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J.K. Wahlstrand, Y.-H. Chen a , Y.-H. Cheng, J. Palastro, S. Varma b , and H.M. Milchberg

UNIVERSITY OF MARYLAND AT COLLEGE PARK. The extreme nonlinear optics of gases and femtosecond optical filamentation. J.K. Wahlstrand, Y.-H. Chen a , Y.-H. Cheng, J. Palastro, S. Varma b , and H.M. Milchberg Dept. of Physics Dept. of Electrical and Computer Engineering

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J.K. Wahlstrand, Y.-H. Chen a , Y.-H. Cheng, J. Palastro, S. Varma b , and H.M. Milchberg

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  1. UNIVERSITY OF MARYLAND AT COLLEGE PARK The extreme nonlinear optics of gases and femtosecond optical filamentation 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 a- LLNL (2012 APS-DPP thesis award) b- JHU-APL Support: ONR, NSF, DoE, Lockheed Martin MIPSE Nov. 7, 2012

  2. CW laser or weak pulse lens CW laser or weak pulse - - - - - - - - - - - - - - - - - - - ‘intense’ ~100fs laser pulse PLASMA FILAMENT Ultra short pulse propagation in gases

  3. 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 ()

  4. Guided high voltage electrical breakdown laser filament Non-guided Filament guided Examples of filament applications: J. Kasparian et al., Science 301, 61-64 (2003). Remote sensing at 20 km - LIDAR

  5. Laser-assisted condensation J. Kasparian et al. Laser filaments promote particle condensation even at « low » humidity (70%) Non-linear scaling with incident power 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)

  6. Laser Heated Air Plasmas and N2 Lasing Ne ~1015 – 1017 cm-3 , Te ~1 eV PLASMA FILAMENT Lasing? - - - - - - - - - - - - - - - - - - - NRL: J.R. Penano et al., J. Appl. Phys. 111, 033105 (2012) ‘intense’ ~100fs laser pulse Vienna: Kartashov et al, PRA 86, 033831 (2012) - got lasing using a 4m driver laser, 5 atm N2 , 1 atm Ar D. Gordon, J. Penano, A. Ting, P. Sprangle, Naval Research Laboratory Jennifer 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.

  7. 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 extinguishing Nonlinearity control:filament lengthening, e-density enhancement, and optical pulse shaping Can filaments be made more useful?

  8. Evolution of laser power Nonlinear QED 24 30 10 10 21 27 10 10 ) 2 18 24 10 10 Laser intensity limit Peak Power (W) Focused intensity (W/cm 15 21 10 10 Nonlinear relativistic optics Free electrons 12 18 10 10 where filaments ‘live’ Chirped pulse amplification Free electrons 9 15 10 10 Bound electrons Free Mode locking running 6 12 10 10 Maiman Q-switching 3 9 10 10 1960 1970 1980 1990 2000 2010 Year

  9. atom Elaser large E-field of laser beam small E-field nonlinear spring Nonlinear response of electrons in simple atom x linear spring pre-1960 Elaser 0 electron atom ‘spring’ x nucleus Nonresonant response is instantaneous Bound electron response

  10. U(x) Bound electron response atom anharmonic Elaser x Interesting intensity scales are set by material response Anharmonic response when eElaser starts to be a perturbation to eEatom~(/Ry)2 e2/a02 linear optics Elaser/Eatom<<<<1, perturbation theory Elaser/Eatom<<1 Elaser> Eatom(H) for I >~1016 W/cm2

  11. In perturbation theory eff P=((1) + (3)E2)E +… P=(1)E + (2)E2 + (3)E3 + … r r nonlinear index profile laser radial profile I(r) neff (r) Important at peak power >10 MW in solids, >1-30GW in gases n0 Self-focusing Phase fronts Perturbation regime example: nonlinear self-focusing 0 neff2 =1+4eff neff= n0+n2E2

  12. Over-the-barrier ionization Multiphoton ionization Tunneling ionization V(x) V(x) V(x) Vlaser= - erElaser x x x -Ip -Ip -Ip Vtot Perturbation regime Strong field regime ~1013 W/cm2 for xenon ~1014 for hydrogen , argon ~1015 for helium Ionization Interesting intensity scales, cont’d…..

