The influence of laser chirp on the formation of femtosecond laser filamentation in Ar was investigated for the generation of few-cycle high-power laser pulses. The condition for the formation of a single filament has been carefully examined using 28-fs laser pulses with energy over 3 mJ. The filament formation and output spectrum changed very sensitively to the initial laser chirp and gas pressure. Much larger spectral broadening was obtained with positively chirped pulses, compared to the case of negatively chirped pulses that generated much longer filament, and compressed pulses of 5.5 fs with energy of 0.5 mJ were obtained from the filamentation of positively chirped 30-fs laser pulses in a single Ar cell.
©2008 Optical Society of America
Laser filamentation, achieved by loosely focusing high-power femtosecond laser pulse in air, has accompanied a number of fascinating phenomena. The filamentation process occurs by the dynamic interplay between self-focusing induced by the Kerr effect and defocusing in plasma . During the formation of a long filament by the laser pulses, the filamentation can induce very large spectral broadening, suitable for pulse compression of high power femtosecond lasers [2, 3]. Compared to a gas-filled hollow-fiber pulse compressor [4, 5], the pulse compression by laser filamentation has good potential for coupling much larger energy as it is not confined within a boundary, in addition to handy alignment. As the critical power for laser filamentation increases with reduced gas density, laser energy can be increased by lowering the density of filamentation medium without forming multiple filaments . The filamentation process could thus be used as an alternative to the gas-filled hollow-fiber pulse compressor for generating high-power few-cycle pulses.
During the filamentation process, the propagating laser pulse experiences the modification of spectral and temporal structures. The self-phase modulation (SPM) due to the refractive index change by plasma formation and by the Kerr effect induces the spectral broadening. The SPM in an ionizing gas induces spectral broadening towards the short wavelength in the leading edge of the pulse [7, 8], while the Kerr effect causes the spectral broadening towards the long wavelength in the leading edge and short wavelength in the trailing edge . The velocity difference between the peak and the wing of the propagating pulse in plasma results in self-steepening of the laser pulse in the trailing edge , which results in strong asymmetrical spectral broadening towards the blue-side. The chirp contained in the laser pulse is also modified from the SPM processes, which affects the temporal structure of the propagating laser pulse . Consequently, the effect of laser chirp on pulse compression needs to be examined to achieve maximum pulse compression. In this paper, the optimum conditions in laser chirp and gas pressure for the generation of few-cycle high-power laser pulses by laser filamentation in an Ar cell are experimentally investigated. Considering applications of compressed laser pulses, the experimental parameters are scrutinized under the condition of single filament formation.
For the generation of few-cycle high-power laser pulses femtosecond laser filamentation was investigated using a 1-kHz, multi-mJ femtosecond laser with wavelength centered at 820 nm . The filamentation setup with a 250-cm-long Ar gas cell is shown in Fig. 1. The laser pulse was loosely focused to the Ar cell so as to generate a single filament, preventing the formation of multiple filaments , while achieving large spectral broadening. The dispersion of the output pulse after filamentation was compensated by chirped mirrors. The temporal characterization of output pulses was undertaken using the second-harmonic-generation (SHG) frequency-resolved-optical-gating (FROG) method [13, 14]. In the FROG measurement, a 10-µm-thick-barium borate crystal was used for sufficient phase-matching bandwidth.
The spectral broadening during the filamentation process was maximized, under the condition of stable filament formation, first by adjusting the pressure of the Ar cell. When the laser power exceeds the critical power, 26 GW for 200-torr Ar, for self-focusing, the laser filamentation can be initiated. With too high laser power, over 5 times the critical power, multiple filaments can be generated , which should be avoided in order to make use of the output from the filamentation. For a given laser power an optimum pressure was determined under the condition of stable single filament formation. In the experiments, the focusing geometry was adjusted by changing the distance between the concave and convex mirrors so that maximum spectral broadening could be achieved. Figure 2 shows the experimental results of spectral broadening obtained with laser energy of 3.1 mJ for the two cases with slightly different chirp. The input pulse durationwas measured with the consideration of the 1-mm thick fused silica front window of the Ar gas cell. In the case of chirp-free 28-fs pulses (Fig. 2(a)) the maximum spectral broadening was obtained with 200-torr Ar, but with positively chirped 30-fs pulses (Fig. 2(b)) the filamentation in 220-torr Ar generated the largest spectral broadening. In the latter case even larger spectral broadening could be obtained with 240-torr Ar, but the filament became unstable, and the output beam pointing could not be stably maintained. The results show that the gas pressure needs to be controlled well for maximum spectral broadening.
The filamentation process was surprisingly very sensitive to laser chirp. The results in Fig. 2 clearly indicate that slight chirp adjustment strongly affected the filamentation process. In order to clarify the effects of Ar pressure and laser chirp on spectral broadening and pulse compression, a systematic survey on measured pulse duration with respect to laser chirp and gas pressure has been performed. The results summarized in Fig.3 show, firstly, that the sign of laser chirp is very critical in the pulse compression. It clearly shows that much shorter pulses were obtained in the case of positively chirped pulses, consistent with the larger spectral broadening shown in Fig. 2. Secondly, the results show that the optimum pressure increases with laser chirp due to the increased pulse duration. In the case of the chirp-free 28-fs pulse the minimum pulse duration was obtained from 200-torr Ar, while in the case of positively or negatively chirped 30-fs pulse it was from 220-torr Ar. The optimum pressure increased further in the cases of longer pulses.
