Transcript Nonlinear Electron and Ion Density Modulation Driven by

Observation of the relativistic cross-phase modulation in a high intensity laser plasma interaction
Shouyuan Chen, Matt Rever, Ping Zhang, Wolfgang Theobald, Ned Saleh, Anatoly Maksimchuk, Donald Umstadter
Department of Physics and Astronomy Lincoln, Nebraska, 68512,
Abstract and Acknowledgment
A novel nonlinear optical phenomenon, relativistic crossphase modulation, is reported. A relativistically intense
light beam (I = 1.31018 Wcm-2, =1.05 m) is
experimentally observed to cause phase modulation of a
lower intensity, copropagating light beam in a plasma.
The latter beam is generated when the former undergoes
the stimulated Raman forward scattering instability.
The bandwidth of a Raman satellite is found to be
broadened from 3.8 nm to 100 nm when the pump laser
power is increased from 0.45 TW to 2.4 TW. A signature
of relativistic cross-phase modulation, namely,
asymmetric spectral broadening of the Raman signal, is
observed at a pump power of 2.4 TW. The experimental
cross-phase modulated spectra compared well with
theoretical calculations. Applications to high-power
attosecond duration light-pulse generation are also
discussed.
This work was supported by the Chemical Sciences,
Geosciences, and Biosciences Divisions of the Office of
Science, U.S. Department of Energy and the National
Science Foundation.
Raman spectrum broadens asymmetrically
with increasing laser power
Nonlinear-index coefficient n2 in the
relativistic plasma
Comparison of the laser spectrum before and
after RXPM
• Refractive Index of Plasma
 p2
 p2
n  1 2  1 2

2
0
where
0
2
4

n
e
e
 p2 
me
 is relativistic factor
of the electron in a
laser field
• For a linear polarized laser
a2
a2
  1
 1
2
4
Where
a  8.5 1010 [m]I 1/ 2[Wcm-2 ]
is the normalized vector potential
• Further simplification of n
 p2
a2
n  1  2 (1  )  n1  n2 I
20
4
where
 p2
n2  2 (8.5 1010 [m])2
80
Analysis of Relativistic XPM
Self phase modulation
  n~k0 z  0t  (n  n2 E )k0 z  0t
2
Experimental Setup
Comparison shows qualitative agreement
between analytical and experimental results
Self-phase modulation
Self-focusing
Frequency Chirp
2
2
n~ ( , E )  n( )  n2 E

I

 n2 k0 z  0
t
t
FIG. 3: The comparison of experimental data (top) and analysis results (bottom)
shows good agreement. (a) The RXPM Raman spectrum at 2.0 TW. The
propagation distance is 400 m as measured from the top view image. (b) The
RXPM Raman spectrum at 2.4 TW. The laser intensity used in the analysis is 1.9×
1018 Wcm-2 instead of 1.3 1018 Wcm-2 from the calculation. The propagation
distance is 1000 m. The relatively higher intensity required in the analysis is due to
the effect of self-focusing, which increased the laser intensity. The pedestal in the
experimental data is due to the strong coupling, which is not included in the model.
RXPM induced chirp with respect to the laser
pulse intensity
Ignore the transverse spatial variance of the
laser pulse along Z direction
~
E (r, )  F ( x, y) A() exp[i () z]
Numerous applications of RXPM
Pulse Intensity
I
0
t
I
0
t
Pulse compression
Self-phase modulation
Nonlinear Schrödinger Equation
Red shift
Blue Shift
A
A i
 A
 1
  2 2  i | A |2 A
z
t 2
t
2
XPM happens when two optical pulses
copropagate in a nonlinear medium
For two optical pulse with different frequency
1nl  n2k0 z(I  I 2 )
2
1
2
For I1>>I2 , one pulse is modulated
by another pulse (XPM)
Analytical solution can be achieved for our
particular experimental parameters
LD 
T02
2
 20 cm LW 
T0
 1.2 cm L  1 mm L  LW  LD
d
The second derivative in the coupled equation can be neglected
SPM XPM
Raman generation, harmonic generation, pump probe.
Asymmetric spectral broadening
Normal Group velocity dispersion dn/d>0
Anomalous Group velocity dispersion dn/d>0
Advantages of this method:
Variable pulse energy
Uniform modulation (probe pulse diameter can be
pump beam)
smaller than
Plasma diagnostics
Time
Spectrum in the forward direction
shows Raman satellite
Generation of high power, single cycle laser pulses
laser intensity
laser pulse duration
plasma density
delay time between pump and probe pulse
Comparison of the duration of the laser pulse
before and after compression
Generation of 15-TW single-cycle laser pulse
Experimental parameters:
Ap ( L, T )  Ap (0, T ) exp(i p p ),
Electron density
11018 cm-3
As ( L, T )  As (0, T  Ld ) exp((g s  i s )s ),
Pump pulse
20 TW
100 fs 2J
800 nm
 p  P0 exp( 2 ) L,
Probe pulse
2 TW
30 fs 60 mJ
650 nm

s  P0
[erf (   )  erf ( )]L,
2
Interaction distance
5 cm
Initial delay
5 fs