«ATTOSECOND ANGULAR STREAKING A dissertation submitted to ETH ZURICH for the degree of DOCTOR OF NATURAL SCIENCES Submitted by PETRISSA ROBERTA ECKLE ...»
ETH Diss. No. 18118
ATTOSECOND ANGULAR STREAKING
A dissertation submitted to
for the degree of
DOCTOR OF NATURAL SCIENCES
PETRISSA ROBERTA ECKLE
Dipl.-Phys. (TU München, Germany)
born on June 19th, 1979
in Heidelberg, Germany
Prof. Dr. U. Keller, Supervisor
Prof. Dr. R. Dörner, Co-Examiner Table of Contents Table of Contents
List of Figures
Time in Tunneling
2.2 The Wigner-Eisenbud-Smith time or phase time
2.3 Buttiker-Landauer Time
2.4 The adiabaticity parameter of Keldysh
2.5 A tunneling delay time in high field ionization
Attosecond Angular Streaking (AAS)
3.2 The concept of attosecond angular streaking
3.3 The pulse field
3.3.1 The Carrier Envelope Offset Phase
3.3.2 CEP in circular polarization
3.3.3 Ellipticity effects
3.3.4 Absolute value of the CEP in circular and elliptical light
3.5 Comparison to energy streaking
4.2 Pulse simulation
4.2.1 Phase and spectrum
4.2.2 Quarter wave plate
4.3 Streaking in the field
4.4 Ionization, ADK rates
4.5 Intensity calibration
Experimental setup I: The Laser Pulse
5.2 Pulse compression by filamentation
5.3 Pulse characterization: Spider
5.4 CEP stabilization
Experimental setup II: COLTRIMS
6.2 Gas Jet
6.4 Signal processing
ITABLE OF CONTENTS - II -
CEP measurement with AAS
7.1 Experimental setup
7.3 Resolution and accuracy
7.5 Data analysis
7.5.1 Temporal accuracy
7.5.2 Temporal resolution
7.5.3 CEP resolution
Absolute time: Tunneling ionization dynamics
8.1.1 Relative and absolute measurement of the tunneling delay time............77 8.1.2 Ellipticity dependence
8.1.3 CEP dependence
8.2 Experimental details
8.2.2 Angular calibration
8.2.3 Measurement procedure
8.3 Measurement of the tunneling delay time in an ellipticity scan
8.3.1 Polarization scan
8.3.2 Ion measurement
8.4 Data analysis
8.4.2 Streaking angle and tunneling delay time
8.4.3 Statistical error limit
8.5 Intensity dependence of the tunneling delay time
8.5.1 Intensity scans
Summary & Outlook
List of Figures Figure 2-1 Tunneling through a time dependent rectangular barrier. The tunneling particle can lose or pick up energy quanta of the barrier oscillation with different probability
Figure 2-2 a) Multiphoton ionization, the electron absorbs multiple photons and thereby more energy than is needed for ionization b) tunneling ionization c) Over barrier ionization, the potential is bent so far that the elctron becomes free
Figure 2-3 The upper panel shows a linearly polarized few cycle pulse. The maximum electric field defines t0,Field. Below the corresponding ionization rate is shown with the maximum rate defined as t0,ion. In an experiment, t0,Field of the electric field is usually not accessible and therefore assumed to be equal to t0,ion of the corresponding ionization rate
Figure 3-1 The two steps in AAS: Ionization and streaking.