The results of maximum spectral broadening obtained with different laser chirp are shown in Fig. 4(a). The spectrum after filamentation by positively chirped 30-fs pulse is extended clearly to shorter wavelengths than that of chirp-free 28-fs pulse. The filamentation spectrum of negatively chirped 30-fs pulse is very weak below 650 nm and intense only around the region of the fundamental laser spectrum. The laser filamentation of chirp-free 28-fs pulse in 200-torr Ar produced 6.3-fs pulse, while it was 12 fs in the case of negatively chirped 30-fs pulse In the case of positively chirped 30-fs pulse the shortest pulse duration of 5.5 fs was achieved with 220-torr Ar, as shown in Fig. 4 (b) with its spectral phase, acquired using the FROG measurement. With larger positive chirp the compressed pulse duration became longer - 5.7 fs with positively chirped 32-fs pulse and 6.8 fs with positively chirped 36-fs pulse. The transform-limited pulse duration was 4.2 fs in the case of positively chirped 30-fs pulse, which is very comparable to the cases of positively chirped 32-fs and 36-fs pulses. The output energy right after the gas cell was about 2.5 mJ. In the case of positively chirped pulse the energy contained in the supercontinuum was, however, about 0.9 mJ with the beam size of 3 mm, and the energy contained in compressed 5.5-fs pulse was 0.5 mJ in the central 2-mm section, while it decreased to 0.4 and 0.3 mJ for positively chirped 32-fs and 36-fs pulses, respectively. Pulse compression after filamentation was thus optimized for the case of positively chirped 30-fs pulse.
Depending on the sign of laser chirp, the spectral broadening and compressed pulse duration showed significant difference. Figure 3 clearly shows that the compressed pulse duration is much shorter in the case of positively chirped pulses than in the case of negatively chirped pulses. The generation of broader spectrum with positively chirped pulses can be understood from the consideration that the spectral composition of positively chirped pulses, increasing frequency in time, can enhance the spectral broadening due to the SPM induced by the Kerr effect - redshift in the leading edge and blueshift in the trailing edge. In the case of negatively chirped pulses, however, the spectral broadening is not so effective with the reversed spectral composition. The spectral broadening may occur also due to the SPM by ionization and due to the self-steepening of laser pulses . The self-steepening process occurring in the trailing edge of the laser pulse contributes to spectral broadening in the blue side, which enhances the spectral broadening in the case of positively chirped pulses. The spectral blueshift due to ionization is induced in the leading edge of the laser pulse, opposite to the Kerr effect. However, the contribution from the ionization would not make much difference in the laser chirp-dependent spectral broadening, because the optical field ionization, estimated using the Ammosov-Delone-Krainov(ADK) formula , is not sensitive to laser chirp.As a consequence positively chirped laser pulses can attain much larger spectral broadening.
The length of filament was also found to be very sensitive to laser chirp. Though the spectral broadening was much more effective with positively chirped pulses, much longer filament length was observed with negatively chirped pulse. In our experiments, the filament length in the Ar cell was about 55 cm for the chirp-free 28-fs pulse, and became shorter with positively chirped pulses and longer with negatively chirped pulses. In the case of positively chirped 30-fs pulse the filament length was about 45 cm, while it became about 75 cm in the case of negatively chirped 30-fs pulse. The experimental results agree with the numerical simulation by Nuter et al.  that showed the formation of longer filament length with negatively chirped pulse than with positively chirped pulse. As the SPM process induces positive chirp to the laser pulse propagating in an ionizing gas medium [9, 11], the negatively chirped pulse can be compressed during the propagation and, thus, the filamentation can be extended to longer distance because of enhanced laser intensity. This is another indication that the filament formation was also delicately influenced by laser chirp.
A further analysis of the laser chirp effect on filamentation was performed from the measurement of group delay dispersion (GDD) contained in laser pulses. The GDD’s of the output pulse obtained from the FROG measurement were 5 and -17 fs2 for the positively chirped and negatively chirped 30-fs pulses, respectively. With the GDD of the input pulse (110 fs2 for 30 fs pulse) and added GDD’s in 2.5-m, 220-torr Ar (10 fs2), 1-mm output window (35 fs2), 1-m air (20 fs2), and chirped mirrors (-160 fs2), the induced GDD’s during the filamentation were estimated to be -10 and 190 fs2 for the positively chirped and negatively chirped 30-fs pulses, respectively. In the case of the chirp-free 28-fs pulse the GDD value is the half-way between the two chirped pulses. Thus, GDD, or induced laser chirp, during filamentation was minimal for the positively chirped pulse, while it was increasing with the decreased laser chirp. This clearly shows that the induced positive chirp during filamentation increases with filament length. Furthermore, it is notable that the difference in GDD values after filamentation became only one tenth of that before filamentation, allowing the final chirp compensation with the same chirped mirrors; the filamentation process adjusts the GDD value contained in a laser pulse by itself.
In summary, we have generated 5.5-fs, 0.5-mJ laser pulses using the filamentation pulse compression in Ar with positively chirped 30-fs pulse. The laser spectrum after filamentation was optimized, under the condition of stable filament formation, by controlling initial laser chirp and gas pressure to obtain broadest spectrum and shortest pulse duration. The positively chirped laser pulse generated broader spectrum, but the filament length was much shorter, compared to chirp-free or negatively chirped 30-fs pulse. The basic physical process could be understood by considering the SPM process during filamentation. Few-cycle high-power laser pulses achieved in this work will be very valuable for ultrafast science investigations such as attosecond physics research.
This work was supported by the Korea Science and Engineering Foundation through the Creative Research Initiative Program.
References and links
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