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Generation and characterization of the highest
laser intensities (1022 W/cm2)
S. Bahk, P. Rousseau, T. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. Mourou,
and V. Yanovsky
CLEO 2004, postdeadline
Abstract: The highest intensity of 0.8´1022 W/cm2 was achieved by using a large NA paraboloid corrected by a deformable mirror. Focused intensity with high spatial resolution is calculated from the precise wavefront characterization.
Modern high intensity experiments in the relativistic and ultra-relativistic regimes require the highest intensities characterized with the highest spatial resolution. These requirements exclude the conventional way to estimate intensity based on spot size measurement or ionization experiments, which do not provide detailed field information.
The generation and spatial resolution of 1022 W/cm2 power density is based on using a deformable mirror and a wavefront sensor. Our CPA, Ti:Sapphire, 45 TW (1.2J, 27fs) HERCULES  laser is focused with a 90º, f/0.6 paraboloid. A deformable mirror (DM) (Xinetics: 96 actuators, 2 mm inter-actuator stroke, 3 inch diameter) is used to correct the paraboloid and the laser beam aberrations. A wavefront sensor (Imagine Optic, 32 by 32 mircrolens array) measures the image of wave-front at the DM plane with a precision of l50. An optimum voltage distribution calculated from the phase is applied to the DM. Once the wave front is characterized, the focused field is calculated by using a vector diffraction integral (Stratton-Chu) anywhere in the focal volume [2,3].
Our approach relies on the precise knowledge of the laser wavefront. It requires an extremely shot-to-shot reproducible laser. It is the laser wavefront fluctuations that will ultimately limit the focused intensity and its spatial resolution. In our case, HERCULES is remarkably stable. The shot-to-shot fluctuation of wave-front has an r.m.s. deviation from its average shape off about l/20.
We first evaluate and correct the aberrations coming from the paraboloid (the main source of aberrations) using the attenuated regenerative amplifier beam (Fig. 1a). The wavefront is measured through an apo-plan infinity corrected objective (N.A.=0.75) . Here we can check that the calculated focal distributions are identical to the camera images of focus within experimental error. The measured spot size after wave-front correction (r.m.s. improved from 0.4 mm to 0.05 mm) is 0.8 mm FWHM (Fig. 2b).
To correct the additional aberrations at high energy, we measured the wavefront difference between the regenerative amplifier and the 45 TW beams near the deformable mirror by using another wave-front imaging line (Fig. 1b). The beam was attenuated through a high reflectivity mirror and by reflecting on two blank mirrors. The measured wavefront r.m.s. difference between the two beams is 0.12 mm. It is used as a reference wave for the wave-front sensor. The same adaptive optic loop is run using the regenerative amplifier beam, which will result in a deformable mirror surface now optimized for high energy beam.
It is calculated that, after correcting the aberrations of the regenerative amplifier beam and the paraboloid, the focused intensity is (0.66±0.07)´1022 W/cm2 with 45 TW beam and an intensity of (0.85±0.08)´1022 W/cm2 can be reached after the second correction (Fig. 3b).
Fig.1. (a) Wave front measurement and correction setup for low energy beam. DM: Deformable Mirror, WS: Wavefront Sensor, PM: 90°[SB1] , f/0.6 paraboloid, OL: Apo-Plan Infinity corrected objective, N.A.=0.75, HM: High reflectivity mirror, DL: doublet lens, VC:vacuum chamber. (b) Relative wave-front measurement setup for high energy beam. BM: Blank Mirror, L1:lens, f=50 cm, L2:lens, f=4cm.
Fig. 2. 3D reconstruction of (a) uncorrected regenerative amplifier focal spot and (b) corrected focal spot. Same vertical scale.
Fig.3. Calculated intensity distribution from the wavefront at 45 TW. (a) without correction (1´1021 W/cm2) and (b)
with correction (8.5´1021 W/cm2). Same vertical scale. Note the spot size of 0.8 mm FWHM.
 S.-W. Bahk et al., "Generation, amplitude and phase characterization of 1021 W/cm2 intensity," Ultrafast Optics IV, 95, p331 (Springer- Verlag, Berlin, 2004)
 P. Varga and P. Török, "Focusing of electromagnetic waves by paraboloid mirrors. I. Theory," J. Opt. Soc. Am. A, 17, p2081 (2000)
 J. A. Stratton and L. J. Chu, "Diffraction theory of electromagnetic waves," Phys. Rev. 56, p99 (1939)
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