misha ivanov surprising strong field dynamics in laser filaments lasing without inversion in the air...

Misha IvanovMisha Ivanov

Surprising strong field dynamics in laser filaments

• Lasing without inversion in the air (N2)

• Bound states of a free electron

• Lasing without inversion in the air

D.Kartashov, S. Haessler, G. Andriukaitis, A. Pugžlys, A. BaltuškaD.Kartashov, S. Haessler, G. Andriukaitis, A. Pugžlys, A. Baltuška

A. ZheltikovA. Zheltikov

J. Möhring, M. MotzkusJ. Möhring, M. Motzkus

M. Richter, F. Morales, O. SmirnovaM. Richter, F. Morales, O. Smirnova

M. SpannerM. Spanner

Laser filamentation: the bare basicsLaser filamentation: the bare basics

)()(

)(

20

20

rInnrn

InnIn

Kerr effect and Kerr lensKerr effect and Kerr lens

tFtntd

cos1

)()(2plasma

• Self-guided beam, can move very far• Interplay of self-focusing and defocusing • Self-guided beam, can move very far• Interplay of self-focusing and defocusing


• Looks pretty •Broad spectrum: UV- IR• Looks pretty •Broad spectrum: UV- IR

Strong field molecular alignment: the bare basicsStrong field molecular alignment: the bare basics

Induced dipole:d(E)= xE cost

- oscillates with the field

Cycle-averaged interaction energy:U()=- ¼ [E2cos2

Induced dipole:d(E)= xE cost

- oscillates with the field

Cycle-averaged interaction energy:U()=- ¼ [E2cos2

N2 Field-free alignment after a short pulseN2 Field-free alignment after a short pulse

F cost

Key facts for today

• Air is made of molecules, mostly N2• Air is made of molecules, mostly N2

Key facts for today


• Filamentation by-product I: They rotate


Key facts for today


• Filamentation by-product II: molecular ions N2+• Filamentation by-product II: molecular ions N2+

1.0 1.2 1.4 1.6 1.8 2.00

2

4

6

8

354,89

356,39

388,43

210

1

B2u

A2u

X2g

Energ

y, eV

internuclear distance, A

0

391,44

427,81

358,21En

ergy

, eV

Ener

gy, e

V

R, ÅR, Å

N2+N2+



Key facts for today


• Filamentation by-product II: molecular ions N2+

• Filamentation by-product III : broad spectra, one-photon transitions can saturate

• Filamentation by-product II: molecular ions N2+

• Filamentation by-product III : broad spectra, one-photon transitions can saturate

1.0 1.2 1.4 1.6 1.8 2.00

2

4

6

8

354,89

356,39

388,43

210

1

B2u

A2u

X2g

Energ

y, eV


0

391,44

427,81

358,21En

ergy

, eV

Ener

gy, e

V

R, ÅR, Å

N2+N2+

B(v=0) -> X(v=0): 391 nmB(v=0) -> X(v=0): 391 nm



Key facts for today

• Air is made of molecules, mostly N2. Filamentation makes them rotate• Air is made of molecules, mostly N2. Filamentation makes them rotate

• You do not even need to saturate X-> B to make it lase !• You do not even need to saturate X-> B to make it lase !

1.0 1.2 1.4 1.6 1.8 2.00

2

4

6

8

354,89

356,39

388,43

210

1

B2u

A2u

X2g

Energ

y, eV


0

391,44

427,81

358,21En

ergy

, eV

Ener

gy, e

V

R, ÅR, Å

N2+N2+

B(v=0) -> X(v=0): 391 nmB(v=0) -> X(v=0): 391 nm

Inversion without inversion

X

B

X

B

• Inversion without inversion: • Inversion without inversion:

• B -> X is a parallel transition • B -> X is a parallel transition

• More X molecules than B molecules: PX>PB

• But more aligned B molecules than X molecules: PB (=0)>PX(=0)

• More X molecules than B molecules: PX>PB

• But more aligned B molecules than X molecules: PB (=0)>PX(=0)

Inversion without inversion

Wup ~ <cos2>X PXWup ~ <cos2>X PX

Wdown ~ <cos2>B PBWdown ~ <cos2>B PB

Gain: Wup - Wdown < 0Gain: Wup - Wdown < 0X

B

X

B

• Inversion without inversion: • Inversion without inversion:

