Fig. 1 A: Optical fluence inside the filament produced by a 10 picosecond‐long laser pulse, vs. input pulse energy.
The fluence is ~100 J/cm 2 for all pulse energies, a direct consequence of intensity clamping inside the filament. B: Fluence vs. pulse duration. The inset shows the far‐field fluence distribution. The shadow pattern is consistent with the screening of the laser beam by thick and dense plasma channel in the middle of the beam surrounded by several smaller plasma filaments. C: Simulation of the on‐axis temporal evolution of a 2 ps‐long laser pulse propagating through the filamentation zone, showing the development of an intense, clamped spike (~80 TW/cm 2 ) on the leading edge of the pulse.
Keywords: laser ﬁlamentation, picosecondlaser pulses, nonlinear propagation, optical ionization
The propagation of intense picosecondlaser pulses inairin the presence of strong nonlinear self- action effects and air ionization is investigated experimentally and numerically. The model used for numerical analysis is based on the nonlinear propagator for the optical ﬁeld coupled to the rate equations for the production of various ionic species and plasma temperature. Our results show that the phenomenon of plasma-driven intensity clamping, which has been paramount in femtosecond laser ﬁlamentation, holds for picosecond pulses. Furthermore, the temporal pulse distortions in the picosecond regime are limited and the pulse ﬂuence is also clamped. In focused propagation geometry, a unique feature of picosecond ﬁlamentation is the production of a broad, fully ionized air channel, continuous both longitudinally and transversely, which may be instrumental for many applications including laser-guided electrical breakdown of air, channeling microwave beams and air lasing.
Pavel Polynkin 1 ,Andreas Schmitt‐Sody 2 , Heiko G. Kurz 3 , Luc Bergé 4 and Stefan Skupin 5
1. College of Optical Sciences, University of Arizona, Tucson, Arizona, USA 2. Air Force Research Laboratory, Albuquerque, New Mexico, USA 3. Institut für Quantenoptik, Leibniz Universität Hannover, Hannover, Germany
du moins dans la partie la plus intense du filament. Au cours des quinze derni` eres ann´ ees de nombreuses applications bas´ ees sur son utilisation ont ´ et´ e propos´ ees comme le paratonnerre la- ser [ Zhao 95a , Chin 99 , Kasparian 03 ], le captage de forts courants [ Houard 07a ], la r´ ealisation de guides d’onde dans l’atmosph` ere [ Musin 07 , Chateauneuf 08 ], d’antennes radiofr´ equence [ D’Amico 08b ] ou la g´ en´ eration de rayonnement T´ erahertz ` a distance [ Proulx 00 , D’Amico 07 ] (voir Partie 3.). Dans la perspectives de toutes ces applications aussi bien que d’un point de vue purement fondamental il est crucial de bien connaˆıtre, voire de contrˆ oler les caract´ eristiques de ce plasma. Or sa caract´ erisation s’av` ere plus complexe que celle de l’impulsion lumineuse du filament, puisque des mesures in situ sont difficilement r´ ealisables, et que sa mod´ elisation par un code num´ erique particulaire s’av` ere quasiment impossible en raison du nombre de parti- cules en jeu et du caract` ere atypique de ce plasma. Comme nous le verrons par la suite, la mise en ´ evidence et l’´ etude exp´ erimentale du plasma peut se faire soit par l’analyse de son rayon- nement (luminescence des mol´ ecules excit´ ees[ Talebpour 99 , Hosseini 04 ] ou ´ emission dans le domaine T´ erahertz [ Proulx 00 , Tzortzakis 02 ]), soit par des exp´ eriences pompe-sonde r´ esolues en temps (diffractom´ etrie femtoseconde [ Tzortzakis 00 ], spectroscopie THz[ Kampfrath 07 ] ou visible, holographie [ Papazoglou 08 ]), soit enfin par des mesures ´ electriques de sa conductivit´ e [ Schillinger 99 , Ladouceur 01 , Tzortzakis 99 ].
inair at 800 nm.
Once the laser pulse has left, it leaves in its trail a thin column of weakly ionized plasma, which recombines in less than 10 ns . During this process, energy from free electrons is transferred to rotational and translational de- grees of freedom of air molecules. Two-photon Raman ex- citation of rotational states has also been shown to be a very efficient path of energy transfer from the laser pulse to the medium [3, 4]. Eventually, this energy is converted into heat of air molecules over a nanosecond timescale and it is mostly confined to the volume initially occupied by the filament . Such a localized, fast energy depo- sition leads to the formation of an outward-propagating pressure wave and a central low-density channel present- ing the same cylindrical geometry as the filament [6, 7]. The system gets back to its initial pressure over a mi- crosecond timescale and the density hole decay is then governed by diffusion and can last for milliseconds .
