1. Wavelength-dependence of Momentum-Space Images
of Low-Energy Electrons Generated by
Short, Intense Laser Pulses
at High Intensities
Chakra Man Maharjan
A S Alnaser, P Ranitiovic , I Litvinuyk and C L Cocke
Department of Physics, Kansas State University
2006

2. MOTIVATION : and angular structure of the laser generated
To understand and resolve the energy
and angular structure of the laser generated
electrons in the low energy region

3. Experimental Setup COLTRIMS Y Z X Parabolic mirror Supersonic jet
Electron detector
Short pulse laser
COLTRIMS

4. γ = γ >1 γ <1 Ionization In Laser field Keldysh Parameter
, Up ~ I λ2
Ip = Ionization potential
Up = Pondermotiv energy
γ >1
Multi photon process
γ <1
Tunneling process

5. Freeman Resonance and Above Threshold Ionization (ATI)
Up=I/4ω2
n=0
n=4
n=5
n=∞
Freeman Resonance
ATI
Intensity

6. Freeman Resonance : sub-structures in ATI peaks5g 4d 6g 4p 4f

7. for different wavelengths
Density plot of the electron monenta along and perpendicular to the laser polarization
for different wavelengths
Figures shows density plots of the electron momnentum spectra for different wavelengths at the intensities indicated. The vertical scale is the numeber of counts in logarithmic presentation , while the horizontal and vertical axes are the lectron moneta parrallel to and prpendicular to the laser polarization, pz and pt respectively. The data are integrated over the azimuthal angle around the polarization vector. We note that this presentation forces the distribution go to zero on the pz=0 axis.The Keldysh parameter y and peak laser intensity are shown in each panel. All the values of y are below the unity.
The spectra show complex structure in both energy and angle in the low energy region. Since the purpose of this project is to examine this low energy structure we donot show the large momentum part of these spectra, but one can already see that beyond a momentum of about 0.6 au the spectra begin to lose the complex structure and revert to the more familiar ATI spectra of electron spectra at high intensities. The part of loss of fine structure in the energy distribution for higher ATI peaks can be due to the finite bandwidth of the laser, and effect which is small for low order ATI but grows for higher orders. In addition , the experimental resolution of approximately 0.01 au in pz results in good energy resolution for low energy electrons but deteriorates for higher energy so that the structure would be lost even if the physics still provided it.

8. ρ Diffraction effect (GRT) Z Laser driven e Kepler Hyperbola
Laser driven e
Kepler Hyperbola
A typical electron trajectories after tunneling shows a quiver motion along the polarization of the laser field. An interesting observation is that motion is strongly driven by the laser field , the motion follows the Kepler hyperobola.The angular momentum of the Kepler hyperbola is identical to that of the asymtotic l of the laser-driven electron.Trajectories released at different times or different maxima of the field reaching the same asymtotic branch of the kepler hyperbola will interfere and generate GRT fringes.

9. The same set of data in two different scale for 640nm
The same set of data in two different scale for 640nm.The upper panel is optimized to reveal weak features for large momenta, while the lower panel is optimized to show stronger low energy features Pt
640nm
30v
18mw
7.08X1014 W/cm2
main features only
γ=0.54
low intensity features
640 nm Pz
How the higher momentum features emerge from the low momentum features can be seen more easily in above fig.where we show same set of data at 640 nm for two different vertical scales. The high momentum ATI features are more easily visible in the more sensitive scale.

10. 640nm
30v
10mw
18mw
21mw
3.94X1014 W/cm2
γ=0.72
7.08X1014 W/cm2
γ=0.54
8.2X1014 W/cm2
γ=0.5
640 nm Pt Pz
Comparison of the energy and angular structure with three different intensities
for 640 nm
The figures show a typical dependence of the spectral features on the laser intensity. We do not control the volume viewed in this experiment, and it is well known that relative yields through different Freeman resonances in the multi-photon region are quite sensitive to the intensities. Indeed , the emergence of the resonance structure in a Freeman resonance results from the fact that the Stark shift of the Rydberg resonant state is approximately equal to that of the continuum, thus yielding the same electron energies regardless of the volume element at which the electron is created. From fig we see that , while the relative strengths of the observed features are intensity dependent , the general character of the angular distributions and many features are not. We note that the shift of the ponder motive energy associated with the intensity changes span nearly 20eV, yet the structures remain.

