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Misha Ivanov Surprising strong field dynamics in laser filaments Lasing without inversion in the air (N 2 ) Bound states of a free electron.

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Presentation on theme: "Misha Ivanov Surprising strong field dynamics in laser filaments Lasing without inversion in the air (N 2 ) Bound states of a free electron."— Presentation transcript:

1 Misha Ivanov Surprising strong field dynamics in laser filaments Lasing without inversion in the air (N 2 ) Bound states of a free electron

2 Lasing without inversion in the air D.Kartashov, S. Haessler, G. Andriukaitis, A. Pugžlys, A. Baltuška A. Zheltikov J. Möhring, M. Motzkus M. Richter, F. Morales, O. Smirnova M. Spanner

3 Laser filamentation: the bare basics Kerr effect and Kerr lens 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

4 Laser filamentation: the bare basics Looks pretty Broad spectrum: UV- IR Looks pretty Broad spectrum: UV- IR

5 Strong field molecular alignment: the bare basics Induced dipole:  d(E)=  x  E cos  t - oscillates with the field Cycle-averaged interaction energy: U(  )=- ¼ [  E 2 cos 2  Induced dipole:  d(E)=  x  E cos  t - oscillates with the field Cycle-averaged interaction energy: U(  )=- ¼ [  E 2 cos 2  N 2 Field-free alignment after a short pulse F cos  t 

6 Key facts for today Air is made of molecules, mostly N2

7 Key facts for today Air is made of molecules, mostly N2 Filamentation by-product I: They rotate Filamentation by-product I: They rotate

8 Key facts for today Air is made of molecules, mostly N2 Filamentation by-product II: molecular ions N 2 + Energy, eV R, Å N2+N2+ N2+N2+ Filamentation by-product I: They rotate Filamentation by-product I: They rotate

9 Key facts for today Air is made of molecules, mostly N2 Filamentation by-product II: molecular ions N 2 + Filamentation by-product III : broad spectra, one-photon transitions can saturate Filamentation by-product II: molecular ions N 2 + Filamentation by-product III : broad spectra, one-photon transitions can saturate Energy, eV R, Å N2+N2+ N2+N2+ B(v=0) -> X(v=0): 391 nm Filamentation by-product I: They rotate Filamentation by-product I: They rotate

10 Key facts for today Air is made of molecules, mostly N2. Filamentation makes them rotate You do not even need to saturate X-> B to make it lase ! Energy, eV R, Å N2+N2+ N2+N2+ B(v=0) -> X(v=0): 391 nm

11 Inversion without inversion X B X B Inversion without inversion: B -> X is a parallel transition More X molecules than B molecules: P X >P B But more aligned B molecules than X molecules: P B (  =0)>P X (  =0) More X molecules than B molecules: P X >P B But more aligned B molecules than X molecules: P B (  =0)>P X (  =0)

12 Inversion without inversion W up ~ X P X W down ~ B P B Gain: W up - W down < 0 X B X B Inversion without inversion:

13 R=P B /P X =1/2 Almost transient inversion Transient inversion induced by rotations W up - W down

14 R=P B /P X =1/2 Almost transient inversion Transient inversion induced by rotations 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 R=P B /P X =3/4 Transient inversion W up - W down

15 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 Universal: has been observed for a single pump 400 nm, 800 nm, 1  m, 2  m, 4  m Universal: has been observed for a single pump 400 nm, 800 nm, 1  m, 2  m, 4  m 9 th 11 th 391 emission in N  m pump 391 nm beam

16 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,... D XB (t)= D XB (  )= FT (D XB (t)) D XB (t)= D XB (  )= FT (D XB (t)) General only needs coherence between N 2 + (X) and N 2 + (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

17 Coherent polarization / Wave mixing: Effect of rotations Requires overlap of  X (t) and  B (t) D XB (t)= + c.c. Rotations with different period kill the overlap and D XB (t)