R=PB/PX=1/2R=PB/PX=1/2

Almost transient inversion

Transient inversion induced by rotations

Wup - WdownWup - Wdown




• Lasing without inversion: transient inversion during rotational revivals• Better alignment – smaller R is needed for transient inversion • Lasing without inversion: transient inversion during rotational revivals• Better alignment – smaller R is needed for transient inversion


Transient inversion

Wup - Wdown Wup - Wdown

Experiment I: Bright emission

• Forward, well collimated• Needs a seed:

Appears only when filamentation generates spectrum around 390

• Forward, well collimated• Needs a seed:

Appears only when filamentation generates spectrum around 390

300 350 400 450 5000

10000

20000

30000

40000

50000S

pect

ral i

nte

nsi

ty

wavelength, nm

9th

11th

391 emission in N2+

4 m pump4 m pump

391 nm beam

Another candidate ?

• Emission due to coherent polarization •a.k.a. Wave mixing, Parametric emission,...

• Emission due to coherent polarization •a.k.a. Wave mixing, Parametric emission,...

DXB(t)= < X(t)|d|B(t) > DXB()= FT (DXB(t))

DXB(t)= < X(t)|d|B(t) > DXB()= FT (DXB(t))

• General • only needs coherence between N2

+ (X) and N2+(B)

• all it needs is a seed around 390 nm• will happen for all pump wavelengths that make filaments

• Will last after the filament is gone, as long as X-B coherence lasts• Natural sensitivity to rotations

Coherent polarization / Wave mixing: Effect of rotations

• Requires overlap of X(t) and B(t)• Requires overlap of X(t) and B(t)

• DXB(t)= <X(t)|d| B(t)> + c.c.• DXB(t)= <X(t)|d| B(t)> + c.c.

• Rotations with different period kill the overlap and DXB(t)• Rotations with different period kill the overlap and DXB(t)

Opposite temporal patterns

‘Wave mixing’ ‘Wave mixing’

• Need time-resolved measurements !• Need time-resolved measurements !

Wup

- W

dow

n W

up -

Wdo

wn Inversion without

inversionInversion without inversion

• Experiment @ 1.03 m, 240 fsec• Experiment @ 1.03 m, 240 fsec

Experiment II: Time-resolved measurements

• Starts immediately, • Lasts ~ 15 psec• Follows revivals in N2

+ B state

• Starts immediately, • Lasts ~ 15 psec• Follows revivals in N2

+ B state

Time-resolved signal: Experiment vs Theory

Experimental FROG SpectraExperimental FROG Spectra ‘Wave mixing’ FROG (Theory)‘Wave mixing’ FROG (Theory)

Time-resolved signal: Experiment vs Theory

Experimental FROG SpectraExperimental FROG Spectra Excellent Disagreement !Excellent Disagreement !

Time-resolved signal: complementary patterns

Transient InversionTransient Inversion ‘Wave Mixing’‘Wave Mixing’Experimental FROG SpectraExperimental FROG Spectra

R=1R=1

Experiment vs Theory

Transient InversionTransient Inversion

• Lasing without inversion:• Threshold effect: better alignment – smaller R=PB/PX is needed• Let us optimize alignment!

• Lasing without inversion:• Threshold effect: better alignment – smaller R=PB/PX is needed• Let us optimize alignment!

R=3/4R=3/4

Experimental FROG SpectraExperimental FROG Spectra ‘Wave Mixing’‘Wave Mixing’

Experiment III: Optimized alignment

3 ba

r

N2+ emission: more

than 104 brighter for optimal pulse sequence

x 10-4

delay,ps

Optimal sequence Optimal sequence

The smoking gun?

Felipe MoralesFelipe MoralesMaria RichterMaria Richter

Serguei PatchkovskiiSerguei Patchkovskii

Olga SmirnovaOlga Smirnova

Bound states of a free electron

NRC Canada

What is common between these?What is common between these?

Laser filamentation in the air

Ilya Repin: Barge haulers on Volga


)()(

)(

20

20

rInnrn

InnIn

Kerr effect and Kerr lensKerr effect and Kerr lens

tFtntd

cos1

)()(2plasma

)(])()([)( *)3( FFFd

Is ionization needed for filamentation?Is ionization needed for filamentation?