α ∼ 2 have been extracted in focused propagation geometries, which reproduce experimental measurements of THz pulse energies [Figure 1(a)]. In contrast, similar scalings cannot be reached in a long-range filamentation geometry that features much lower plasma densities at longer wavelengths, as illustrated by Figure 1(b).
associated with nonlinear absorption of laser energy and with a decrease of the local refractive index. Both ef- fects act against the growth of intensity by self-focusing and eventually arrest the collapse. The interplay between nonlinear effects leads to the formation of a narrow light filament leaving a plasma channel in its wake, surrounded by a laser energy reservoir. This reservoir maintains an energy flux toward the filament core that compensates for nonlinear absorption. This optical entity can live over several meters and be generated at long distances [2, 3]. Ionization in the atmosphere by filamentation has been reported at a distance of 1 km from the laser . When the reservoir is exhausted and fails to feed the filament efficiently, a slowly diverging bright channel is observed and can be detected at several kilometers away from the laser source. Several teams have reported an effect called beam self-cleaning in the low power regime P ≈ P cr [5–
2 phasis on KDP crystals. Section III compares the fila-
mentation dynamics of short 50-fs pulses in silica glass and in KDP. Despite the comparable size of band gaps in silica and KDP, we report significant differences in the ionization rates leading to three times higher clamping intensities in KDP and a longer plasma channel. The former effect is caused by a weak 5-photon ionization cross-section; the latter is supported by transitions from the SLG states. At the same time, we identify very simi- lar spatio-temporal filamentation dynamics in both silica and KDP after rescaling the pulse power. Section IV examines longer pulses, for which we expect to enhance the impact of defect states over longer relaxation times, since the associated electron recombination time lies in the picosecond timescale. Most of the filamentation char- acteristics for short pulses are, however, retrieved.
OCIS codes: 190.5530 Pulse propagation and solitons, (350.5400) Plasma.
THz spectroscopy is rapidly emerging as a new domain with rich implications in both fundamental and applied sciences. However, up to now a major obstacle for its use has been the strong attenuation (100 dB/km) that THz radiation experiences while propagating inair, due to the presence of water vapor. Recently, a method of generating THz was demonstrated which provides a solution to this problem . It was shown that a femtosecond laser pulse undergoing filamentation emits a strong THz pulse confined in a narrow cone oriented along the forward direction. By simple manipulation on the laser pulse undergoing filamentation, it is possible to place the filament formation, hence the THz radiation source, in the immediate proximity of a remote sample. Therefore in terms of effective irradiance at long distance, this method easily surpasses other known THz sources in spite of the fact the overall efficiency of the transition-Cherenkov emission is relatively low. A first demonstration showed the production of THz at a distance of 30 meters from the laser. Another advantage of this method is its extreme simplicity: filamentation being a self-action does not require any precise alignment.
4.1. THz generation by one filament, two filaments
In 2007, D’Amico et al. reported a forward THz pulsed radiation stemming from a femtosecond laser filament inair . They observed that the THz is radiated in a hollow-cone structure in the laser propagation direction, with a radial polarization (see figure 13). The authors developed a Transition- Cherenkov model which reproduced the above observed features . In this model, the heavily damped longitudinal plasma oscillation produced in the wake of the propagating pulse is at the origin of the THz pulsed emission. Terahertz (THz) radiation produced by ultrashort laser pulses inair attracted much attention in recent years, since it has some unique properties. The THz source can be positioned at the proximity of a remote target by displacing the onset of filamentation. This solves the long-standing problem of the poor propagation of THz through atmosphere due to strong absorption by water vapor. In contrast to other THz generation techniques with short laser pulses, there is no obvious limit to the laser power that can be used, since there is no material in the path of the pulse that can be damaged.
It is now well known that nonlinear propagation of femtosecond laser pulses and lamen- tation inair open the way to many atmospheric applications. Actually, the high intensity delivered by the laments provides unique features for these applications. Since the atmo- spheric propagation is complex, there still remains challenges about lamentation inair. One of them is considering realistic conditions. Indeed outdoor applications of ultrashort laser pulses require a knowledge about the lamentation over long propagation distances. Another important issue which could be mentioned here is enhancement of backward emission signal created in interaction zone; this aspect is extremely important for remote sensing experiments. Other remarkable matter which we consider in this thesis is developing a diagnostic technique of multiple gases inair based on femtosecond lamentation. However the high intensity deliv- ered by the laments provide an advantage for performing remote identication of pollutants inair using uorescence spectrum of the excited species, since there are some diculties in this detection technique, it is very challenging to nd some ways to overcome existing problems.