Figure 3-2 Left panel: The ‘atto-clock’: mapping time to momentum. Right panel:
red solid: electric pulse field of a circularly polarized 6 fs pulse, blue dotted:
corresponding ionization rate with FWHM ~2 fs
Figure 3-3 left:CEP in a linearly polarized ultrashort pulse for CEP = 0 (red solid) and ! / 2 (blue broken line). Right: Intensity as a function of time of the pulse on the left. Again for CEP = 0 (red solid) and ! / 2 (blue broken line)................23 Figure 3-4: Circularly polarized pulse in space and time (upper panel) and the temporal evolution (lower panel). In b, the CEP is shifted by ! / 4 compared to a, rotating the pulse in space by ! / 4 without changing the shape of the temporal evolution
Figure 3-5 The polarization ellipse is shown in black, broken line. On the left, the spatial evolution of an elliptically polarized few-cycle pulse in the polarization plane is shown, where the envelope maximum of the electric field points into the direction of the major axis of the electric field. On the right the same pulse is shown but oriented along the minor axis of the polarization ellipse........26 Figure 3-6: CEP dependence of the electric field depicted in Figure 3-5 in elliptically polarized light. The black broken line shows the temporal envelope of a circularly polarized pulse. On the left (red solid line), the temporal field evolution is shown for the envelope pointing into the direction of the major axis of the ellipse, corresponding to a CEP=0, on the right (blue, solid line), the envelope points along the minor axis of the ellipse, CEP=! / 2....27 Figure 3-7 Shown is the evolution of an elliptically polarized pulse with a field envelope wit FWHM =3.7 fs in the polarization plane for different ellipticities. In blue, solid line the pulse’s electric field is depicted. The polarization ellipse is oriented vertically (90 degrees), the electric field envelope points along the minor axis of the ellipse. Black dotted lines indicate the pointing of the electric field maxima. The ellipticities from left to right are: ! =0.8, 0.9, 0.98 and 1, i.e. circular, respectively
III - IV -
Figure 3-8 Left: Streaking angle for a Gaussian pulse for perfectly circular light (blue solid line) and an ellipticity of 0.048 (green dotted).
On the right:
corresponding ionization rates.
Figure 3-9 Adapted from . The initial electron distribution is mapped depending on the timing between the attosecond pulse and the streaking field....32 Figure 4-1 The refractive index of quartzglass in the wavelengt range around 800 nm
Figure 4-2 Data of the ! 4 plate. Phase, angle of the principal axis and ellipticity as a function of wavelength. The dotted line in the first panel indicates the ! / 4 phase shift required for perfectly circularly polarized light
Figure 4-3 Ionization rates for circularly polarized pulses calculated with ADK.......41 Figure 4-4 Ionization rate as a function of time for the same pulse field but different intensities of an elliptically polarized pulse calculated with ADK formulas. The rates are normalized to peak rates. The dotted line corresponds to a peak intensity of 1 ! 1015 W cm 2, the dashed line to 5 ! 1014 W cm 2 and the solid line to 1 ! 1014 W cm 2.
Figure 5-1 The essentially transform limited oscillator pulse is stretched by chirping it, then amplified and recompressed.
Figure 5-2 The laser system consisting of the fs-oscillator, amplifier and prism compressor. Pump light is shown as green, thick lines, the IR pulse is shown in red, thin lines. Only four passes through the amplifier crystal are visible since the pulse travel out of the plane
Figure 5-3 Spectrum and phase of a 34 fs pulse (left) and the temporal intensity envelope (right)
Figure 5-4 The two mechanisms that form a dynamic equilibrium leading to filamentation
Figure 5-5 The two stage filamentation setup. The gas cells were filled with 650mbar of argon. Chirped mirrors were used for compression
Figure 5-6 Left: Spectrum (solid line) and phase (broken line) of a 5 fs pulse.
Right: The temporal intensity envelope
Figure 5-7 SPIDER setup: Short pulses are depicted as dotted lines, the stretched pulse is depicted as a solid line.
Figure 5-8 f-to-2f scheme for determining the CEO frequency of a pulse train.......54 Figure 5-9 Measured (black trace) and reconstructed (gray trace) single-shot CEO spectral interference pattern. The reconstructed pattern was calculated using the phase(ψ (ω)) and amplitude information obtained from the Fourier filtering phase reconstruction technique.
Figure 6-1 Coltrims setup showing the gas jet, laser and spectrometer with detectors for ions and electrons
Figure 6-2 Raman mapping of rotational temperatures in a supersonic jet of CO2 under a stagnation pressure of 2 bars. Isothermal lines are depicted at steps of 20 K.