18 Opposite temporal patterns ‘Wave mixing’ Need time-resolved measurements ! W up - W down Inversion without inversion

19  m, 240 fsec Experiment II: Time-resolved measurements Starts immediately, Lasts ~ 15 psec Follows revivals in N 2 + B state Starts immediately, Lasts ~ 15 psec Follows revivals in N 2 + B state

20 Time-resolved signal: Experiment vs Theory Experimental FROG Spectra ‘Wave mixing’ FROG (Theory)

21 Time-resolved signal: Experiment vs Theory Experimental FROG Spectra Excellent Disagreement !

22 Time-resolved signal: complementary patterns Transient Inversion ‘Wave Mixing’ Experimental FROG Spectra R=1

23 Experiment vs Theory Transient Inversion Lasing without inversion: Threshold effect: better alignment – smaller R=P B /P X is needed Let us optimize alignment! Lasing without inversion: Threshold effect: better alignment – smaller R=P B /P X is needed Let us optimize alignment! R=3/4 Experimental FROG Spectra ‘Wave Mixing’

24 Experiment III: Optimized alignment 3 bar N 2 + emission: more than 10 4 brighter for optimal pulse sequence x delay,ps Optimal sequence The smoking gun?

25 Felipe Morales Maria Richter Serguei Patchkovskii Olga Smirnova Bound states of a free electron NRC Canada

26 What is common between these? Laser filamentation in the air Ilya Repin: Barge haulers on Volga

27 Laser filamentation: the bare basics Kerr effect and Kerr lens

28 Is ionization needed for filamentation? Intensity W/cm 2 n(I) Kerr effect, n(I), in 800 nm Is this really possible, and if possible – when, why, and how?

29 Acceleration of neutrals: ‘free’ electron pulling the parent ion But how is the rope made? Very strong laser field : U p =F 2 /4  2 ~ KeV k r e-e- e-e- + ~  m He, 800 nm, ~10 16 W/cm 2

30 -zFcos  t What happens when the laser intensity is very high? Oscillation amplitude  0 =F/  2 >> Angstrom -zFcos  t ionization Does above-barrier decay necessarily mean ionization? Again NO! ionization Does above-barrier decay necessarily mean ionization? Again NO! How the rope is made: frustrated ionization

31 How the rope is made: The Kramers-Henneberger atom Include both: Bound again! Bound electron Idea: W. Henneberger PRL, 1968 Very strong laser field: nearly free oscillations + Bound states of the KH potential make the rope

32 Bound states of the free electron -zFcos  t W/cm nm The electron is placed at the exit from the barrier, simulating tunnel ionization. It refuses to behave ionized in % of cases.

33 Kerr response in strong low-frequency laser fields -zFcos  t Note: at I~10 13 W/cm 2 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 W/cm 2 Kr, Xe, Ar, O 2, N 13 W/cm 2 - zFcos  t

34 Analysis In the KH regime for the excited states, E n (F)=E n +U p +  E n The ground state still goes down: E g (F)=E g -  E g Intensity,>10 13 W/cm 2 E n (F,  ) – bound states of a ‘free’ electron E g (F,  ) Energy Intensity  inst (I,  ) Can this be seen with everything else (ionization, real excitation) piling up on top?

35 Any signatures of this physics? TDSE for 3D Hydrogen Grid Spacing  Z Time step 1: / : / x: / : / x 21 Field, z axis  axis 400 a.u. 800 a.u a.u.

36 Role of box size 2x 21 Field, z axis  axis 400 a.u. 800 a.u 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

37 High order Kerr effect: TDSE for 3D Hydrogen Short pulse: sin 2 with 4 cycles turn-on and turn-off, =0.9  m

38 High order Kerr effect: TDSE for 1D Hydrogen Short pulse: sin 2 with 4 cycles turn-on and turn-off, =1.8  m

39 High order Kerr effect: TDSE for 1D Hydrogen Short 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

40 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’

41 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

42 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 floor Misha: No, we shouldn’t. Sanded floors get slippery when wet, we can slip and fall Rob: No, Misha, we should. If we don’t sand the floor, we’ll get splinters into our bare feet!

