1. Discussion of measurement methods for femtosecond and attosecond pulses

2. Duration & Phase Long pulse = one color Short pulse = many colors; perfectly synchronized. 0.7  1.3   This is mathematical. It cannot be avoided

3. What is fast enough for measurement? Streak Camera (currently ~500 fs) ½ ns Produce photoelectron replica Rapidly changing field Space charge, operating over many nanoseconds is a problem photocathode

4. Measuring femtosecond pulses Why not ask the pulse to measure itself! c c  x or c  t Transmission, Fluorescence, Ions, Electrons, Diffraction question: What can be used for mirrors and beam splitters? What can be the nonlinear medium for attosecond pulses?

5. Attosecond pulses were generated using laser fields and electrons (Why not use the streak camera?) 1.Photoionization 2.Use the pre-existing re-collision electron replica

6. Laser fields easily push electrons around Making single attosecond pulses --- controlling the laser field 1 fs

7. Atomic ionization produces a replica photoelectron pulse V 1/2 mV 2 =   x - IP Measurement of the photo-electron replica is a measurement of the pulse

8. F=ma once again linear polarization initial velocity (V 0x, V 0y, V 0Z ) V drift, x = V 0x - {V d = qE 0 (t)/m  Sin (  t I +  )} V drift, y = V 0y V drift, z = V 0z Drift velocity distribution Polarization

9. A single sub-cycle X-ray pulse VxVx VyVy --- photoelectron replica is streaked (attosecond streak camera)

10. Streaked photoelectron of 100 eV pulse -- parallel observation 70 attosecond I = 6x10 14 W/cm 2

11. 30 Å gg  c =a(k)e ikx-i  t Attosecond pulses are generated by a pre-existing photoelectron replica

12. We need to do a similar thing to the pre-existing replica A (weak) 2 2  field breaks symmetry, generating even harmonics Each moment of birth (re-collision) has an optimum phase difference (  ) between  and 2 

13. 60  BBO /2 Wave plate Supersonic gas jet Experimental Set-Up calcite glass Ti:sapphire amplifier 1mJ, 27 fs @ 50 Hz grating MCP

14. 16 18 20 22 24 26 Harmonic order Delay [fs] What Phase difference moves the interferometer arms optimally?

15. Re-collision time [rad]  (t) Harmonic number  (N  ) Attosecond Temporal Phase Gate d ,2  (t) ~ d  (t) e i  (t) SFA  : two color delay which maximizes the even harmonic signal

16. Electron Wave-Packet Reconstruction Re-collision time [rad] Short trajectories Long trajectories Harmonic order SFA Electron wave packet measurement is equivalent to a xuv pulse measurement up to the transition dipole.

17. Discussion of Orbital Imaging What are the meausred quantities?

18. High Harmonics/Attoseconds pulses d(t)={  ra(k)e ikx d 3 r} e i{(IP+KE)t +  }  d(t) is essentially the Fourier transform of the wave function

19. Transient alignment of molecules time

20. The Experiment “Pump” Alignment pulse “Probe” HHG pulse (60fs, 5 x 10 13 W/cm 2 ) (30fs, 1.5 x 10 14 W/cm 2 ) H15 23.3eV H21 32.6eV H27 41.9eV H33 51.2eV H39 60.5eV Space Ti:sapphire CPA 1 TW, 27 fs @ 50 Hz

21. Angle Dependent High Harmonic Spectrum

22. Harmonics from N 2 and Ar  2 d(  )=  2 a(k)  g re ikx dx Note the relation to Photoelectron spectroscopy

23. Normalized Harmonic Intensities Harmonic intensities from N2 at different molecular angles ELEL

24. Reconstructed N 2  g Orbital Reconstructed from 19 angular projections wave function, not its square We see electrons! Amplitude and Phase!

25. Final comment: Another perspective on the re-collision electron The probability of the electron being driven back is 50% The area of the electron wave packet when it returns is ~(10 Angstroms) 2 The time window is about 1 femtosecond Charge per unit area per unit time is current density. J~10 11 Wcm 2. This is a truly phenomenal number--- the electron can hardly miss. Why not allow it to diffraction from the molecule?