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UNIVERSITY OF MARYLAND AT COLLEGE PARK. The extreme nonlinear optics of gases and femtosecond optical filamentation. J.K. Wahlstrand, Y.-H. Chen a , Y.-H. Cheng, J. Palastro, S. Varma b , and H.M. Milchberg Dept. of Physics Dept. of Electrical and Computer Engineering - PowerPoint PPT Presentation
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J.K. Wahlstrand, Y.-H. Chena, Y.-H. Cheng, J. Palastro, S. Varmab, and H.M. Milchberg
Dept. of Physics Dept. of Electrical and Computer Engineering
Institute for Research in Electronics and Applied Physics
UNIVERSITY OF MARYLAND AT COLLEGE PARK
MIPSENov. 7, 2012
Support: ONR, NSF, DoE, Lockheed Martin
The extreme nonlinear optics of gases and femtosecond optical filamentation
a- LLNL (2012 APS-DPP thesis award)b- JHU-APL
Ultra short pulse propagation in gases
CW laser or weak pulse
lensCW laser or weak
pulse
‘intense’ ~100fs laser
pulse PLASMA FILAMENT
- - - - - - - - - - - - - - - - - - -
Some applications (?) of filaments
• directed energy (?)• triggering and guiding of electrical discharges (?)• triggering of rain (?)• remote lasing of air molecules (?)• remote detection: LIBS, LIDAR ()• directed, remote THz generation ()• high harmonic generation ()• broadband light generation for few-cycle pulse generation ()
Examples of filament applications:
Remote sensing at 20 km - LIDAR
Guided high voltage electrical breakdown
Non-guided Filament guided
laser filament
J. Kasparian et al., Science 301, 61-64 (2003).
Laser-assisted condensation
P. Rohwetter et al., Nature Photonics 4, 451 (2010)S. Henin et al., Nature Communications 2, 456 (2011)M. Petrarca et al., Appl. Phys. Lett. 99, 141103 (2011)
Laser filaments promote particle condensation even at « low » humidity (70%)
Non-linear scaling with incident power
J. Kasparian et al.
Laser Heated Air Plasmas and N2 LasingD. Gordon, J. Penano, A. Ting, P. Sprangle, Naval Research LaboratoryJennifer Elle, S. Zahedpour, H. Milchberg, Univ. of Md
1960s: Nitrogen discharge UV laser @337nm (electronic excitation of N2 by electron collisions) Ne ~1015 - 1016 cm-3, Te ~1 eV.
‘intense’ ~100fs laser
pulse PLASMA FILAMENT- - - - - - - - - - - - - - - - - - -
Ne ~1015 – 1017 cm-3 , Te ~1 eV
Lasing?
NRL: J.R. Penano et al., J. Appl. Phys. 111, 033105 (2012)
Vienna: Kartashov et al, PRA 86, 033831 (2012) - got lasing using a 4m driver laser, 5 atm N2 , 1 atm Ar
• First, understand in detail the offsetting nonlinearities responsible for filament generation
Plasma: defocusing
Bound electron nonlinearity: focusing
(Are ‘bound’ and ‘free’ artificial distinctions?)
In any case, the atoms exposed to the laser field in the core of a filament ‘live’ right near the ionization threshold: Is there some interesting transitional behaviour there?
• Exploit this basic understanding to control air filaments
Quantum effects: filament steering, enhancing and extinguishingNonlinearity control: filament lengthening, e-density enhancement, and optical pulse shaping
Can filaments be made more useful?
Evolution of laser power
Maiman
Free electrons
1960 1970 1980 1990 2000 2010103
106
109
1012
1015
1018
1021
1024
Bound electrons
Laser intensity limit
Nonlinear QED
109
1012
1015
1018
1021
1024
1027
1030
Foc
used
inte
nsity
(W
/cm
2 )
Nonlinear relativistic optics
Chirped pulseamplification
Freerunning
Q-switching
Mode locking
Pea
k P
ower
(W
)
Year
Free electrons
wherefilaments‘live’
Bound electron response
x
x
Elaser0
pre-1960
atom
Elaser
small E-field large E-fieldof laser beam
atom‘spring’
nonlinear spring
linear spring
nucleus
electron
Nonlinear response of electrons in simple atom
Nonresonant response is instantaneous
Interesting intensity scales are set by material response
Anharmonic response when eElaser starts to be a perturbation to eEatom~(/Ry)2 e2/a0
2
linear optics Elaser/Eatom<<<<1, perturbation theory Elaser/Eatom<<1
Elaser> Eatom(H) for I >~1016 W/cm2
Bound electron response
Elaser
x
U(x)
x
UFspring
anharmonic
atom
P=(1)E + (2)E2 + (3)E3 + … P=((1) + (3)E2)E +…
In perturbation theory eff
neff2 =1+4eff neff= n0+n2E2
Perturbation regime example: nonlinear self-focusing
0
I(r)
rlaser radial profile
Phase fronts
neff (r)
r nonlinear index profile
n0
Self-focusing
Important at peak power >10 MW in solids,
>1-30GW in gases
IonizationInteresting intensity scales, cont’d…..
