ratio of the pulse energy contained in the centre and annular structure of the beam was about 4:1 as the energy of the M-pulse was 0.4mJ. As the M-pulse energy increased monotonously from 0.2 to 0.4 mJ, the centre part of the UV pulse intensity increased at parallel molecular alignment revivals (shown in Fig. 5) and the beam intensity distribution was optimized simultaneously. For the defocusing effect induced by the perpendicular molecular alignment revivals, the UV pulse beam profile was more diffused as the M-pulse energy increased. In addition, the central part intensity of the UV pulse decreased as the M-pulse energy increased.
Fig. 5 Measured 3D graphs of the UV pulse beam while the M-pulse energy was (a) 0.2mJ, (b) 0.3mJ and (c) 0.4mJ for parallel molecular alignment revivals. The central part intensity of the UV pulse increased as the aligning M-pulse increased in energy.
The M-pulse underwent filamentation in air as its intensity exceeded the critical power. The plasma produced by the M-pulse imported a negative refractive index change (δnplas~-ρ/2ρcr, where ρ is the electron density of the plasma and ρcr~λ−2 is the critical density closely related to the laser wavelength). Similar to the reduction of the refractive index induced by the perpendicular molecular alignment revival, the formed plasma functioned as a spatial concave lens leading to plasma defocusing. This effect played only a small role in comparison with the perpendicular molecular alignment revival induced defocusing effect and the plasma induced divergence of the UV pulse beam profile could be neglected.
4. Conclusion
In conclusion, the dual-color pulse filament was an efficient method to produce stable and high-quality UV pulse generation. We demonstrated to modulate the generated UV pulse intensity and optimize the pulse beam profile with molecular alignment revivals, which served as an all-optical approach at femtosecond scale to control the UV pulses, and played an important role at ultrafast imaging and detection in ultraviolet wavelengths.
Acknowledgments
We acknowledge financial supports from the National Basic Research Program of China (2011CB808105), National Natural Science Fund of China (11274115 & 10990101), International Science and Technology Collaboration Program (2010DFA04410 & 11530700900), and National Key Scientific Instrument Project (2012YQ150092).
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