High Harmonic Transient Grating Spectroscopy Paul.Corkum@nrc.ca

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.

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

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 + 

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

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

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.

If we can “see” electrons, We can “see” them move! Attosecond Imaging PRL 94, 083003 (2005)

The two wave packets collide

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

If a pre-existing replica can be used for imaging So can a photoelectron replica produced with the attosecond pulse PRL 94, 083003 (2005)

Photo-ionization in reverse.

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

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

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

Transient diffractive elements 17 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

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

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.

Transient grating spectroscopy

XUV Interferometry --- a two slit grating

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

Harmonic phase as a function of molecular alignment

No Transient Grating H17 H31 Dt < 0: No alignment

Transient Grating Spectroscopy in HHG

(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

Transient Grating Present Dt=4.1 ps: Alignment H17 H31 Direction of diffracted peaks for H17: +- 3.5 mrad. Corresponding interfringe in the near field: 13.5 microns 13 microns 10 percent in each diffracted peak for harmonic 17 Very efficient diffraction

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

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

Angle Dependent High Harmonic Spectrum

We are working hard to obtain tomographic images of CO2

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

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

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)

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

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

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

Image (laser polarization 450 to writing direction) Nano-planes are spaced and aligned by the laser field PRL 96, 067404 (2006)

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

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

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).