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 Institute for Research in Electronics and Applied Physics UNIVERSITY OF MARYLAND AT COLLEGE PARK MIPSE Nov. 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 lens CW 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, (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, (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 N 2 Lasing D. Gordon, J. Penano, A. Ting, P. Sprangle, Naval Research Laboratory Jennifer Elle, S. Zahedpour, H. Milchberg, Univ. of Md 1960s: Nitrogen discharge UV (electronic excitation of N 2 by electron collisions) N e ~ cm -3, T e ~1 eV. ‘intense’ ~100fs laser pulse PLASMA FILAMENT N e ~10 15 – cm -3, T e ~1 eV Lasing? NRL: J.R. Penano et al., J. Appl. Phys. 111, (2012) Vienna: Kartashov et al, PRA 86, (2012) - got lasing using a 4  m driver laser, 5 atm N 2, 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 extinguishing Nonlinearity control: filament lengthening, e-density enhancement, and optical pulse shaping Can filaments be made more useful?

Bound electron response x x E lase r 0 pre-1960 atom E laser small E-field large E-field of 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 eE laser starts to be a perturbation to eE atom ~(  /Ry) 2 e 2 /a 0 2 linear optics E laser /E atom <<<<1, perturbation theory E laser /E atom <<1 E laser > E atom(H) for I >~10 16 W/cm 2 Bound electron response E laser x U(x) anharmonic atom

P=  (1) E +  (2) E 2 +  (3) E 3 + … P=(  (1) +  (3) E 2 )E +… In perturbation theory  eff n eff 2 =1+4  eff  n eff = n 0 +n 2 E 2 Perturbation regime example: nonlinear self-focusing 0 I(r) r laser radial profile Phase fronts n eff (r) r nonlinear index profile n0n0 Self-focusing Important at peak power >10 MW in solids, >1-30GW in gases

Ionization Interesting intensity scales, cont’d….. V(x) -Ip-Ip x Over-the-barrier ionization V(x) -Ip-Ip x Tunneling ionization V laser = - erE laser V tot V(x) x -Ip-Ip Multiphoton ionization Perturbation regime ~10 13 W/cm 2 for xenon ~10 14 for hydrogen, argon ~10 15 for helium Strong field regime

Plasma defocusing Ionization important at peak intensity> few W/cm 2 n 2 = 1+4  free elec =1  p 2 /  2 = 1  N e /N cr, n~ 1  N e /2N cr dN e /dt =  N 0  I K Multiphoton ionization with K photons, I < W/cm 2 I(r) r laser radial profile Laser phase fronts n eff (r) r index profile n0n0 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 P cr ~ 2-10 GW for air beats Self-focusing diffraction Collapse happens when  gives P cr

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 (P cr occurs at 1.25 mJ for a 130fs pulse) Far field filament images 5 mm 0.8P cr 1.3P cr 1.8P cr 2.3P cr 2.8P cr 3.5 mJ 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. Limitations on filament usefulness Beam profile 1000 P cr Rodriguez et. al., Physical Review E 69, (2004) Low electron density (~0.1% atmosphere) with gaps -- difficulty for guiding large current over long distances. Y.-H. Chen et al, PRL 105, (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 extinguishing Nonlinearity 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 Laser polarization Prompt electronic response Atoms: 1% argon Delayed inertial response Molecules: 78% nitrogen, 21% oxygen

Laser field alignment of linear gas molecules random orientation “some” alignment time-dependent refractive index shift n 0 =n( random orientation ) degree of alignment t : time-dependent ensemble average intense laser field (~10 13 W/cm 2 ) -laser field applies a net torque to the molecule -molecular axis aligns along the E field -delayed response (ps) due to inertia induced dipole moment Classical picture molecular axis 

Ultrafast measurements: conventional streak camera linear voltage sweep time Light pulse I(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 z CCD 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= 400  m d

Spatially resolved temporal evolution of O 2 alignment x (  m) (ps) (fs) x (  m) 0T0T 0.25 T 0.5 T 0.75 T 1T1T 1.25 T pump peak intensity: 2.7x10 13 W/cm atm O 2 at room temperature T =11.6 ps T = fundamental rotation period

Field alignment and quantum echoes of rotational wavepacket Quantum description of rigid rotor where (“rotational constant”) : 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 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 = T beat

Measurement showing alignment and anti-alignment “wake” traveling at the group velocity of the pump pulse. Rotational quantum wakes in air v g pump T N2, ¾T O2 Light speed molecular lens v g pump PRL 101, (2008) pump

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

5 mm (ps) B A C D Probe filaments are steered/trapped or destroyed T N2, ¾T O2 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 N 2 and O 2 in air, t = 8 ps CCD camera saturation

2-pulse filament experiment*– e-density measurement and optical pulse shaping Diagnostic for measuring optical pulse envelope and phase injection Interferometry probe *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: N 2, pump 38fs, ~75 TW/cm 2 Molecules: delayed response due to rotational alignment Now we see two features – instantaneous and rotational response phase 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 N2N2 inst rot JK Wahlstrand et al., PRA 85, (2012)

Absolute measurement of n 2  enables absolute measurement of n 2  Folded wavefront interferometer: measure linear phase shift through hole in tube to find L eff.  SSSI provides image of pump spot, allowing precise measurement of spot size.  know I(x,y)  The effective interaction length L eff is unknown. two unknowns

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

Higher-order Kerr effect?* 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/cm 2

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

Results in Kr with 0.5 mm gas target plasma 38 TW/cm 2 57 TW/cm 2 instantaneous response 38 fs duration, 25  m width

Argon No apparent instantaneous negative phase shift Time (fs) Probe phase shift Peak moves forward, and back is chopped off (masked by plasma response) Increasing pump intensity

Results in Ar with thin gas target N e =2x10 16 cm -3 Inst. positive response plasma

Peak inst. phase shift vs. peak intensity In both Ar and N 2, no hint of saturation or negative instantaneous nonlinear phase 1 response is linear in intensity up to ionization! We think original HOKE experiment observed a plasma grating 2. N2N2 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, , (2011). 2. JKW and HMM, Opt. Lett. 36, 3822 (2011)

Enabled: Single shot measurement of rotational revivals in H 2 and D 2 Experiment Theory: dens matrix Quantum revivals plus ionization revivals ionization

n 2 ( cm 2 /W)  n=n 2 I holds until ionization occurs, beyond the range of perturbation theory, and appears to be a universal scaling Results in noble gases* *PRL 109, (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.