Figure 9 and Figure 10 present the different phases of the interaction. First the formation of the heated channel and the cylindrical blast wave is observed (T0+0.3 µs to T0+8.9µs), as in the tests in quiescent air (Figure 5). These features are also revealed in the zoomed viewed in Figure 11. The heated core is convected downstream and interacts with the detached bow shock. Because of the high temperature in the heated core, the flow becomes locally subsonic and enables the formation of a recirculating bubble expanding upstream from T0+4.6 µs to T0+35.7 µs in Figure 9 and Figure 11. Then the recirculating bubble expands radially between T0+60.5 µs and T0+112.1 µs (Figure 9 et Figure 10), and is convected downstream by the flow. One should note that, during this phase, the recirculating flow is probably turbulent. In addition, during the convection downstream of the bubble, the flow becomes unstable and no longer axisymmetric. The flow recovers its initial configuration approximately 250 µs after the laser energy deposition.
experimental setup. The first step of the E-field calculation consisted in assessing the E-field distribution in a perfect and infinite mirror structure. The mirror parameters (layers thicknesses and optical indexes of HfO 2 and SiO 2 ) were identical to those of the mirror
described in Section 2. Then, this E-field was considered as a source term for the E-field calculation in the damaged structure represented on Fig. 7 (a), using a scattered field method provided by COMSOL. The damaged structure for the simulation was chosen to fit the engineered hole in terms of dimensions and depth. Perfect Matched Layers (PML) were used in order to truncate the substrate, the air and each layer of the multilayer stack (see the four rectangular borders in Fig. 7). It is a numerical concept already implemented in COMSOL that avoids reflections due to edge of the calculation window. PML thickness was set at 1030nm, i.e. the working wavelength. The EFI was calculated on each point of the structure, as shown in Fig. 7 (b). Due to the mirror design, the light does not penetrate deep in the structure (EFI goes to zero towards the substrate) and the EFI maximum values are reached in the top layers. Given this result and knowing the intrinsic LIDT of each material reported in Table 2, the effective LIDT of each point of the structure was calculated using Eq. (2). It is represented in Fig. 7 (c). In the given example, one can observe that most part of the structure withstood laser irradiation at fluence higher than 1.5J/cm 2 . However, some points at the right
In this Letter we describe the scheme of a tabletop laser that enables us to perform SFG spectroscopy from 10 to 21 µm. The picosecond pump laser consists of a Nd:YAG oscillator mode locked by a frequency-doubling nonlinear mirror combined with a GaAs platelet acting as a two-photon absorber. Careful adjustment of the mirror elements (i.e., telescope distance, air space between the crystal and the dichroic mirror, diameter of the intracavity aperture) allows us to achieve pulse durations as short as 8.3 ps. A train of ~100 pulses (train repetition rate of 25 Hz, pulse repetition rate inside the train of 100 MHz) is extracted from the laser cavity: The train envelope is illustrated in Fig. 1. 5,6
The ionization front produced by an intense femtosecond laser pulse propagating inair is the source of a THz radiation emitted in a narrow cone in the forward direction [1, 2]. The radiation is produced by the longitudinal oscillations of the plasma left in the wake of the moving ionization front. These plasma oscillations are excited by the ponderomotive force of the laser pulse and are heavily damped by electron collisions on a picosecond timescale. The radiation is emitted by a dipole-like structure moving at the speed of light, it is therefore similar to the Cerenkov emission created by a pair of opposite charges. Because of the simplicity in its implementation, this THz source is suitable for many applications. It requires no optical element or crystal in the path of the femtosecond laser which would be prone to damage or induce dispersion, and is therefore easily scalable to higher laser intensities. In contrast to other methods such as four wave mixing of femtosecond pulses at frequencies ω and 2ω, there is no phase sensitive adjustment or precise alignment between pulses. Another attractive feature is the fact that such a source can be placed in the proximity of distant targets, solving thereby the longstanding problem posed by the strong attenuation of THz radiation inair due to water vapor. Displacing the onset of ionization is easily achieved by either imposing a negative linear chirp to the femtosecond laser pulse or by enlarging the beam diameter [3, 4].