Figure 6-3 Detector with MCP (right) and delay line anode (left)
-VFigure 6-4 the left panel shows electron data. The distribution in the x-direction of the detector is plotted versus the time of flight of the electrons, clearly showing the refocusing in time caused by the magnetic field of the detector.
On the right some electron trajectories are plotted, in light blue the refocusing times are marked
Figure 7-1 The upper panel shows the CEP values over measurement time for each single shot as a gray level encoded histogram, darker colors correspond to a higher density of measured CEP values. The center of the distribution is the CEP value, the width of the distribution is the uncertainty in CEP. The lower panel shows the corresponding error signal for the feedback, slowly shifting the phase shot by shot. The full range of the feedback signal is 4095 steps, in the first 30 minutes the error signal was almost constant meaning that the system was drifting.
Figure 7-2 Overview over the measured helium ion momentum distributions while scanning the CEP over 2! and comparison with a semi classical simulation. The top row shows measured momentum distribution for four different values of the CEP. In the lower panel the momentum distributions are radially integrated and their angular dependence on the CEP is shown for the full scan of the CEP over 2! for both data (on the left) and simulation (on the right)
Figure 7-3 CEP dependence of the ionization angle in helium using attosecond angular streaking: a, b: Radially integrated ion momentum distributions for two values of the CEP, the ellipticity peaks are fitted with double Gaussians to extract !1, 2 c, d: The angular position of the two peaks !1 and ! 2 as a function of the CEP with simulations indicated as a dashed line.
Figure 8-1 Left: the polarization ellipse in red, solid line. Center: the ionization rate ellipse depending on the CEP. On the right: The rate ellipse is streaked in the pulse field and rotated by approximately 90 degrees
Figure 8-2 shows the strong dependence of the streaking angle on the ellipticity of the pulse. The streaking angle is simulated using the measured pulse
parameters and the calculated broadband wave plate used in the experiment:
The green dotted line gives the ellipticity as a function of wave plate angle, the black solid line shows the corresponding streaking angle. The streaking angle shows the strongest variation around 45 degrees, where the light is closest to circular
Figure 8-3 Shown are the ionization rate distributions of a few cycle elliptically polarized pulse in the polarization plane for two different CEP values as a solid line. The broken line shows the orientation of the polarization ellipse.
On the left, the distribution is shown for a CEP of ! 2, on the right for a CEP of !" 2. If the two distributions are averaged, the resulting maxima are aligned with the polarization ellipse
Figure 8-4 The upper panel shows the setup for the polarization measurement, in the lower panel polarizer and power meter are removed to measure the corresponding ion momentum distributions.
Figure 8-5 Calibration with linear light. On the left the ion momentum distribution in the plane perpendicular to the laser propagation is shown.
Vertically polarized light along the y-direction creates a cigar-shaped
- VI momentum distributions along the y-direction. On the right the polarization measurement and fit to the radially integrated ion momentum distribution from the right panel is shown, since this measurement is used to calibrate the coordinate system between ion measurements and polarization measurements the angle !" is set to zero
Figure 8-6 On the left, a typical ion momentum distribution projected onto the polarization plane is shown. On the right as in Figure 8-5, in the upper panel the polarizer scan is shown with the angular orientation of the polarization ellipse, ! field. The lower panel shows the corresponding angular distribution of the ions with the maximum ! ions shifted by the streaking angle !"
Figure 8-7 Measurement of ! field. Scan of the wave plate angle and thus the ellipticity. Shown as dots is the measured orientation of the polarization ellipse, the solid line shows the simulated orientation. The green squar dots show the ellipticity extracted fom the measurement and the dotted line gives the corresponding simulated ellipticity curve.
Figure 8-8 Measurement of ! ions Scan of the wave plate angle and thus the ellipticity. Shown as dots is the measured orientation of the ellipticity peaks on the ion momentum distribution, the dashed line shows the simulated orientation.
Figure 8-9 The streaking angle !" from the measurement is shown as dots with error bars derived from the individual measurements of ! field and ! ions. The black broken line shows the corresponding simulation. The calculated values were corrected by the effect of the coulomb potential yielding the values shown as a black solid line. The green dotted line gives the corresponding ellipticity indicated on the axis on the right