43 Proposal for HOKE Consensus Misha Ivanov and Bob Levis agreed to build a Russian wet-sauna. But they could not agree on what floor is best Rob : We should shave and sand the floor Misha: No, we shouldn’t. Sanded floors get slippery when wet, we can slip and fall Rob: No, Misha, we should. Otherwise we’ll get splinters! They went to ask the Rabbi. Rabbi, who is right?

44 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 floor Misha: No, we shouldn’t. Sanded floors get slippery when wet, we can slip and fall Rob: No, Misha, we should. Otherwise we’ll get splinters! They went to ask the Rabbi. Rabbi, who is right? You are both right!

45 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 floor Misha: No, we shouldn’t. Sanded floors get slippery when wet, we can slip and fall Rob: No, Misha, we should. Otherwise we’ll get splinters! They went to ask the Rabbi. We can’t both be right! You are both right!

46 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 floor Misha: No, we shouldn’t. Sanded floors get slippery when wet, we can slip and fall Rob: No, Misha, we should. Otherwise we’ll get splinters! They went to ask the Rabbi. We can’t both be right! Yes you can!

47 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 floor Misha: No, we shouldn’t. Sanded floors get slippery when wet, we can slip and fall Rob: No, Misha, we should. Otherwise we’ll get splinters! 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!

48 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 floor Misha: No, we shouldn’t. Sanded floors get slippery when wet, we can slip and fall Rob: No, Misha, we should. Otherwise we’ll get splinters! They went to ask the Rabbi. You should sand the floorboards, But put them sanded side down You should sand the floorboards, But put them sanded side down

49 Conclusions Looking inside a dressed atom is not easy!

50 High order Kerr effect: TDSE for 3D Hydrogen Short pulse: Gaussian FWHM=4 cycles, =0.9  m W/cm 2 Kerr is saturated No box size dependence! W/cm 2 Kerr is saturated No box size dependence! W/cm 2 Kerr is reversed Box-size dependence W/cm 2 Kerr is reversed Box-size dependence Field, a.u.

51 Short pulse: Gaussian FWHM=4cycles, =1.8  m High order Kerr effect: TDSE for 3D Hydrogen W/cm 2 Kerr is saturated No box size dependence! W/cm 2 Kerr is saturated No box size dependence! W/cm 2 Kerr is reversed Box-size dependence W/cm 2 Kerr is reversed Box-size dependence Field, a.u.

52 Short pulse: Gaussian FWHM=4 cycles, =1.8  m High order Kerr effect: TDSE for 3D Hydrogen W/cm 2 Kerr is saturated No box size dependence! W/cm 2 Kerr is saturated No box size dependence! W/cm 2 Kerr is reversed Box-size dependence W/cm 2 Kerr is reversed Box-size dependence 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.

53 High order Kerr effect: TDSE for 3D Hydrogen Short pulse: Gaussian FWHM=4 cycles, =1.8  m W/cm 2 Kerr is saturated No box size dependence! W/cm 2 Kerr is saturated No box size dependence!

54 Are the KH states really there? TDSE for 1D Hydrogen  m  m Flat-top pulse: sin 2 Turn-on/off in N cycles =4 cycles, 40 cycles flat top W/cm 2 Strong resonance Comes from KH states W/cm 2 Strong resonance Comes from KH states Field, a.u. Calculations by M. Richter, F. Morales Moreno, S. Patchkovskii

55 Are the KH states really there? Origin of resonance 6-photon Freeman resonance? - Happens at W/cm 2 ! - Do we see it in the Floquet analysis of  (t)? 6-photon Freeman resonance? - Happens at W/cm 2 ! - Do we see it in the Floquet analysis of  (t)? Intensity

56 The Floquet analysis 3,4, 5 photons at W/cm No large 6-photon component! Why?

57 No 6-photon resonance in the KH picture!  0 =F/  W/cm 2

58 Are the KH states really there? Origin of resonance  0 =F/  2 1-photon resonance between 1 st and 2 nd excited KH states 2 nd and 3 rd excited KH states This Floquet ladder is felt by the ground state 1-photon resonance between 1 st and 2 nd excited KH states 2 nd and 3 rd excited KH states This Floquet ladder is felt by the ground state Transition energies, a.u. Calculations by M. Richter, F. Morales Moreno

59 Are the KH states really there? TDSE for 1D Hydrogen  m Resonances are still present, even for =3  m =3  m Flat-top pulse: sin 2 Turn-on/off in N cycles =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.