Intensity

1013 W/cm2

n(I) Kerr effect, n(I), in air @ 800 nm

• Is this really possible, and if possible – when, why, and how?• Is this really possible, and if possible – when, why, and how?

Acceleration of neutrals: ‘free’ electron pulling the parent ionAcceleration of neutrals: ‘free’ electron pulling the parent ion

But how is the rope made? But how is the rope made?

Very strong laser field:Up=F2/42~ KeV

k

r

e-e-

+

~ m

He, 800 nm, ~1016 W/cm2

-zFcost

What happens when the laser intensity is very high?

Oscillation amplitude 0=F/2 >> AngstromOscillation amplitude 0=F/2 >> Angstrom

-zFcost

Does above-barrier decay necessarily mean ionizationionization? Again NO!Does above-barrier decay necessarily mean ionizationionization? Again NO!

How the rope is made: frustrated ionizationHow the rope is made: frustrated ionization

How the rope is made: The Kramers-Henneberger atomHow the rope is made: The Kramers-Henneberger atom

Include both:Bound again!

Bound electronIdea: W. Henneberger PRL, 1968

Very strong laser field:nearly free oscillations

+

Bound states of the KH potential make the ropeBound states of the KH potential make the rope

Bound states of the free electronBound states of the free electron

-zFcost

6.1014 W/cm2

800 nm

The electron is placed at the exit from the barrier, simulating tunnel ionization. It refuses to behave ionized in 15-20% of cases.

The electron is placed at the exit from the barrier, simulating tunnel ionization. It refuses to behave ionized in 15-20% of cases.

Kerr response in strong low-frequency laser fieldsKerr response in strong low-frequency laser fields

-zFcost

Note: • at I~1013 W/cm2 all excited states are way above barrier, and ground state is well below• Oscillation amplitude 0> 6 a.u is large

Pertinent to all phenomena which include response of bound states in strong fields, e.g. Kerr effect around and above 1013 W/cm2

Kr, Xe, Ar, O2, N2, @1013 W/cm2

- zFcost

AnalysisAnalysis

In the KH regime for the excited states, En(F)=En+Up+En

The ground state still goes down: Eg(F)=Eg-Eg

Intensity ,>1013W/cm2

En (F,) – bound states of a ‘free’ electron

Eg(F,)

Energy

Intensity

inst(I,)

Can this be seen with everything else (ionization, real excitation) piling up on top?Can this be seen with everything else (ionization, real excitation) piling up on top?

n gn

ng

tFEtFE

tFztFtd

),(),(

|),(|2cos)(

2

Any signatures of this physics? TDSE for 3D HydrogenAny signatures of this physics? TDSE for 3D Hydrogen

Grid Spacing Z Time step 1: 0.2 0-100 +/-200 0.0052: 0.2 0-100 +/-400 0.005 2x: 0.2 0-200 +/-800 0.005 3: 0.1 0-100 +/-400 0.00125

2x2 1

Field, z axisField, z axis

axis

400 a.u.

800 a.u.1600 a.u.

Role of box sizeRole of box size

2x2 1

Field, z axisField, z axis

axis

400 a.u.

800 a.u.1600 a.u.

Role of the box size: • Absorb more, or less, free electrons• See how this changes the Kerr response

Role of the box size: • Absorb more, or less, free electrons• See how this changes the Kerr response

High order Kerr effect: TDSE for 3D HydrogenHigh order Kerr effect: TDSE for 3D Hydrogen

Short pulse: sin2 with 4 cycles turn-on and turn-off, =0.9 mShort pulse: sin2 with 4 cycles turn-on and turn-off, =0.9 m


Short pulse: sin2 with 4 cycles turn-on and turn-off, =1.8 mShort pulse: sin2 with 4 cycles turn-on and turn-off, =1.8 m


Short pulse: Gaussian FWHM=4 cycles, =1.8 mShort pulse: Gaussian FWHM=4 cycles, =1.8 m

Saturation of the Kerr response• Happens just before ionization kicks in• Once ionization kicks in, it takes over• HOKE is real, but is important in a very narrow intensity window• KH states are playing major role

