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Holographic Time-Resolved Imaging of Plasma Generated by High-Intensity Laser Pulses
Martin Centurion, Demetri Psaltis

Abstract. We study the formation and time-evolution of plasma generated in air by high intensity femtosecond pulses. We recorded holographic images of the plasma filaments on a CCD camera, which allowed us to reconstruct the phase change induced by the plasma on a probe. The distribution of the free electrons in the plasma is derived from the phase change, revealing multiple filaments and their breakup and recombination. We also demonstrated the capability of this holographic technique for capturing the time evolution of the plasma generation process by capturing a sequence of images of the filaments in a single-shot experiment.

Summary. One of the most exciting areas of research in nonlinear optics is the formation of light filaments with intense ultra-short laser pulses. A high-energy femtosecond pulse will focus into a thin filament and either propagate for a long distance or spontaneously break up and coalesce. The propagation of the pulses is mainly determined by the interplay of self-focusing, multi-photon absorption and defocusing due to plasma formation. There are also numerous other non-linear effects which can play a role but are not yet fully understood. We have experimentally studied the propagation of intense femtosecond laser pulses in air by measuring the plasma generated by the pulses.

Our holographic probing technique uses a probe femtosecond pulse to measure the phase change induced in the probe by the plasma. The free electron density can then be inferred from this phase change. Figure 1 illustrates the experimental setup. We use a Ti:sapphire laser amplifier operating at 800nm wavelength to generate the ultrafast event and to record it. The energy and duration of the laser pulse is 2 mJ and 150 fs FWHM, respectively. The pulse is split in two, with a major portion of the energy (1.2mJ) going into the pump beam. After a variable delay, the pump beam is focused with an achromatic lens (L3) of 5 cm focal length. The probe pulse propagates in a direction perpendicular to the pump and captures the plasma trail of the pump pulse in the air. The plasma is magnified by a factor of M = f2/f1. We record in-line (Gabor) holograms with the CCD camera at distance L from the image plane. The in-line hologram is essentially the interference between the diffraction of the plasma filaments and the probe beam. The hologram is then digitally reconstructed to retrieve the phase in the plasma filaments.

Figure 2a shows the hologram captured by the CCD camera. The pulse propagates from left to right. We numerically back propagate this hologram to reconstruct the object wave front and retrieve the phase change due to the object. The reconstruction algorithm calculates the convolution between the holographic fringes and a Fresnel phase kernel, i.e. an emulation of optical reconstruction.

Figure 1: Holographic setup. An intense femtosecond laser pulse (the pump pulse) is focused by L3 and left a plasma trail. A probe pulse transverses the plasma trail a few picoseconds after the pump pulse goes through. The system has a magnification of . L1, L2, L3: Lenses. M1, M2, M3, M4: Mirrors.

Figure 2: In-line hologram of the filament. The image resolution is 2184_1472, pixel size 6.8 _m _ 6.8 _m. The hologram is captured at L = 30 cm with a magnification of M = 12.5. A separate image frame of the probe beam alone is subtracted from the hologram.

From the digital reconstruction we obtain the phase change, from which we can obtain the free electron density. We show the spatial map of free electron density in Figure 3. The initial filament splits into several filaments after propagating for 0.1mm and then recombines into a single filament after another 0.2mm. The width of the smallest filament in the image is roughly 4micrometers, which is very close to the diffraction limit of the system, suggesting that finer filament structure could exist. The filament breakup and recombination process is better illustrated by plotting the free electron density at several lateral cross sections as marked with numbers in Figure 3. In view of the possible finer filament structure than the diffraction limit, it should be noted that the density of free electrons in the filament could be much higher.

The holographic recording method is also capable of capturing time sequences of the plasma generation process. We employ a similar setup as depicted in Figure 1, where mirror M4 is replaced with a mirror array consisting of four mirror segments, each of which has independent controls for angular and axial displacements. The displacements of the mirror segments are carefully tuned such that the four reflected probe pulses propagate with a small relative time delay and angular separation. The four pulses spatially overlap in the region of the air discharge, albeit temporally separated. Therefore, each probe pulse samples the event at a time set by the displacement of the mirror. The CCD camera records the four holograms with a magnification M = 2.5 at L = 16 cm, where the four probe beams (and thus the holograms) spatially separate. The variable delay line synchronizes the pump and probe pulses at the onset of the filament. We set the separation angle between the probe pulses sufficiently small (<3º) so that the events are recorded at approximately the same angle. However, to spatially separate the four holograms in the CCD sensor plane, the effective angular aperture of each individual hologram is limited to the separation angle between the probe pulses.

Figure 4 shows the digital reconstructions of the holograms recorded on the camera with relative time of each image t1 = 0, t2 = 1 ps, t3 = 2 ps, and t4 = 2.7 ps. The energy of the pump laser pulse is the same as the previous experiment. Despite the reduced spatial resolution due to the limited angular aperture, this result gives a dynamic picture for the time evolution of the plasma density.

Figure 4: Instantaneous time evolution of electron density in the filament. The relative time of the snapshots is t1 = 0, t2 = 1 ps, t3 = 2 ps, and t4 = 2.7 ps. Due to the small angular aperture, multiple filament structure is not recovered.

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