V(x)
-Ip
x
Over-the-barrier ionization
62
4
128
.).(
eZ
PIcIthreshold
V(x)
-Ip
x
Tunneling ionization
Vlaser= - erElaser
Vtot
V(x)
x
-Ip
Multiphoton ionization
Perturbation regime
~1013 W/cm2 for xenon~1014 for hydrogen , argon~1015 for helium
Strong field regime
Plasma defocusingIonization important at peak intensity> few 1012 W/cm2
n2 = 1+4free elec =1p2/ 2 = 1Ne/Ncr
, n~ 1Ne/2Ncr
dNe /dt =N0IK Multiphoton ionization with K photons, I < 1013 W/cm2
I(r)
rlaser radial profile
Laser phase fronts
neff (r)
rindex profile
n0
defocusing
I K
High power, femtosecond laser pulses propagating through gases form extremely long filaments due to the interplay of nonlinear self-focusing ((3)) and plasma-induced defocusing.
Idealized picture of filamentation in gases
Pcr~ 2-10 GW for airPcr~ 2-10 GW for airbeatsSelf-focusing diffraction
Collapse happens when
gives Pcr
A.Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).M. Mlejnek, E. M. Wright, and J. V. Moloney, Opt. Lett. 23, 382 (1998)
Real picture: multiple self- and de-focusing events
many Rayleigh lengths,
white light generation
Filament images at increasing power
(Pcr occurs at 1.25 mJ for a 130fs pulse)
Far field filament images
5 mm
0.8Pcr 1.3Pcr 1.8Pcr 2.3Pcr 2.8Pcr 3.5 mJ
0 0
0
( )
( )
eff
nt k z
t tn
t k zt
White light generation
Filaments can be unstable. Within a single laser beam, filaments of different sizes and lengths exist, and they vary shot to shot.
Filaments can be unstable. Within a single laser beam, filaments of different sizes and lengths exist, and they vary shot to shot.
Limitations on filament usefulness
Beam profile1000 Pcr
Beam profile1000 Pcr
Rodriguez et. al., Physical Review E 69,
036607 (2004)
Low electron density (~0.1% atmosphere) with gaps -- difficulty for guiding large current over long distances.
Low electron density (~0.1% atmosphere) with gaps -- difficulty for guiding large current over long distances.
Y.-H. Chen et al, PRL
105, 215005 (2010)
• First, understand in detail the offsetting nonlinearities responsible for filament generation
Plasma: defocusing
Bound electron nonlinearity: focusing
(Are ‘bound’ and ‘free’ artificial distinctions?)
In any case, the atoms exposed to the laser field in the core of a filament ‘live’ right near the ionization threshold: Is there some interesting transitional behaviour there?
• Exploit this basic understanding to control air filaments
Quantum effects: filament steering, enhancing and extinguishingNonlinearity control: filament lengthening, e-density enhancement, and optical pulse shaping
Can filaments be made more useful?
Consider air: prompt and delayed optical response of air constituents
Las
er p
ola
riza
tio
n
Prompt electronic response
+ +++ +
--
--
-
Atoms: 1% argon
Delayed inertial response
+ +++ +
--
--
-
+ +++ +
--
--
-
Molecules: 78% nitrogen, 21% oxygen
Laser field alignment of linear gas molecules
2cos 1/ 3 2cos 1/ 3
randomorientation “some” alignment
time-dependentrefractive index shiftE
n0=n(random orientation)
2
0
2 1( ) cos
3t
Nn t
n
degree of alignment
< >t : time-dependent ensemble average
E
intense laser field(~1013 W/cm2)
/ /pp -laser field applies a net torque to the molecule
-molecular axis aligns along the E field
-delayed response (ps) due to inertia
induceddipolemoment
Classical picturemolecular axis
Ultrafast measurements: conventional streak camera
0-1
-2
-3
12
linearvoltagesweep time
3 2 1 0 -1 -2 -33
Light pulseI(t)
e- current pulse j(t)
electron optics
photocathode
Phosphor Screen or CCD
Ultimate time resolution limited to few hundred femtoseconds by• beam and electron optics dispersion• photocathode time response
A pump pulse generates transient
refractive index n(r, t)
Extract probe (x, t) to obtain n(x, t) with ~5fs time resolution.