  13. , n~ 1Ne/2Ncr n2 = 1+4free elec=1p2/ 2= 1Ne/Ncr n0  I K r r index profile laser radial profile I(r) neff (r) defocusing Laser phase fronts Plasma defocusing Ionization important at peak intensity> few 1012 W/cm2 dNe /dt =N0IK Multiphoton ionization with K photons, I < 1013 W/cm2

  14. 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. Collapse happens when beats diffraction Self-focusing gives Pcr Idealized picture of filamentation in gases Pcr~ 2-10 GW for air

  15. Real picture: multiple self- and de-focusing events many Rayleigh lengths, white light generation A.Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007). M. Mlejnek, E. M. Wright, and J. V. Moloney, Opt. Lett. 23, 382 (1998)

  16. Filament images at increasing power (Pcr occurs at 1.25 mJ for a 130fs pulse) 5 mm 0.8Pcr 1.3Pcr 1.8Pcr 2.3Pcr 2.8Pcr 3.5 mJ Far field filament images White light generation

  17. Filaments can be unstable. Within a single laser beam, filaments of different sizes and lengths exist, and they vary shot to shot. 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) Limitations on filament usefulness Rodriguez et. al., Physical Review E 69, 036607 (2004) Beam profile 1000 Pcr

  18. 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 extinguishing Nonlinearity control:filament lengthening, e-density enhancement, and optical pulse shaping Can filaments be made more useful?

  19. Delayed inertial response + + + + + + + + + + - - - - - - - - - - Molecules: 78% nitrogen, 21% oxygen Consider air: prompt and delayed optical response of air constituents Prompt electronic response + + + + + Laser polarization - - - - - Atoms: 1% argon

  20. Classical picture molecular axis induced dipole moment • laser field applies a net • torque to the molecule • -molecular axis aligns along • the E field • delayed response (ps) • due to inertia intense laser field (~1013 W/cm2) time-dependent refractive index shift random orientation “some” alignment degree of alignment < >t : time-dependent ensemble average n0=n(random orientation) Laser field alignment of linear gas molecules 

  21. Ultrafast measurements: conventional streak camera Phosphor Screen or CCD e- current pulse j(t) linear voltage sweep Light pulse I(t) time -3 -2 -1 electron optics 0 1 2 3 2 1 0 -1 -2 -3 3 photocathode • Ultimate time resolution limited to few hundred femtoseconds by • beam and electron optics dispersion • photocathode time response

  22. Single-shot Supercontinuum Spectral Interferometry (SSSI) –a streak camera with 10fs resolution A pump pulse generates transient refractive index n(r, t) x Imaging lens Pump pulse z Supercontinuum Probe Ref. Probe Ref. Imaging spectrometer CCD medium y Extract probe (x, t) to obtain n(x, t) with ~5fs time resolution.

  23. Thin gas target in vacuum chamber:For accurate measurement of highly nonlinear response d thin flow d= 400m

  24. Spatially resolved temporal evolution of O2 alignment • pump peak intensity: • 2.7x1013 W/cm2 0.5T 0T 0.25T • 5.1 atm O2 at room temperature T=11.6 ps x (mm) (fs) 0.75T 1T 1.25T x (mm) (ps) T=fundamental rotation period

  25. Field alignment and quantum echoes of rotational wavepacket Quantum description of rigid rotor even (“rotational constant”) (j: ≥0 integer) where : moment of inertia Rotational wavepacket An intense fs laser pulse “locks” the relative phases of the rotational states in the wavepacket– (non-resonant Raman pumping of many j states) eigenstate

  26. Quantum revival of rotational response The time-delayed nonlinear response is composed of many quantized rotational excitations which coherently beat. t = Tbeat t = 0 We can expect the index of refraction to be maximally disturbed at each beat.