60 ‘The KH atom exists’ means ‘Only few V n matter’ + harmonics Vn ( ,2  ) free electron oscillations If the KH harmonics act like perturbative fields, we can use standard Photo-Electron Spectroscopy idea: E n,k photo =E n +k  Photo-electron spectroscopy of the KH atom

61 Ip = 4.34 eV : Barrier suppression intensity I=1.5 x W/cm 2 Barrier suppression regime is easily achieved with routine setup Laser wavelength 800 nm, 3D, linear polarization, TDSE The system: Potassium atom

62 How the rope is made: frustrated ionization Oscillation amplitude  0 =F/  2 >> Angstrom T. Nubbemeyer, K. Gorling, A. Saenz, U. Eichmann, and W. Sandner, Phys. Rev. Lett. 101, (2008) G. Yudin and M. Ivanov, Phys. Rev. A, 63, (2001) T. Nubbemeyer, K. Gorling, A. Saenz, U. Eichmann, and W. Sandner, Phys. Rev. Lett. 101, (2008) G. Yudin and M. Ivanov, Phys. Rev. A, 63, (2001) -zFcos  t Suppose the electron tunneled out. ionization Does this really mean ionization? – No! Suppose the electron tunneled out. ionization Does this really mean ionization? – No!

63 Kerr response in strong-field limit -zFcos  t EgEg E n (F,t,  ) – bound states of a ‘free’ electron; On average, go up as Up=F 2 /4  2 Instantaneous response (virtual transitions only!) – almost like usual linear susceptibility – only for dressed states.

64 FROG UV- spectrometer SHG SHG spectrometer Pharos (Light Conversion) SLM Yb, Na:CaF 2 Regen. 1,03  m, 500 Hz, 7 mJ, 240 fs Experimental setup

65 FROG UV- spectrometer SHG SHG spectrometer Pharos (Light Conversion) SLM Yb, Na:CaF 2 Regen. 1,03  m, 500 Hz, 7 mJ, 240 fs Experimental setup

66 Optimal pulse sequence 3 bar N 2 fluorescence delay,ps

67 Spectroscopy of N 2 + What is the physical origin? Bright coherent emission in forward direction Observed lines

68 Physical origin: Possible Candidates Stimulated emission due to population inversion in N 2 + : more B than X Universal mechanism for creating population 400 nm, 800 nm, 1  m, 2  m, 4  m ??? Ionization into N 2 + X state dominates Requires seed – but seed can’t create inversion Collisions – why >10 4 enhancement by optimizing alignment ? Universal mechanism for creating population 400 nm, 800 nm, 1  m, 2  m, 4  m ??? Ionization into N 2 + X state dominates Requires seed – but seed can’t create inversion Collisions – why >10 4 enhancement by optimizing alignment ?

69 Transient inversion induced by rotations 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 R=P B /P X =3/4 Transient inversion R=P B /P X =1/2 Almost transient inversion W down - W up

70 Filamentation-based remote sensing of bad guys Lasing backward Send laser beam Filament Make a laser in the air, detect backward emission Collect information

71 Filamentation-based remote sensing of bad guys Lasing backward Send laser beam Filament Laser in the air that shoots backwards – not yet, not today  Collect information Laser in the air that shoots forward & without inversion - today

72  m, 240 fsec Time-resolved measurements Frequency-integrated cross-correlation Starts immediately, Lasts ~ 15 psec Sensitive to rotations – but in N 2 + B state! Starts immediately, Lasts ~ 15 psec Sensitive to rotations – but in N 2 + B state!


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