1. High Harmonic Transient Grating Spectroscopy

2. Mapped by classical physics to here
The key idea; F=ma
Attoseconds arise first here
First the electron is releases --- usually via tunneling, but even classical physics will do.
The electron moves in the field of the laser, first away, then back to the parent ion
There it collides:
Elastically scattering --- ie. diffracting
Exciting a second electron or knocking it free --- collision physics
Emitting a photon
Note
The field times the collision.
Complex fields can do much better
The field labels the time of birth of any charged fragment
and
Classically an atom’s own electron, driven by a strong electric field can interact with its parent within a cycle.

3. The key idea c=a(k)eikx-it g
30 Å
Kinetic energy, amplitude and phase of the re-collision electron is transferred to photons. Observing photons is equivalent observing electrons. One is a replica of the other

4. High Harmonics/Attoseconds pulses
d(t) is essentially the Fourier transform of the wave function
d(t)={|r|a(k)eikx d3r}e(IP+KE)t + 

5. Reconstructed N2 g Orbital
Reconstructed from 19 angular projections
wave function, not its square
We see electrons! Amplitude and Phase!

6. Review: In the same experiment
We have laser Electrical Forces that can be as strong as (or stronger than) those binding electrons to molecules.
We can control these forces on the natural time scale of molecules. And it will improve covering all visible and ir frequencies
We can also apply internal and external dipole forces that are significant with respect to bond strengths

7. Review continue:
We can probe and excite molecules with attosecond pulses --- exceeding the electronic time scale.
And we have a re-collision electron with wavelength of ~ 1 Angstrom, giving us access to molecular scale spatial resolution.
These are powerful and natural tools for molecular science.

8. If we can “see” electrons,
We can “see” them move!
Attosecond Imaging
PRL 94, (2005)

9. The two wave packets collide

10. Time maps into electron KE
1×1014W/cm2
1600 nm, ~6 fs
Fixed carrier phase

11. If a pre-existing replica can be used for imaging
So can a photoelectron replica produced with the attosecond pulse
PRL 94, (2005)

12. Photo-ionization in reverse.

13. The key idea c=a(k)eikx-it g
30 Å
Kinetic energy, amplitude and phase of the re-collision electron is transferred to photons. Phase is determined by the path length and the velocity --- each scales with E

14. A diffraction grating Since the control field is weak
=
Since the control field is weak
we separate the generation from control.

15. Like 4-wave mixing grating Supersonic gas jet Generating beam
Dressing beams
Generating beam
grating
Supersonic gas jet
MCP

16. Transient diffractive elements17 19 21 23 25 27 29 31 17 19 21 23 25 27 29 31
This is the nth order analogue to 4-wave mixing

17. Since we control phase, we can construct any phase element
-Lenses
prisms
-Digital optics
lasting less than one period if needed.

18. Reaching below the electron wavelength
Optical interferometers measure subtle changes in interference – Phase changes much less 2 (10-6 x 2).
In electron wavelengths, this is a very small distance.
Can small molecular features be resolved? - dimension and local fields?
These parameters --- shape and local fields influence a molecule’s reactivity.

19. Transient grating spectroscopy

20. XUV Interferometry --- a two slit grating

21. Alignment Scan in N2
Visible phase shift, increasing with harmonic order
Accuracy about 1/100 of a fringe

22. Harmonic phase as a function of molecular alignment

23. No Transient Grating
H17
H31
Dt < 0: No alignment

24. Transient Grating Spectroscopy in HHG

25. (rotational temperature ~ 90°K.) J=J(J+1) 1/2; 1=B/2; T1=2/1
2-D measurement of N2
(rotational temperature ~ 90°K.)
J=J(J+1) 1/2; 1=B/2; T1=2/1

26. Transient Grating Present
Dt=4.1 ps: Alignment
H17
H31
Direction of diffracted peaks for H17: mrad.
Corresponding interfringe in the near field: 13.5 microns
13 microns
10 percent in each diffracted peak for harmonic 17
Very efficient diffraction

27. Zero order and diffracted signal
Diffracted signal is too great to be only an amplitude grating

28. Amplitude and phase information are projected to direction with zero background
Resonance

29. Angle Dependent High Harmonic Spectrum

30. We are working hard to obtain tomographic images of CO2

31. What about collisions? Immediately the atom sees a huge current surge.

32. Is there any hope for attosecond science inside liquids and solids?
I think so. Sub-cycle science seems perfectly compatible with transparent solids and liquids

33. Highly multiphoton phenomena are not limited to atomic and molecular gases
In gases, saturation is running out of atoms
In solids, saturation is running out of photons
Solids, acts back on the light -- locally and globally
In gases, we have a new sample each shot
In solids, the debris gives a shot-to-shot memory (positive feedback in SiO2)

34. Image of an Etched Structure (~1000 shots)
A uniform focus produces lines spaced sub-wavelength

35. Image (laser polarization 900 to writing direction)
Nanoplanes (< 5 nm wide) stretching for 100’s of m

36. Image (laser polarization parallel to writing direction)
Ionization produces dense plasmas, but with p<  --- This is a unique nano-plasmonics.

37. Image (laser polarization 450 to writing direction)
Nano-planes are spaced and aligned by the laser field
PRL 96, (2006)

38. Attosecond and multiphoton physics are entwined in dielectrics
A 5-eV electron experiences a momentum changing collision in ~ 100 attoseconds in SiO2
Field assisted collisional ionization must be ubiquitous
(conventionally, avalanche ionization is assumed to be absent for less than 100 fs)
Enhanced ionization must also be ubiquitous
Understanding laser interaction with dielectrics, cells, tissue, etc, will need attosecond techniques

39. The absorption is greater for the major axis than the minor axis.
Polarization analyzer
spectator
/4
SiO2
More circular

40. The Atto sub-group (2007)
Scientists: Paul Corkum, David Villeneuve, Eli Simova, Andrei Naumov and David Rayner
Technologists: Bert Avery, John Parsons
Postdoctoral Fellows: Nirit Dudovitch, Rajeev Pattathil, Domagoj Pavicic and Yann Mairesse.
Visitors: Hiromichi Niikura (JST), Gennady Yudin and Andre Staudte
Ph. D. Students: Kevin Lee (McMaster), Julien Bertrand and Marina Gertsvolf (Ottawa).