  27. Rotational quantum wakes in air TN2 , ¾TO2 Light speed molecular lens vg pump pump vg pump PRL 101, 205001 (2008) Measurement showing alignment and anti-alignment “wake” traveling at the group velocity of the pump pulse.

  28. 20 cm 2m filament f#,lens ~300 Object plane f#, molecule ~ 200 Polarizing beamsplitter CCD Pump-probe filament experiment– dual pulse interferometer 30 fs steps

  29. TN2 , ¾TO2 B R=0 A Probe filaments are steered/trapped or destroyed 5 mm Pump filament position C D (ps) (ps) 8.4 8.0 8.8 8.0 8.8 8.4

  30. probe spatially misaligned, but moved into coincidence with alignment wake of N2 and O2 in air, t = 8 ps CCD camera saturation 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

  31. e-density measurement and optical pulse shaping 2-pulse filament experiment*– injection Interferometry probe Diagnostic for measuring optical pulse envelope and phase *See talk by J. Palastro on pulse-stacking

  32. Pump+probe: density profile changes on 10fs timescale Delays for molecular lens focusing Delays for molecular lens defocusing

  33. SPIDER measurements: pulse shaping and compression of probe pulse with 10 fs sensitivity

  34. Electronic Rotational Molecules: delayed response due to rotational alignment Now we see two features – instantaneous and rotational response Electronic + rotational: N2 , pump 38fs, ~75 TW/cm2 phase

  35. instantaneous rotational Rotational response dominates for >90fs pulses N2 inst rot Experiment: vary pulse width, keeping pulse energy constant JK Wahlstrand et al., PRA 85, 043820 (2012) Simulation: using parameters extracted from short pulse data, calculate

  36. Absolute measurement of n2 • 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 • Folded wavefront interferometer: measure linear phase shift through hole in tube to find Leff.  enables absolute measurement of n2

  37. Molecular gases – absolute measurements transient birefringence self-phase modulation harmonic generation adiabatic where J. K. Wahlstrand, et al., Phys. Rev. A 85, 043820 (2012). Talks/posters Friday

  38. Higher-order Kerr effect?* Usual ‘Kerr’ term …but ionization turns on at ~100 TW/cm2 Hugely negative response well below ionization threshold *See talk by J. Wahlstrand, Thurs 9.35am 

  39. 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 conical emission: Kosareva et al., Opt. Lett. 36, 1035 (2011) Bejot and Kasparian, arXiv:1106.1771 Effect of HOKE on filamentation: Kolesiket al., Opt. Lett. 35, 3685 (2010) Chen et al., Phys. Rev. Lett. 105, 215005 (2010) Polynkinet al., Phys. Rev. Lett. 106, 153902 (2011) Bejotet al., Phys. Rev. Lett106, 243902 (2011) Wang et al., JOSA B 28, 2081 (2011) …and more! All focus on the consequences of HOKE, not original measurement Underlying physics of HOKE (theory): Teleki et al., PRA 82, 065801 (2010) – any HOKE should be masked by plasma Bree et al., PRL 106, 183902 (2011) – Kramers-Kronig calc. “confirms” HOKE

  40. Results in Kr with 0.5 mm gas target instantaneous response plasma 38 fs duration, 25 mm width 38 TW/cm2 57 TW/cm2

  41. Argon Peak moves forward, and back is chopped off (masked by plasma response) Probe phase shift Increasing pump intensity No apparent instantaneous negative phase shift -300 -200 -100 0 100 200 300 400 500 Time (fs)

  42. Results in Ar with thin gas target Inst. positive response plasma Ne=2x1016 cm-3

  43. 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 Ar Loriot 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)

  44. Enabled: Single shot measurement of rotational revivals in H2 and D2 Experiment Theory: dens matrix Quantum revivals plus ionization revivals ionization

  45. Results in noble gases* *PRL 109, 113904 (2012) n2 (10-19 cm2/W) n=n2Iholds until ionization occurs, beyond the range of perturbation theory, and appears to be a universal scaling

  46. 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.

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