1. (LASER) PLASMA DIAGNOSTICS
Leonida A. Gizzi
Intense Laser Irradiation Laboratory
Istituto Nazionale di Ottica – CNR
Pisa, Italy

2. DENSITY: USE OPTICAL PROBINGDt
Probe pulse
ANALYZER
Plasma
Interaction of fs pulses with gas-jets;
Short-pulse interferometry
Phase shift and Fringe Visibility Depletion
Time-resolved propagation with pump and probe approach

3. OPTICAL PROBING ANALYZER SHADOWGRAPHY: MAP OF TRANSPARENT PLASMADt
Probe pulse
ANALYZER
Plasma
SHADOWGRAPHY: MAP OF TRANSPARENT PLASMA
KNIFE-EDGE (SCHLIEREN): MAP OF DENSITY GRADIENTS
INTERFEROMETRY: MAP OF DENSITY
POLARIMETRY (FARADAY ROTATION): MAP OF MAGNETIC FIELDS

4. EXAMPLE: OPTICAL PROBING OF CPA PROPAGATION IN GASES
The position of the focus relative to the jet is usually a critical parameter
probe
beam
gas jet
main
pulse
Fine tuning
nozzle
3mm x 300µm slit or
1mm diam cyl.

5. Interferogram taken after pulse propagation: T=+5 ps
EVIDENCE OF ASE EFFECT
Depending on the relative position of best focus and gas jet, early ionisation may take place due to Amplified Spontaneous Emission.
ASE-induced precursor plasma
200 µm
Second Harmonic emission from main CPA
Main laser pulse
GAS ionised by CPA
Interferogram taken after pulse propagation: T=+5 ps
Simultaneous detection of electron energy spectrum and plasma interferometry enables identification of the role of ASE

6. PLASMA INTERFEROMETRYDt
Probe pulse
Plasma
fringe pattern
phase difference
electron density
The phase difference map is obtained from the fringe pattern with FFT analysis (M. Takeda, H. Ia, and S. Kobayashi, J. Opt. Soc. Am. 72, 156, (1988), L.A.Gizzi et al. Phys. Rev. E, 49, (1994)), or with an original numerical technique based on Wavelet Transform (P. Tomassini et al., Appl. Optics, 40, 6561 (2001))
The electron density map is obtained from the phase difference map with an original algorithm based on Abel inversion extended to moderate axial asymmetric distributions: P. Tomassini & A. Giulietti , Optics Comm. 199, 143 (2001)

7. OPTICAL DIAGNOSTICS: FEMTOSECOND INTERFEROMETRY
All-optical way to retrieve the electron density map of the accelerating medium
Exploit a laser beam to probe the plasma via its refractive index effect on the interference fringe pattern
Use of ultrashort laser pulse enables femtosecond resolution measurements
i.e. : Mach-Zehnder interferometer
From the refractive index we can get to ne…
• L.A. Gizzi et al., AIP Conf. Proc. Vol. 827, 3 Editors M. Lontano et al., Melville, N.Y. (2006).
• L.A.Gizzi et al., PRE, 2009

8. THE NOMARSKI INTERFEROMETER
It’s an in-line set-up
Enables control of imaging parameters (resolution, f.o.v …)
R.Benattar et al, Rev.Sci.Inst. 50(12),1583 (1979)
O.Willi, in Laser-Plasma Interactions 4, Proceedings of the XXXV SUSSP, St. Andrews, 1988, edited by M.B. Hooper (SUSSP, Edinburgh, 1989).
L.A.Gizzi et al. Phys. Rev. E 49, (1994); M.Borghesi et al., Phys. Rev. E 54 , 6769 (1996).

9. BASIC PRINCIPLES Comparing the phase difference between the two arms:
The total phase shift in the plasma arm (WKBJ approx.) is:
Comparing the phase difference between the two arms:
The plasma refractive index is
nc (0.4 m)  6.91021 cm-3
that can be inverted to obtain ne(x,y,z)
(under suitable geometrical symmetry, i.e. cylindrical)
Abel inversion
P. Tomassini et al., Appl.Opt., 40(35):6561, (2001).

