APPLIED PHYSICS LETTERS 87, 161105 共2005兲
Ultrafast control of multiple filamentation by ultrafast laser pulses Jiansheng Liua兲 Max-Planck-Institut für Quantenoptik, Laserchemie, Hans-Kopfermann-str.1, 85748 Garching, Germany and State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Shanghai 201800, People’s Republic of China
Hartmut Schroeder Max-Planck-Institut für Quantenoptik, Laserchemie, Hans-Kopfermann-str.1, 85748 Garching, Germany
See Leang Chin Center for Optics, Photonics and Laser (COPL), Department of Physics, Engineering Physics and Optics, Laval University, Quebec City, Canada G1K 7P4
Ruxin Li and Zhizhan Xu State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Shanghai 201800, People’s Republic of China
共Received 22 April 2005; accepted 9 September 2005; published online 12 October 2005兲 Control of multiple filamentation by laser-induced microlens effect due to a nonlinear interaction of two overlapping laser beams inside a glass plate was demonstrated. Individual or multiple spots on the white light pattern which is a product of multiple filamentation through a mesh can be switched on and off with a very high contrast ratio on a femtosecond time scale. This phenomenon can find applications such as ultrafast optical switch and high-speed sampling. © 2005 American Institute of Physics. 关DOI: 10.1063/1.2106022兴 Filamentation and white light production from the nonlinear propagation of ultrashort laser pulses in transparent media is a universal phenomenon and is still of major interest since many applications have been found1,2 or will become possible. Filamentation is normally observed in early experiments by softly focusing a laser beam into optical media or observed when an ultrashort laser pulse propagates over a long distance in air or solids. When the laser power is much higher than the critical power for strong self-focusing, multiple filaments occur. Multiple filamentation originates from local random inhomogeneities in the medium or irregularities of the beam profile and is unavoidable normally.3,4 Moreover, such multiple filaments will undergo competition for energy.5 However, by inducing strong intensity gradients or phase distortion in the input beam profile, the multiple filamentation effect of the irregularities can be overcome and controlled.3,6–9 By inserting a slit or mesh into the beam to produce highly structured diffraction patterns, we have shown partially and fully controlled multiple filamentation in liquids.3,6 However, until now all of these multiple filamentation processes are controlled by using passive diffractive optical elements. In this letter we demonstrate that multiple filamentation can be controlled by another femtosecond laser beam. The white light spot patterns as a product of multiple filamentation can be switched on and off with a very high contrast ratio on a femtosecond time scale, which can find new applications such as ultrafast optical switch10 or switching array and high-speed sampling. The underlying physics behind this control of multi-filamentation is also discussed. Our experimental setup is shown in Fig. 1. A Ti:sapphire laser beam 共1.9 mJ, 60 fs, 1 kHz兲 is divided by a beam splitter into two. One beam 共pump laser兲 which has 80% of the total energy is launched through a metallic wire mesh a兲
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共5 ⫻ 5 meshes, unit cell 497⫻ 497 m, wire width 54 m兲 into a 10-mm-thick cell filled with ethanol. A 2-mm-thick BK7 glass plate which is used as the optical medium for the interaction of the two beams is placed in the beam between the cell and the mesh. The wire mesh creates on the surface of the cell a symmetric diffraction pattern which can be controlled by changing the distance from the mesh to the cell. Although the generated diffraction patterns appear to be very rich and complicated, only those peaks whose intensities are higher than the threshold for strong self-focusing can develop into mature filaments and produce white light.6 The output white light patterns are imaged onto a charge coupled device camera by using a green filter 共transmission is high only for ⬍ 500 nm兲. The other beam 共switching laser兲, which has 20% of the total energy, is focused by a lens before it passes through the glass plate. The centers of the two laser beams overlap on the surface of the glass plate at a small angle of 4.5° and the time delay between them can be changed by a computer-controlled optical delay line. The pump laser beam before the mesh has a Gaussian profile with a radius of 4 mm and the intensity is about 6 ⫻ 1010 W cm−2. The distance from the mesh to the cell is selected as 170 mm. The glass plate is inserted in the beam 8 cm away from the cell. The maximum intensity of the pump laser inside the glass plate increases by a factor of ⬃4 at the
FIG. 1. Experimental setup for the control of multiple filamentation in ethanol by using a switching femtosecond laser pulse.
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FIG. 2. 共a兲 Numerically calculated diffraction pattern of the pump laser beam on the surface of the cell after diffraction of a wire mesh identical to that used in the experiment. 共b兲 Measured diffraction pattern. 共c兲 Line profile along one row of peaks shown in 共a兲. 共d兲 White light pattern 共experiment兲 produced by the multiple filamentation of the corresponding major 8 ⫻ 8 peaks in the diffraction pattern.
