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Self-guided propagation of femtosecond light pulses in water A. Dubietis, G. Tamoˇsauskas, I. Diomin, and A. Varanaviˇcius ˙ Department of Quantum Electronics, Vilnius University, Sauletekio Avenue 9, Building 3, LT-2040 Vilnius, Lithuania Received December 6, 2002 We report experimental evidence of self-guided propagation of femtosecond laser pulses in water. A light filament induced by 170-fs, 527-nm pulses has a diameter of 60 mm (at the 1兾e 2 level) and persists over a distance of 20 mm. The filamentary mode is sustained over a wide range of input power, and the energy excess is converted into conical emission. In the time domain, the pulse trapped in a filamentary mode experiences a number of splittings occurring in the early stage of filament formation. © 2003 Optical Society of America OCIS codes: 190.5530, 190.7110, 320.2250.
The discovery of self-channeling of femtosecond light pulses in air1 revived a considerable interest to self-action phenomena. Self-guided propagation of ultrashort (from 50 fs to 5 ps) IR, visible, and UV pulses in air was recently reported.2 – 5 The most exciting feature of self-guided propagation is that formation of light f ilaments is observed with powers well above critical, preventing collapse of the beam. Now there is agreement in the literature that self-guiding of the beam occurs as a consequence of dynamic balance between Kerr self-focusing and defocusing effects in the electron plasma generated through the multiphoton ionization. The f ilamentation process involves a rich variety of nonlinear processes, including space – time coupling effects, playing a key role in the propagation dynamics. To this end, nondiffracting in space and nondispersing in time structures, persisting over distances greater than a couple of Rayleigh ranges, are foreseen.6,7 Recently, self-guiding of femtosecond laser pulses in fused silica has been experimentally observed.8 – 10 Although the intrinsic linear and nonlinear properties of gases and condensed media are very distinct, the underlying physical phenomena leading to the formation of self-organizing spatially and temporally localized light structures are very similar. The characteristic parameters of the condensed media —group-velocity dispersion, Kerr nonlinearity, and ionization levels—differ by orders of magnitude compared with those in gases; thus the typical f ilament diameter is a few tens of micrometers, and the energy and the length of the f ilament scale down by several orders of magnitude. For clarity, it must be noted that condensed media for the white-light continuum generation have been used for decades. Except for short-scale filamentation, no apparent effect of self-guiding was observed. Preliminary indications of beam f ilamentation in water have already been reported.11 – 14 However, the tight focusing geometry used in these experiments promotes competition between the f ilament formation and the optical breakdown as a result of avalanche ionization, thus preventing self-guided propagation. In this Letter we report apparent self-guiding of femtosecond laser pulses in water that was achieved in conditions of relatively weak focusing geometry 0146-9592/03/141269-03$15.00/0
( f -number, 150). We present experimental data on formation, propagation, and temporal characteristics of the filamentary mode. We used a chirped pulse amplifier –based Nd:glass laser system, TWINKLE, provided by Light Conversion, Ltd., Vilnius, Lithuania. The laser system runs at a 33-Hz repetition rate and initially delivers a 1-ps, 4-mJ pulse at 1055 nm. A 170-fs pulse at the second-harmonic wavelength (527 nm) was generated with the nonlinear pulse compression technique.15 A small fraction 共⬃10 mJ兲 of the second-harmonic radiation was transmitted through a dielectric mirror and was used in the experiment. The energy was varied by means of a half-wave plate and a polarizer. An iris diaphragm was used for setting the desired beam diameter on the focusing lens. A pair of f 苷 1800 mm lenses and a pinhole served as a spatial filter, wiping out the diffraction fringes. The water cell was placed at 49.5 mm with respect to the focusing lens 共 f 苷1500 mm兲, with the geometrical focus inside the cell. The output face of the water cell was then imaged onto the CCD camera (Pulnix TM-6CN and frame grabber from Spiricon, Inc., Logan, Utah) with 53 magnification by means of an achromatic objective 共 f 苷 150 mm兲. Our setup allowed us to easily vary the initial diameter of the beam (thus the diameter of the focal spot varied from 350 to 50 mm as a consequence), and we found that multiple f ilaments could be excited when we approached tighter focusing conditions. For our experiment we chose the initial 1兾e2 diameter of the incident beam d 苷 3.0 mm (all further diameter estimates are given at this intensity level) that resulted in an ⬃140-mm beam waist at the input face of the water cell. Under these focusing conditions, only a single filament is formed in a wide range of incident power. The f ilament starts emerging as the incident energy reaches 0.6 mJ. This value corresponds to P 艐 3.5 MW, approximately three times that of Pcrit 苷 3.77l2 兾共8pnn2 兲 艐 1.15 MW, with n 苷 1.34 and n2 苷 2.7 3 10216 cm2 兾W taken from Ref. 16. After the filament is formed, the spot diameter shrinks to 60 mm and stays almost constant over tens of millimeters of propagation. This result was verified by measurement of the diameter of the output spot of the cell lengths of 20, 31, 41, and 53 mm. © 2003 Optical Society of America
