S. Varma, Y.-H. Chen, and H. M. Milchberg
Institute for Research in Electronics and Applied PhysicsDept. of Electrical and Computer Engineering
Dept. of Physics
UNIVERSITY OF MARYLAND AT COLLEGE PARK
Trapping and destruction of long range high intensity optical/plasma filaments by molecular
quantum wakes
HEDLP - 2008 Support: DoE, NSF, JHU-APL
Some applications of filaments
• directed energy
• triggering and guiding of lightening
• remote detection: LIDAR, LIBS
• directed, remote THz generation
• High power, femtosecond laser beams propagating through air form extremely long filaments due to nonlinear self-focusing ((3)) dynamically balanced by ionization and defocusing.
Introduction to Filamentation
neff = n0 + ngas + nplasma
0
Pcr ~ 2/8n0n2
Filament images at increasing power
(Pcr occurs at 1.25 mJ for a 130fs pulse)
What does a filament look like?
5 mm
0.8Pcr 1.3Pcr 1.8Pcr 2.3Pcr 2.8Pcr 3.5 mJ
“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
Field alignment and “revivals” 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
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
A pump pulse generates transient
refractive index n (r, t)
Extract probe (x, t) to obtain n(x, t).
medium
Probe Ref.
Pump pulse
x
y
z
Probe and Ref.
• Temporally stretched (chirp) for long temporal field of view (~ 2 ps).
• ~100 nm bandwidth supercontinuum gives ~10 fs resolution.
CCDImaging
spectrometer
Probe Ref.
Imaging lens
Single-shot Supercontinuum Spectral Interferometry (SSSI) – Imagine a streak camera with 10fs resolution!
Experimental setup and sample interferogram
Chen, Varma, York and Milchberg, Opt. Express 15, 11341 (2007)
0 ps ~ 2 ps
723nm652nm
250
m
N2O gas
Sample interferogram
Rotational wavepacket of D2 and H2 molecules
P=7.8 atmI=4.4x1013 W/cm2
room temperature
SSSI measurement showing alignment and anti-alignment “wake” traveling at the group velocity of the pump pulse.
Rotational quantum “wakes” in air
Vg pump
vg pump
TN2 , ¾TO2
Pump-probe filament experiment
Polarizing beamsplitter
Object plane
2m filament
CCD
f/300 focusing
5 m
m
8.0 8.4 8.8 (ps)
B
A
C D
(ps)8.0 8.4 8.8
Filaments are trapped/enhanced or destroyed
TN2 , ¾TO2
Trapped filaments are ENHANCED
White light generation, filament length and spectral broadening are enhanced.
Aligning filament (left) and probing filament (right), misaligned
Both beams collinear, probe filament coincident with alignment
wake of N2 and O2 in air
CCD camera saturation
Conclusions
• SSSI enables us to probe refractive index transients with ~10fs resolution over 2ps in a single shot, allowing us to observe room-temperature molecular alignment.
• A high intensity laser filament propagating in the quantum wake of molecular alignment can be controllably and stably trapped and enhanced, or destroyed.
• Applications: directed energy, remote sensing, etc...
Response near t=0
(ps)(ps)
Increasing aligning pulse energy
0.68Pcr
1.12Pcr
1.72Pcr
2.20Pcr
2.60Pcr
3.72Pcr
Pump power
scan (probe=3.4Pcr)
A
Alaser
Spectral broadening
The spatio-temporally varying refractive index of the wake of molecular alignment causes predictable spectral modulation and broadening of the probe filament.
Alignment v. delay
A
B
C
D
E
Filament spectrum v. delay
AB
CD
E
Molecular rotational wavepacket revivals
mode-locking analogy: coherent sum of longitudinal modesmode-locking analogy: coherent sum of longitudinal modes
pulse width ≈ (round trip time) / (# of modes)pulse width ≈ (round trip time) / (# of modes)
typ. spectrum
Example: N2
Example: N2
peak width ≈T / jmax(jmax+1) ~ 40 fs for N2peak width ≈T / jmax(jmax+1) ~ 40 fs for N2
ps
T/4
T=8.2ps
nitrogen
T/23T/4
modes
1D spatially resolved temporal evolution of O2 alignment
x (m)
(ps)
(fs)
x(m)
0 0.25 0.5
0.75 1 1.25
• pump peak intensity:2.7x1013 W/cm2
• 5.1 atm O2 at room temperature
• =11.6 ps
• High power, femtosecond laser beams that propagate through air form extremely long filaments due to nonlinear self-focusing ((3)) dynamically balanced by ionization and defocusing.
• Filaments can propagate through air up to 100s of meters, and are useful for remote excitation, ionization and sensing.
Introduction to Filamentation
Rotational wavepacket of H2 molecules at room temperature
Fouriertransform 2HB =61.8 cm1
=270 fs
The pump intensity bandwidth (~2.5x1013 s-1) is even less adequate than in D2 to populate j=2 and j=0 states.
Weaker rotational wavepacket amplitude.
P=7.8 atmI=4.4x1013 W/cm2
2H 0.3010-24 cm3
Experiment:
Lineout at x=0 Calculation:
Charge density wave in N2 at 1 atm
• Filament ionization fraction ~10-3 2x1016 cm3
• ~0.5% ponderomotive charge separation at enhanced intensity ~5x1014 W/cm2 over 50-100 fs alignment transient Ne~ 1014 cm-3 E~ 0.75 MV/cm
• Many meters of propagation
Quantum beat index bucket
vg
“probe” pulse
-- +
Experimental setup and sample interferogram
xenon gas cell
1 kHz Ti:Sapphire regenerative amplifier
110 fs
Michelson interferometer
P: pinholeBS: beamsplitterHWP: /2 plateSF4: dispersive materialsupercontinuum
(SC)
~300 J
(up to ~8 atm)
(1-2 atm)
0 ps ~ 2 ps
723nm652nm
250
m
N2O gas
Optical Kerr effect ((3)) and the molecular rotational response in the gas induce spectral phase shift and amplitude modulation on the interferogram.
Both spectral phase and amplitude information are required to extract the temporal phase (refractive index).
high pressureexp gas cell
Sample interferogram
Experimental setup and sample interferogram
xenon gas cell
1 kHz Ti:Sapphire regenerative amplifier
110 fs
Michelson interferometer
P: pinholeBS: beamsplitterHWP: /2 plateSF4: dispersive materialsupercontinuum
(SC)
~300 J
(up to ~8 atm)
(1-2 atm)
0 ps ~ 2 ps
723nm652nm
250
m
N2O gas
Optical Kerr effect ((3)) and the molecular rotational response in the gas induce spectral phase shift and amplitude modulation on the interferogram.
Both spectral phase and amplitude information are required to extract the temporal phase (refractive index).
high pressureexp gas cell
Sample interferogram