Discussion of measurement methods for femtosecond and attosecond pulses

1. Discussion of measurement methods for femtosecond and attosecond pulses

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

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

4. Measuring femtosecond pulses Why not ask the pulse to measure itself! Transmission, Fluorescence, Ions, Electrons, Diffraction c c x or ct 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?) • Photoionization • Use the pre-existing re-collision electron replica

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

7. Atomic ionization produces a replica photoelectron pulse V 1/2 mV2 =x - IP Measurement of the photo-electron replica is a measurement of the pulse

8. F=ma once again • linear polarization • initial velocity (V0x, V0y, V0Z) • Vdrift, x = V0x- {Vd= qE0(t)/m Sin ( tI + )} • Vdrift, y = V0y • Vdrift, z = V0z Polarization Drift velocity distribution

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

10. Streaked photoelectron of 100 eV pulse -- parallel observation 70 attosecond I = 6x1014 W/cm2

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

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

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

15. (t) (N) Re-collision time [rad] Harmonic number 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 Short trajectories Long trajectories Harmonic order SFA Re-collisiontime [rad] 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) is essentially the Fourier transform of the wave function d(t)={ra(k)eikx d3r}ei{(IP+KE)t +} 

19. Transient alignment of molecules time

20. The Experiment “Pump” Alignment pulse “Probe” HHG pulse Ti:sapphire CPA 1 TW, 27 fs @ 50 Hz (60fs, 5x1013 W/cm2) (30fs, 1.5x1014 W/cm2) Space H15 23.3eV H21 32.6eV H27 41.9eV H33 51.2eV H39 60.5eV

21. Angle Dependent High Harmonic Spectrum

22. Harmonics from N2 and Ar Note the relation to Photoelectron spectroscopy 2 d()= 2 a(k)greikxdx

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

24. Reconstructed N2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~1011Wcm2. This is a truly phenomenal number--- the electron can hardly miss. Why not allow it to diffraction from the molecule?