11. Plots of the energy spectra, integrated over all angles, in the region of the first ATI group
We use the measured wavelength dependence to address the question of whether the observed energy structure can be attributed to Freeman resonances. In fig we show the low energy portion of our spectra integrated over angle and plotted versus energy. For each spectrum, the energy of a single photon has been subtracted from the measured photon energy so that the horizontal scale becomes the binding energy of the resonant Rydberg state through which a multiphoton process would occur if a single additional photon is then absorbed to put electron into the continuum. The spectra show evidence for the ubiquitous 5g resonance, and possibly a weak higher 6l-nl Rydberg series above it, at a binding energy of 0.6 eV.In fig we indicate the location of the highest l values in this series, but do not mean to imply this is unambiguous identification. In addition, a feature centered near the 4f states of argon is seen at a binding energy of 0.86 eV.

12. Energy Vs Angle Θ (deg) E (eV) 400nm 640nm 590nm 680nm 800nm 615nm10 20 30 40 50 60 70 80 90
E (eV)
Θ (deg)
The angular structure seen in the figures is quite marked in the low-energy region and shows a distribution which appears not to be related to the nature of any resonant structure which produces it. For example, while the 5g resonance, which appears in many published spectra, shows a dominantly l=6 pattern in all cases, as do the features at slightly higher and slightly lower energies. Indeed ,the dominance of l=6, with a weaker l=5 participant ,is a general feature of nearly all of our spectra for all wavelenghts ,extending at least to an electron momentum of about 0.6 au or about 5 eV. This encompasses up to the three photons into the ATI structure.
The angular structure is presented in a more convenient form in fig which shows a density plot of the electron energy versus angle. We note that this plot is represents the yield per unit angle plotted versus angle, not the more conventional yield per unit solid angle.

13. Projections of the data from energy spectrum onto the angle axis for a wavelength of 640 nm for selected energy slices
4f resonance
5g resonance
In order to reach the limiting case of the dominance in the semi classical domain of a single Plo, it is necessary that Interference trajectories at fixed energy exist that approximately cover the entire range of scattering angle ,all of which with angular momenta close to lo.
The ability of the angular structure to remain constant over a wide range of energy structure suggests that the angular structure is not to be associated with the quantum numbers of any particular resonant state but with behavior of the continuum wave in the field of the argon ion. Just such a behavior was suggested and calculated by arbo for an atomic hydrogen.
The square of the Legendre polynomial P6(cosθ), multiplied by sinθ

14. Energy and angular structure of electrons in momentum image generated by a laser field from align N2 and 02 molecules

15. PUMP – PROBE SETUP λ/4 KLS, VP Probe Detector chamber Source N2
Delay Stage
A Mach-Zender interferometer was used to divide the laser output into aligning and exploding pulse , to introduce the relative time delay and to recombine the two beams collinearly. A narrow aperture was used in the aligning pulse to decrease the beam diameter. This produced an aligning focus whose minimum cross sectional area and confocal parameter were greater than those of the exploding pulse and ensure that only those molecules upon which the aligning pulse had acted most strongly were exploded.
Pump
Probe

16. Test of alignment of molecules (N2)
N2+/N2+
Coulomb explosion
Probe Pulse
only
With both
Pump and Probe
pulses

17. Rotational revival ( N2)1 2 1 2
Ipump = 1.1 x1014 W/cm2
Iprobe=5.5X1014 W/cm2
The molecular alignment axis (i.e. the polarization axis of the linearly polarized aligning pulse) lay in the polarization plane of the circularly polarized exploding pulse. We measured the angle theta between the alignment axis and the projection of each three dimensional fragment velocity onto the polarization plane.
We characterized the degree of alignment at each aligning exploding delay by calculation <cos2theta> for each normalized theta distribution. In our scheme < cos2theta> reflects an isotropic distribution of molecular orientations while <cos2theta>=1 indicates complete alignment . The limiting case in which all the molecules are perpendicular to the alignment axis is denoted by < cos2theta>=0.
The time evolution of the N2 alignment parameter <cos2theta> is depicted in figure. Prior to the arrival of the aligning pulse (i.e. t<0), the molecular ensemble are isotropic.

18. Rotational revival N2 1 2 ATI STRUCTURES 2 1 theta> <cosB
3600
3800
4000
4200
4400
4600
4800
5000
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75 1
theta> N2 2
<cos 2
ATI STRUCTURES
Delay(fs) 2 1

19. Rotational revival 1 N2 2
Photoelectron angular
distribution 1 2

20. O2 Ipump=4.0 x1013 W/cm2 Iprobe=1.0X1014 W/cm2 2920 fs 3100 fs
Probe only
Ipump=4.0 x1013 W/cm2
Iprobe=1.0X1014 W/cm2

21. O2
ATI STRUCTURES
2920 fs
3100 fs
Probe only

22. Photoelectron angular distribution (5-6 eV)
2920 fs
3100 fs
Probe only

23. Thanks for your attention !!