Figure 5-3(a) displays the spectral evolution when measuring the spectrum along z, with pulse energy of 2.4 mJ focused by the 3 m lens. Two new IR peaks started to appear inside the filament zone (around z=300 cm). They continuously shifted to longer wavelength when z increased. We now follow the continuous wavelength shift of the dominant new IR peak. The wavelength shift as a function of z is shown in Figure 5-3(b) (squares). A strong red-shift (roughly from 800 nm to 865 nm) occurred during propagation inside the filament zone and saturated around 865 nm for propagation beyond the filament zone. The conversion efficiency, defined as the ratio of the resolved dominant new IR peak over the whole spectrum through integration in frequency scale, is about 22%. Figure 5-3(b) also shows the wavelength shift with input pulse energies of 1.0 mJ (circles) and 3.6 mJ (triangles). The wavelength shift for 1.0 mJ is about 35 nm, and 100 nm for 3.6 mJ. By comparing the three curves in Fig. 5-3(b), we can conclude that, at higher pulse energies (3.6 mJ), the self-frequency down shift starts earlier (around 260 cm) because filamentation begins at shorter z, which results in a longer self-guided column. In this case, the wavelength shift is more pronounced (about 100 nm). Figure 5-3(c) shows the spectral evolution when the laser pulses were focused by 4 m lens with pulse energy of 2.4 mJ. And the corresponding wavelength shifts are displayed in Fig. 5-3(d). Compared to the situation with 3 m lens, the red-shift is stronger (about 100 nm for 2.1 mJ and 130 nm for 3.6 mJ). This is due to a longer filament (self-guided column) generated in the case of 4 m lens. It is important to note
fluency is uniform, as evidenced by Fig. 5 (a). The correspond- ing spatio-temporal electric field profile in Fig. 5 (b) shows that plasma has only started to deplete the trailing part of the pump pulse, as one would expect from the usual filamentation dy- namics [ 34 , 35 ]. The generated THz vortex at this early stage of pump propagation has a single phase singularity in the center. The intensity is circular with azimuthal modulation, and the modulation depth is larger for lower frequencies, as predicted by Fig. 1 . In contrast, at (z = − 4 mm) the pump pulse has un- dergone severe transverse distortion [see fluency in Fig. 5 (c)], and the spatio-temporal field profile in Fig. 5 (d) looks much more complex. These strong perturbations of the pump clearly affect the intensity distribution of the THz vortex and produce secondary singularities in the generated THz field. Neverthe- less, additional singularities have alternating signs such that the total topological charge of the singular THz | l THz | = 1 is pre- served during propagation at all relevant frequency components. Overall, our simulations results suggest that the produced THz vortices are surprisingly stable against pump distortions.
with the laserin the absence of air flow. In this image, recorded 6.2 s after the laser shot, one can observe a 10-cm-long central hot channel of low air density generated by the filament and a radially expanding shock front, more apparent in movies S1 and S2. In the presence of air flow, the hot channel is convected toward the test model front nose where it interacts with the detached bow shock. The simulation shows that the combination of the radial density gradient of the hot channel with the axial pressure gradient of the shock front induces a baroclinic torque that produces vorticity (14) and induces a forward-propagation recirculating bubble. During this phase, the pressure at the model nose front rises, and the drag signal shows a small increase, as shown in Fig 2. This transient in- crease is due to the interaction of the conical shock formed by the expanding recirculating bubble and the detached shock of the blunt body. This interaction deflects the incoming flow inward, resulting in a high-pressure jet impinging on the front nose. When the hot chan- nel is entirely convected in the recirculating zone, the forward prop- agation ceases. The recirculating flow forms a toroidal vortex that expands radially and then progressively flows downstream along the test body surface (Fig. 4). As can be seen in Fig. 5, these schlieren images are well restituted by the hydrodynamic code CEDRE from ONERA, where the measured deposited laser energy and the air flow conditions are taken as input conditions (15). The lower pres- sure at the core of the vortex is at the origin of the drag reduction. It corresponds to a peak reduction of drag amounting to more than 50% when the deposited laser energy reaches 10 mJ (see Fig. 2). The quantity of absorbed laser energy is obtained from absolute mea- surements of density in the heated air channel.
surfaces triggers collisionless current filamentation, thus giving rise to electromagnetic structures such as those sketched in Fig. 2e. In order to investigate the large-scale hot-electron dynamics in a self-consistent way, we have performed a 2D particle-in-cell (PIC) simulation using the code calder . This simulation describes the laser-plasma interaction (and related collisional and ionization processes) in the x − y plane shown in Fig. 1, with half-reduced Al density to alleviate the computational effort (see Methods). Hereafter, the time origin is when the pulse maximum reaches the target surface. We see in Fig. 3a that, already at t = 0.41 ps (i.e., 1.44 ps after the start of the simulation ), the rear target surface has moved a distance > 10 µm, and that magnetic modulations have developed in the expanding plasmas from the two target sides (see Fig. 3b and Supplementary Information, Figs. S1 and S7). At the backside (x > 44 µm), they extend up to y ' 150 µm from the laser spot, with a typical wavelength λ p ' 6 µm.