Supercontinuum
Probe Ref.
Pump pulse
medium
x
y
zCCD
Imaging spectrometer
Probe Ref.
Imaging lens
Single-shot Supercontinuum Spectral Interferometry (SSSI) –a streak camera with 10fs resolution
Thin gas target in vacuum chamber:For accurate measurement of highly nonlinear response
thin flow d= 400m
d
Spatially resolved temporal evolution of O2 alignment
x (m)
(ps)
(fs)
x(m)
0T 0.25T 0.5T
0.75T 1T 1.25T
• pump peak intensity:2.7x1013 W/cm2
• 5.1 atm O2 at room temperature
T=11.6 ps
T= fundamental rotation period
Field alignment and quantum echoes of rotational wavepacket
Quantum description of rigid rotor , exp( )jj m i t
where / 2π ( 1)j jE cBj j 2 1(8 )B h cI (“rotational constant”)
I : moment of inertia
(j: ≥0 integer)
even
An intense fs laser pulse “locks” the relative phases of the rotational states in the wavepacket– (non-resonant Raman pumping of many j states)
Rotational wavepacket
,,, exp( )j m jj m
a j m i t
eigenstate
Quantum revival of rotational response
The time-delayed nonlinear response is composed of many quantized rotational excitations which coherently beat.
We can expect the index of refraction to be maximally disturbed at each beat.
t = 0 t = Tbeat
Measurement showing alignment and anti-alignment “wake” traveling at the group velocity of the pump pulse.
Rotational quantum wakes in air
vg pump
TN2 , ¾TO2
Light speedmolecular lens
vg pump
PRL 101, 205001 (2008)
pump
Pump-probe filament experiment– dual pulse interferometer
Polarizing beamsplitter
Object plane
2m filament
CCD
f#,lens ~300f#, molecule ~ 200
20 cm
30 fs steps
5 m
m
8.0 8.4 8.8 (ps)
B
A
C D
(ps)8.0 8.4 8.8
Probe filaments are steered/trapped or destroyed
TN2 , ¾TO2
Pump filament position
R=0
Trapped filaments are ENHANCED
White light generation, filament length and spectral broadening are enhanced.
Aligning filament (left) and probing filament (right), misaligned and
detuned in time
probe spatially misaligned, but moved into coincidence with
alignment wake of N2 and O2 in air, t = 8 ps
CCD camera saturation
2-pulse filament experiment*– e-density measurementand optical pulse shaping
Diagnostic for measuring optical pulse envelope and phase
injection
Interferometryprobe
*See talk by J. Palastro on pulse-stacking
Pump+probe: density profile changes on 10fs timescale
Delays for molecular lens focusing
Delays for molecular lens defocusing
SPIDER measurements: pulse shaping and compression of probe pulse with 10 fs sensitivity
Electronic + rotational: N2 , pump 38fs, ~75 TW/cm2
time (fs)
po
sitio
n (
m)
0 200 400 600 800 1000
20
40
60
80
100
120 -0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
time (fs)
po
sitio
n (
m)
0 200 400 600 800 1000
20
40
60
80
100
120 -0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 100 200 300 400 500 600 700-0.2
0
0.2
0.4
0.6
0.8
time (fs)
ph
ase
(ra
dia
ns) Molecules: delayed response
due to rotational alignment
Now we see two features – instantaneous and rotational response
phase
pumpprobe EE
|| pumpprobe EE
Electronic
Rotational
Experiment:vary pulse width, keeping pulse energy constant
Simulation:using parameters extracted from short pulse data, calculate
instantaneous
rotational
Rotational response dominates for >90fs pulses
N2inst
rot
JK Wahlstrand et al., PRA 85, 043820 (2012)
Absolute measurement of n2
enables absolute measurement of n2
Folded wavefront interferometer: measure linear phase shift through hole in tube to find Leff.