strongest spots of the diffraction pattern. The diameter of the switching laser beam on the surface of the glass plate is ⬃2 mm and the intensity is ⬃2.5⫻ 1011 W cm−2. In Fig. 2共a兲 we show the numerically calculated diffraction pattern of the laser beam on the surface of the cell after diffraction of the wire mesh. The measured diffraction pattern is shown in Fig. 2共b兲. By the diffraction of the wire mesh the uniform beam profile is transformed into a very rich and complicated pattern. There are mainly 8 ⫻ 8 peaks symmetrically distributed inside the beam together with a lot of secondary peaks with lower intensities. The line profile along one row of peaks of Fig. 2共a兲 is shown in Fig. 2共c兲. Since the selffocusing effect strongly depends on the radial gradient, filamentation preferably happens around each peak and this structure of electric field will be maintained except for the increase of the contrast ratio. The evolution of the beam profile will not abide by the Talbot effect of diffraction any more during propagation in ethanol since self-focusing will be dominant. The consequence is that the main diffraction pattern is likely to be “frozen” by the nonlinear effect during its propagation. Only those peaks whose intensities are higher than the threshold 共⬃1 ⫻ 1011 W cm−2兲 for strong self-focusing within 1 cm can transfer into mature filaments and produce white light.3,6 Figure 2共d兲 shows the experimental result of the propagation of the corresponding patterns shown in Figs. 2共a兲 and 2共b兲 through the ethanol cell. The output white light patterns show a one to one correspondence to the input patterns. No random hot spot can be detected. In Fig. 3 we only show the four typical white light patterns when the switching laser overlaps with the pump laser inside the glass plate at different time delays. Since the two laser beams overlap at a small angle, the time delay between the two pulses at different spatial positions is different even if the delay between the two is fixed. The zero time delay in Fig. 3 is thus defined as the time t0 when the switching effect
Appl. Phys. Lett. 87, 161105 共2005兲
FIG. 3. White light patterns when the switching laser overlaps with the pump laser inside the glass plate at different time delays. 共a兲 tdelay = t0. 共b兲 tdelay = t0 + 9 fs. 共c兲 tdelay = t0 + 61 fs. 共d兲 tdelay = t0 + 82 fs.
could be clearly observed while reducing the relative delay between the two pulses from “infinity.” At the beginning 共t = t0兲, as shown in Fig. 3共a兲, the left two columns of white light spots have been switched off and some spots have shifted positions a little bit from the original position to the right or the left compared to the white light patterns shown in Fig. 2共d兲 when the switching laser beam is off. When the switching laser is delayed by 9 fs, it is shown in Fig. 3共b兲 that a new column of spots appears which comes from the filamentation of the weaker peaks between the third and fourth columns of main peaks as shown in Figs. 2共a兲–2共c兲. In fact, this new column of spots appeared when we increased the delay from 9 to 40 fs, and another new column of “secondary” peaks 共between the fifth and sixth columns of main peaks兲 can also appear when we increased the delay from 100 to 130 fs. This kind of result indicates that mature filamentation can be switched on and off by a laser beam on a femtosecond scale. Different columns of white light spots can be switched on and off as shown in Figs. 3共c兲 and 3共d兲 when the switching laser is delayed by 61 and 82 fs, respectively. The switching is very stable from shot to shot. The switched pattern changes only when the time delay between the two laser pulses is changed. Generally, the column of “suppressed” peaks 共switched off兲 moved from left to right when we increased the delay from 0 to 150 fs since the overlapping zone of the two beams moves from left to right. However, some columns of suppressed peaks moved from right to left as shown in Fig. 3共d兲. This kind of phenomenon is mainly caused by our experimental arrangement where two laser beams overlap inside a glass plate which is placed between a mesh and ethanol cell. After interaction with the switching laser, the pattern of the pump laser will change due to the diffraction in free space before it arrives at the ethanol cell, which will not guarantee that changes of the pattern only take place at the overlapping zone. That is why we have observed that some columns of suppressed peaks move from right to left as shown in Fig. 3共d兲. The physics lying behind this switch on and off experiment of white light production can be explained as follows:
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rienced by the wave k1 at peak intensity after it comes out of the glass plate is expressed as
冕 冋 2mm
⌬共x兲 = 4n2
0
冉
E01 + E02exp −
共d1 − d2兲2 T2c2n
冊册
2
dz . 共2兲
FIG. 4. 共a兲 Schematic of two traveling waves propagating along different wave vectors k1 , k2 and overlapping at an angle . 共b兲 Phase shift ⌬共x兲 experienced by the pump laser due to the nonlinear interaction of two laser beams in glass.
In a nonlinear regime, when two laser beams propagate and overlap in optical media, they will be coupled by cross-phase modulation via the nonlinear refractive index. After separation, each beam has been changed in its phase front by the other. For two traveling waves which propagate along different wave vectors k1 , k2 共in x-z plane兲 and overlap at an angle in glass as shown in Fig. 4共a兲, their overlap both in space and time is localized within a small area. If the polarization of the electric field is in the direction 共y兲 normal to the x-z plane, their combined electric field can be described as
The calculated phase shift experienced by the pump laser in our case is shown in Fig. 4共b兲 when the two waves overlap at the center. The phase shift is space dependent and looks like a Gaussian profile in the x direction while in the y direction, the control beam has a broader intensity profile, hence a broader phase shift. If there is no second wave, the phase shift will be flat or only depend on the profile of one laser beam. Therefore, the second laser beam works as a micro quasi-cylindrical lens which brings about phase change in the pump beam “locally” 共in the x direction兲 and lengthwise along the y direction. That is why we observe changes along columns of spots in Fig. 3. The size, shape, and position of such microlenses could be modified by adjusting the overlapping angle, the laser’s spot size, and intensity distribution as well as the pulse duration. In the current experiment, the size of the microlens is estimated ⬃500 m in the x direction and the focusing length is ⬃37 mm in this case. Changing the time delay between the two laser beams acts as moving a microlens inside the pump beam. In this way, the diffraction pattern including the intensity and phase on the surface of the ethanol cell can be changed and so the multi-filamentation can be controlled. If the switching laser beam consists of a train of femtosecond laser pulses, it will work as a dynamic microlens array which can control the multiple filamentation in a more complicated way. And an optical switching array or high-speed sampling working in this way would be possible. In conclusion, we have demonstrated that multifilamentation and white light production can be controlled optically at ultrafast speed. The overlap of two femtosecond laser beams in an optical medium can reorganize multifilaments on a femtosecond scale. The white light patterns can be switched on and off and also shifted by controlling the second laser pulse. This new phenomena might be very useful in optical communications. 1
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