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Three-dimensional beam profiles as recorded with different incident energies and cell lengths are depicted in Fig. 1. Figure 1(a) represents the transient regime of the f ilament formation, but Figs. 1(b)– 1(f ) refer to a filamentary mode with a diameter of 60 6 5 mm. Because of the discrete cell lengths we were not able to measure exactly at which propagation distance the filament started and ended. Therefore, we estimated the f ilament length to be at least 20 mm. At the output of the 53-mm-long water cell we measured a spot diameter of 120 mm, indicating that diffraction finally started dominating the propagation process. Formation of the f ilament is accompanied by generation of a white-light continuum that extends over several hundreds of nanometers [Fig. 2(a)]. In fact, the continuum covers the entire visible spectral range but is beyond the detection limit of the photodiode array that we used. In our experimental conditions we found that thresholds for continuum generation and filament formation coincided. The spectral-angular distribution of radiation exiting the water cell is represented by a digital camera snapshot taken from a milky glass placed at the output plane of a polychromator [Fig. 2(b)]. The following structure could be seen: A continuous white-light spectrum is trapped within the filamentary mode, whereas the conical emission is seen as a combination of several overlapping colored cones. In fact, the conical emission represents a pair of interrelated cones extending to the blue and the red sides from the central frequency. In the blueshifted cone the wavelength decreases outward from the propagation axis, whereas the reverse wavelength dependence is observed in the redshifted cone. The half-angle of the emission cone is a function of the incident energy, and we believe that the number of cones is directly related to the temporal features of the f ilamentary mode; i.e., each of the split pulses (see the text below) generates its own pair of emission cones. The energy content of the radiation was measured with a large-aperture calibrated photodiode and an iris aperture placed in the image plane of the output face of 31-mm-long water cell. The open aperture transmitted the whole spatial structure (filament 1 conical emission), whereas the closed aperture isolated only the central part (filament); see Fig. 3. Once the filament is formed, the character of the trend Etransmit 兾Ein is no longer linear, pointing to a nonlinear loss mechanism, which could be attributed to the plasma generation and subsequent absorption. The energy trapped within the f ilamentary mode is fairly constant at f ixed propagation length, and the energy excess is converted to conical emission. The filament energy as a function of propagation length exhibits a gradual decrease and differs by a factor of 2 for cell lengths of 20 and 41 mm. The pulse emerging from the water cell was scanned in time with the original 527-nm, 170-fs pulse by means of sum-frequency mixing. The output face of the water cell was imaged onto a 20-mm-thick b-barium borate crystal, which made possible phase matching across the whole spectrum of the filamentary mode. With temporal resolution limited to the duration of the scanning pulse, we were not able
to evaluate temporal features shorter than 170 fs. However, the shapes of the cross-correlation traces clearly indicated that pulse splitting occurred, and the distance between the split pulses grew with increasing incident energy and propagation length (Fig. 4). The same result applies to the number of split pulses. With input power P . 6Pcrit , we clearly identif ied a sequence of three pulses. The f itting procedure reveals that the peak width almost coincides with the duration of the sampling pulse, thus pointing to shorter duration of the split pulses. This observation confirms the general trend of pulse temporal behavior under conditions of self-guided propagation in condensed and gaseous media with positive group-velocity
Fig. 1. Normalized three-dimensional beam prof iles at the output plane of the water cell. The output power is 3.5 Pcrit (left column) and 6.6 Pcrit (right column). Cell lengths are 20, 31, and 41 mm for the top, middle, and bottom rows, respectively.
Fig. 2. (a) On-axis spectrum and (b) spectral-angular distribution of the radiation at the exit of the 31-mm-long water cell at P 苷 6Pcrit .
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and propagation processes. Conical emission could be seen as an energy-stabilizing factor, since the energy trapped within the f ilamentary mode remains almost constant and is not dependent on the incident power. In the time domain the filament represents a sequence of short split pulses, with the number of splittings depending on the incident energy and on the propagation length. We gratefully acknowledge fruitful discussions with Paolo Di Trapani. A. Dubietis’s e-mail address is
[email protected]. References
Fig. 3. Transmitted energy versus incident energy as measured with open and closed iris aperture. The cell length is 31 mm.
Fig. 4. Cross-correlation traces of the filamentary mode scanned by a 527-nm, 170-fs pulse.
dispersion.6,17,18 To be precise, the situation of pulse splitting as well as the number of splittings from a general point of view is still a concern. In conclusion, we have observed apparent self-guiding of femtosecond light pulses in water. A single f ilament, which has a white-light spectral content and a finite 1兾e 2 diameter of 60 mm, propagates over a distance of 20 mm. Our observations point to the importance of conical emission during the f ilament formation
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