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.