Saturation of the Kerr response• Happens just before ionization kicks in• Once ionization kicks in, it takes over• HOKE is real, but is important in a very narrow intensity window• KH states are playing major role

Conclusions: Lasing without inversion

• Laser filamentation leads to• Very broad spectrum

-> Easy saturation of 1-photon transitions in the ion: IR-nearUV• Ionization • Molecular alignment

• Rotational revivals naturally create time-windows with population inversion• Better alignment – better lasing ‘without inversion’

Conclusions: HOKE

• In general, saturation of the Kerr effect comes from:• Ionization (major player) • Real excitations to ‘bound states of the free electron’• Modification of the instantaneous response (i.e. virtual transitions) due to restructuring of the dressed atom.

• Restructuring of the atom leads to saturation and – partly – to the onset of the reversal of the Kerr effect

• This happens just before ionization kicks in• Ionization starts to dominate as soon as it kicks in

• The interplay of the three effects is strongly pulse-shape dependent

Proposal for HOKE Consensus

Misha and Rob agreed to build a Russian wet-sauna. But they could not agree on what floor is best

Rob : We should shave and sand the floorMisha: No, we shouldn’t. Sanded floors get slippery when wet,

we can slip and fallRob: No, Misha, we should. If we don’t sand the floor, we’ll get splinters into our bare feet!


Misha Ivanov and Bob Levis agreed to build a Russian wet-sauna. But they could not agree on what floor is best


we can slip and fallRob: No, Misha, we should. Otherwise we’ll get splinters!

They went to ask the Rabbi.

Rabbi, who is right? Rabbi, who is right?






Rabbi, who is right? You are both right!You are both right!






We can’t both be right!We can’t both be right!You are both right!






We can’t both be right!Yes you can!Yes you can!





They went to ask the Rabbi. OK, Rabbi, we can’t argue with you. But what shall we do with the floor? Shall we sand the floorboards or not?

OK, Rabbi, we can’t argue with you. But what shall we do with the floor? Shall we sand the floorboards or not?

Yes you can!






You should sand the floorboards, But put them sanded side down

You should sand the floorboards, But put them sanded side down

Conclusions

•Looking inside a dressed atom is not easy!



4.3 1013 W/cm2

• Kerr is saturated• No box size dependence!

4.3 1013 W/cm2


5.6 1013 W/cm2

• Kerr is reversed• Box-size dependence

5.6 1013 W/cm2


Field, a.u.

Short pulse: Gaussian FWHM=4cycles, =1.8 mShort pulse: Gaussian FWHM=4cycles, =1.8 m


4.3 1013 W/cm2


4.3 1013 W/cm2


5.6 1013 W/cm2


5.6 1013 W/cm2


Field, a.u.



4.3 1013 W/cm2


4.3 1013 W/cm2


5.6 1013 W/cm2


5.6 1013 W/cm2


Saturation of the Kerr response• Happens just before ionization kicks in• Once ionization kicks in, it takes over• HOKE is real, but is important in a very narrow intensity window

Saturation of the Kerr response• Happens just before ionization kicks in• Once ionization kicks in, it takes over• HOKE is real, but is important in a very narrow intensity window

Field, a.u.

Are the KH states really there? TDSE for 1D HydrogenAre the KH states really there? TDSE for 1D Hydrogen

m

Resonances are still present, even for =3 m

=3m

Flat-top pulse: sin2 Turn-on/off in Ncycles=4 cycles, 40 cycles flat topFlat-top pulse: sin2 Turn-on/off in Ncycles=4 cycles, 40 cycles flat top

• Deviations from standard model are much more prominent for flat-top pulses• KH states are responsible for resonances

• Deviations from standard model are much more prominent for flat-top pulses• KH states are responsible for resonances

Field, a.u.