10. INTERFEROMETIC MAP FROM EXPLODING FOIL PLASMA
TARGET
LASER
PLASMA
LASER
PROBE
… FFT analysis
M. Takeda, H. Ia, and S. Kobayashi, J. Opt. Soc. Am. 72, 156, (1988)

11. EXAMPLE FFT OF INTERFEROGRAM

12. RECONSTRUCTED ELECTRON DENSITY MAP

13. Geometry of beam propagation (He)
T= ps
#141255
200 µm
f/2.5

14. Geometry of beam propagation
T= ps
#141260
200 µm
f/2.5
Region of loss of fringe visibility

15. Geometry of beam propagation
T= ps
#141267
200 µm
f/2.5

16. Loss of fringe visibility
Longitudinal
Transverse

17. Fringe pattern: modelling - 1

18. Fringe pattern: modelling - 2

19. Fringe pattern: modelling - 3
Phase shift
L.A.Gizzi et al. Phys. Rev. E, 49, (1994);
Fringe visibility

20. Advanced: Optical probing of Laser Wakefield
Wakefield structure:
>Electron density modulations (≈1%);
>Fast evolution(fs)
>Small spatial scale (µm)
Under Self-injection conditions:
>High current electron bunch(es);
>Azimuthal magnetic field generation;
In general, INTENSITY, PHASE and POLARIZATION of a probe pulse will be affected.

21. Optical probing of Laser Wakefield
INTENSITY MODULATIONS:
In a Shadowgraphy or Schlieren (knife-edge) configuration, measurements will show (qualitatively) density modulations due to absorption or refraction effects;
POLARIZATION ROTATION:
Plane of polarization of linearly polarized light propagating in a magnetic field parallel to the k-vector will rotate (Faraday rotation). Polarimetric analysis of the beam will yield map of the B-field component along k.

22. Experimental Setup
Courtesy of

23. Faraday-Rotation
Transverse probing of B-fields in underdense plasma with linearly-polarized probe pulse:
if  B-field induced difference of h for circularly- polarized probe components
 rotation of probe polarization:
 measure frot to get signature of B-fields!
J. Stamper et al. Phys. Rev. Lett. (1975)

24. EXPERIMENTAL SET-UP

25. JETI-Results: Faraday-Rotation
Two polarograms from two (almost) crossed polarizers:
polarogram 1
560 µm
340 µm
polarogram 2

26. JETI-Results: Faraday-Rotation
Two polarograms from two (almost) crossed polarizers:
polarogram 1
560 µm
340 µm
polarogram 2
Deduce rotation angle frot from pixel-by-pixel division of polarogram intensities:

27. JETI-Results: Faraday-Rotation
polarogram 1
560 µm
340 µm
polarogram 2
simulated feature
experimental Faraday feature
Experimental evidence for B-fields from MeV electrons and bubble!
MCK et al., Physical Review Letters 105, (2010)

28. LWS-20 Results: Faraday-Rotation
Two polarograms from two (almost) crossed polarizers:
polarogram 1
polarogram 2
Electron bunch length: z = 4 µm   = 13 fs  deconvolved = (62) fs

29. LWS-20 Results: Faraday-Rotation
Polarimetry: visualize e-bunch via associated B-fields
change delay between pump and probe  movie of e-bunch formation
observe electron acceleration on-line! 29

30. LWS-20 Results: Shadowgraphy
Polarimetry: visualize e-bunch via associated B-fields
change delay between pump and probe  movie of e-bunch formation
Shadowgraphy: visualize plasma wave
change electron density  change plasma wavelength
observe electron acceleration on-line! 30

31. LWS-20 Results: Shadowgraphy
Shadowgraphy: visualize plasma wave
change electron density  change plasma wavelength
A. Buck, M. Nicolai, K. Schmid, C.M.S. Sears, A. Sävert, J. Mikhailova, F. Krausz, MCK, L. Veisz, Nature Physics doi: /NPHYS1942 (2011)

32. SUMMARY
Plasma interferometry can be used to determine plasma density with high spatial resolution – a limitation exists on the minimum density x length (≈10E18 cm-3 x 1 mm )
Optical probing with fs resolution can be used to investigate ultrafast dynamics of laser plasma interactions;
Probing with “ultra short” (<10fs) laser pulse can be used to unfold dynamics of laser-wakefield acceleration.
Detailed analysis of diagnostic specifications requires range of specs of COMB plasmas to be defined.