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