diode
efflinear
Ln
02
SSSI provides image of pump spot, allowing precise measurement of spot size. know I(x,y)
The effective interaction length Leff is unknown.
two unknowns
probec
effnonlinear
LIn
,
2 )(2
Molecular gases – absolute measurements
J. K. Wahlstrand, et al., Phys. Rev. A 85, 043820 (2012). Talks/posters Friday
self-phase modulation
harmonic generation
transient birefringence
where
adiabatic
Higher-order Kerr effect?*
...510
48
36
242
InIn
InInInnnonlinear
Usual ‘Kerr’ term
*See talk by J. Wahlstrand, Thurs 9.35am
Hugely negative response well below ionization threshold
…but ionization turns on at ~100 TW/cm2
Higher-order Kerr effect (HOKE) controversy
Effect of HOKE on harmonic generation:Kolesik et al., Opt. Lett. 35, 2550 (2010)Bejot et al., Opt. Lett. 36, 828 (2011)Ariunbold et al., arXiv:1106.5511
Effect of HOKE on filamentation:Kolesik et al., Opt. Lett. 35, 3685 (2010)Chen et al., Phys. Rev. Lett. 105, 215005 (2010)Polynkin et al., Phys. Rev. Lett. 106, 153902 (2011)Bejot et al., Phys. Rev. Lett 106, 243902 (2011)Wang et al., JOSA B 28, 2081 (2011)
Underlying physics of HOKE (theory):Teleki et al., PRA 82, 065801 (2010) – any HOKE should be masked by plasmaBree et al., PRL 106, 183902 (2011) – Kramers-Kronig calc. “confirms” HOKE
Effect of HOKE on conical emission:Kosareva et al., Opt. Lett. 36, 1035 (2011)Bejot and Kasparian, arXiv:1106.1771
…and more!All focus on the consequences of HOKE, not original measurement
Results in Kr with 0.5 mm gas target
plasma
38 TW/cm2 57 TW/cm2
instantaneousresponse
38 fs duration,25 m width
Argon
No apparent instantaneous negative phase shift
-300 -200 -100 0 100 200 300 400 500
Time (fs)
Pro
be p
hase
shi
ftPeak moves forward, and back is chopped off (masked by plasma response)
Increasing pump intensity
Results in Ar with thin gas target
pumpprobe EE
||pumpprobe EE
Ne=2x1016 cm-3
Inst. positive response
plasma
Peak inst. phase shift vs. peak intensity
• In both Ar and N2, no hint of saturation or negative instantaneous nonlinear phase1
• response is linear in intensity up to ionization!
• We think original HOKE experiment observed a plasma grating2.
N2
Ar
HOKE in ArLoriot et al.
1. J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, Phys. Rev. Lett. 107, 103901, (2011).2. JKW and HMM, Opt. Lett. 36, 3822 (2011)
-200 0 200 400 600 800 1000 1200 1400
0
0.05
0.1
0.15
0.2
0.25
0.3D2 parallel
time (fs)
(rad
)
40AC45AC
46AC
56AC
66AC76AC
D2 parallel phase 53AC
50 100 150 200 250 300 350 400 450 500
10
20
30
40
50
60
70
80
90
100
0 200 400 600 800 1000 1200 1400 1600-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
D2
time (fs)
(rad
)
inst.
rot.
Enabled: Single shot measurement of rotational revivals in H2 and D2
Experiment Theory: dens matrix
Quantum revivalsplus ionization revivals
ionization
Gas Our result Shelton and Rice (derived from THG or ESHG)
He 0.031±0.005 0.037 Ne 0.087±0.013 0.094 Ar 0.97±0.15 1.09 Kr 1.62±0.24 2.47 Xe 6.36±0.95 6.39
n2 (10-19 cm2/W)
n=n2I holds until ionization occurs, beyond the range of perturbation theory, and appears to be a universal scaling
Results in noble gases**PRL 109, 113904 (2012)
Summary
• Filament physics is highly interdisciplinary, with significant worldwide activity
plasma physics, (extreme) nonlinear optics, atomic& molecular physics, atmospheric physics
• Improvements and intriguing applications are possible, but these rest on detailed understanding of femtosecond atomic/molecular response in a laser intensity range where the physics is incompletely understood.