‘The KH atom exists’ means ‘Only few Vn

matter’

+ harmonics Vn (,2)

free electron oscillations

If the KH harmonics act like perturbative fields, we can use

standard Photo-Electron Spectroscopy idea: En,kphoto=En+k

Photo-electron spectroscopy of the KH atomPhoto-electron spectroscopy of the KH atom

Ip = 4.34 eV : Barrier suppression intensity I=1.5 x 1012

W/cm2

Barrier suppression regime is easily achieved with routine setup

Laser wavelength 800 nm, 3D, linear polarization, TDSE

The system: Potassium atomThe system: Potassium atom

How the rope is made: frustrated ionizationHow the rope is made: frustrated ionization

Oscillation amplitude 0=F/2 >> AngstromOscillation amplitude 0=F/2 >> Angstrom

• T. Nubbemeyer, K. Gorling, A. Saenz, U. Eichmann, and W. Sandner, Phys. Rev. Lett. 101, 233001 (2008)

• G. Yudin and M. Ivanov, Phys. Rev. A, 63, 033404 (2001)

-zFcost

-zFcost

Suppose the electron tunneled out. Does this really mean ionizationionization? – No!

Suppose the electron tunneled out. Does this really mean ionizationionization? – No!

Kerr response in strong-field limitKerr response in strong-field limit

-zFcost

n gn

ng

tFEtFE

tFztFtd

),(),(

|),(|2cos)(

2

Eg

En (F,t,) – bound states of a ‘free’ electron;

On average, go up as Up=F2/42

n gn

ng

EE

ztFtd

2||2cos)(

Instantaneous response (virtual transitions only!) – almost like usual linear susceptibility – only for dressed states.Instantaneous response (virtual transitions only!) – almost like usual linear susceptibility – only for dressed states.

FROG

UV-spectrometer

UV-spectrometer

SHG

SHG spectrometer

Pharos(Light Conversion)SLM

Yb, Na:CaF2

Regen.

1,03 m, 500 Hz, 7 mJ, 240 fs

Experimental setupExperimental setup

Optimal pulse sequence

3 ba

r

N2 fluorescence N2 fluorescence

delay,ps

Spectroscopy of N2+

1.0 1.2 1.4 1.6 1.8 2.00

2

4

6

8

354,89

356,39

388,43

210

1

B2u

A2u

X2g

Energ

y, eV


0

391,44

427,81

358,21

What is the physical origin?What is the physical origin?

Bright coherent emission in forward directionBright coherent emission in forward direction

Observed linesObserved lines

Physical origin: Possible Candidates

• Stimulated emission due to population inversion in N2+: more B than X • Stimulated emission due to population inversion in N2+: more B than X


• Lasing without inversion: transient inversion during rotational revivals• Better alignment – smaller R is needed for transient inversion • Lasing without inversion: transient inversion during rotational revivals• Better alignment – smaller R is needed for transient inversion


Transient inversion



Wdown - Wup Wdown - Wup

Filamentation-based remote sensing of bad guys

Lasing backwardLasing backward

Send laser beamSend laser beam

FilamentFilament

Make a laser in the air, detect backward emissionMake a laser in the air, detect backward emission

Collect informationCollect information

Filamentation-based remote sensing of bad guys

Lasing backwardLasing backward

Send laser beamSend laser beam

FilamentFilament

Laser in the air that shoots backwards – not yet, not today Laser in the air that shoots backwards – not yet, not today

Collect informationCollect information

Laser in the air that shoots forward & without inversion - today Laser in the air that shoots forward & without inversion - today

• Experiment @ 1.03 m, 240 fsec• Experiment @ 1.03 m, 240 fsec

Time-resolved measurements

Frequency-integrated cross-correlation

-2 0 2 4 6 8 10 12 140.0

0.1

Revival of the excited ionic

state B2 B=2.073 cm-1

(anti-Stokes branch)

Cro

ss-C

orre

latio

n In

tens

ity

Delay, ps

Theory P(N

2)=1.8 bar (J une 28)

P(N2)=2.1 bar (J une 27)

Revival of the ground ionic

state X2B=1.92 cm-1

(Stokes branch)

Starts immediately, Lasts ~ 15 psecSensitive to rotations – but in N2

+ B state!Starts immediately, Lasts ~ 15 psecSensitive to rotations – but in N2

+ B state!

misha ivanov surprising strong field dynamics in laser filaments lasing without inversion in the air...

Documents

inversion x b x b inversion

p x p b

p b p x

x molecules

x p x w

n2 slide

n2 filamentation byproduct

n2 n2 n2 n2 bv