Nhng tin b trong Quang hc, Quang ph vÃ ng dng VI ISSN 1859 - 4271

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Advances in Optics, Photonics, Spectroscopy & Applications VI ISSN 1859 - 4271II. EXPERIMENTSA 1 kHz multi-stage multi-pass chirped-pulse amplifier laser system, which produces 10 mJpulses with a duration of 30 fs centred at 805 nm, with beam diameter 15 mm and beam qualityM 2 ~ 1.6, is used for the HHG experiment. The detailed experimental arrangement for generationand detection of the XUV radiation has been published elsewhere [3]. The laser pulses arefocussed by a 300 mm focal length lens into a 200 mm-long gas cell with 150 µm pinholes at theexit which are also used to isolate the vacuum chamber from the gas-filled cell. The pressure inthe vacuum chamber outside the gas cell is kept at < 1 × 10 -3 Torr. The beam radius at the focusis about 50 µm and the Rayleigh length is 10 mm. The effective peak intensity at the focus isapproximately 5 × 10 14 − 10 15 W/cm 2 . An aperture with variable diameter, which is placed in thepath of the laser beam before the focussing lens, has a s<strong>trong</strong> influence on the intensity and beamprofile of the HHG signal [3]. The influence of the size of the aperture is attributed to theeffective f-number, the spatial quality of the laser beam and the peak intensity in the focus area.The variation of the aperture introduces <strong>ph</strong>ase variations in the laser wave-front that can be usedto minimize the mismatch between the laser <strong>ph</strong>ase and the intrinsic <strong>ph</strong>ase of the harmonics. Thehigh harmonics created on-axis or close to the optical axis pass through a 200 nm-thickaluminium (Al) or zirconium (Zr) filter, which removes the fundamental beam. A very broadrange of XUV wavelengths (5 – 80 nm) can be analyzed with high spectral resolution by agrazing incidence XUV spectrometer equipped with a set of four different gra<s<strong>trong</strong>>tin</s<strong>trong</strong>>gs (150, 300,600 and 1200 grooves/mm).For coherent diffractive imaging the sample is mounted on a holder inside an experimentalvacuum chamber. The diffraction pattern is detected with a CCD camera (Princeton Instruments)having a 1340 x 1300 array of 20 µm pixels or a 1024 x 1024 array of 13 µm pixels. Thedistance between the CCD and the sample is < 6.5 cm. To further reduce scattered light a 5 mmdiameter aperture is placed directly downstream from the sample. As a test target we have used aregular pinhole sample. The sample is micro-machined in a thin (~100 nm) gold layer on a Si 3 N 4substrate and exhibits an array of 2 µm-diameter pinholes spaced by 3 µm and arranged in theform of a 20 µm-diameter circle.II. 1. Generation of few harmonic orders30Fig. 1. Argon gas cell: harmonic intensity versus laser focus position. Inset: harmonic intensity versuspressure, and spectral power distribution for position of maximum flux. Red solid line: quadratic fit for<strong>ph</strong>ase-matched harmonic emission. Green dashed line (marked by large circles): fit of exponentialdecay curve.
Những tiến bộ <strong>trong</strong> <strong>Quang</strong> học, <strong>Quang</strong> <strong>ph</strong>ổ và Ứng dụng VI ISSN 1859 - 4271The intensity of theq th harmonic order in a non-absorbing gas scales as2 2Iq∝ Nasinc( ∆kleff) [1], where s inc (x) = sin( x)/ x , Nais the atom density, l effis the effectiveinteraction length between the fundamental laser field and the nonlinear medium, and ∆ k is the<strong>ph</strong>ase mismatch between the fundamental and harmonic field. If the atomic response is constantor varies only slightly over a propagation length that corresponds to the coherence length and the<strong>ph</strong>ases between the fundamental and harmonic field are matched, then the harmonic intensity22scales as Iq∝ Naor Iq∝ p , where p is the pressure of the genera<s<strong>trong</strong>>tin</s<strong>trong</strong>>g gaseous medium. Also,2the harmonic intensity will scale as ∝ ∆zwith increasing interaction length ∆ z .IqThe dependence of the intensity for all harmonics for argon and helium gas at the focus pointof the laser relative to the exit pinhole of the cell is shown in the Fig. 1 and Fig. 2, where positivedistance indicates that the focus position is in the gas cell. Typical XUV HHG spectra are shownin the inset of Fig. 1 and Fig. 2. For these measurements all parameters except the focus positionare kept constant. The number of harmonics, the relative intensity and the beam profile areoptimized by varying the focus position of the lens, the gas pressure and the size of the aperture.The variation of these parameters influences the atom density and the ionization, and thusmacroscopic <strong>ph</strong>ase matching can be achieved for a certain interaction length for a few harmonicorders near the cut-off region.The inset of figure 1 shows the intensity dependence on the pressure in the argon gas cell.The optimized value for the pressure is pAr= 58 Torr . For 20 Torr ng>ph</strong>ase-matched and Iq ∝ N a,Ar∝ pAr(fitted solid red line). For pAr>> 58 Torr reabsorptionby the gas dominates, and an exponential decay curve can be fitted (dashed greenline, marked by large circles). The x-axis is calibrated such that the global intensity maximum isat z = 0 mm . The laser focus is close to the exit plane and deeper inside the gas cell for largervalues of z . The harmonic intensity scales quadratically with increasing values of z over apropagation length of about 7 mm (fitted solid red line) and thus indicates <strong>ph</strong>ase-matchedharmonic emission. Thus, when the laser focus is properly positioned inside the gas cell theHHG is <strong>ph</strong>ase-matched over the whole Rayleigh range of the laser focus. When the laser focus isplaced deeper inside the gas cell, re-absorption by the genera<s<strong>trong</strong>>tin</s<strong>trong</strong>>g medium dominates and anexponential decay curve can be fitted (dashed green line, marked by large circles).Fig. 2. Helium gas cell: harmonic intensity versus laser focus position. Inset: spectrum for position ofmaximum flux. Red solid line: quadratic fit for <strong>ph</strong>ase-matched harmonic emission. Green dashed line(marked by large circles): fit of exponential decay curve.31
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Nhng tin b trong Quang hc, Quang ph vÃ ng dng VI ISSN 1859 - 4271

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