1. S. Varma, Y.-H. Chen, and H. M. Milchberg Institute for Research in Electronics and Applied Physics Dept. of Electrical and Computer Engineering Dept. of Physics UNIVERSITY OF MARYLAND AT COLLEGE PARK Trapping and destruction of long range high intensity optical/plasma filaments by molecular quantum wakes HEDLP - 2008 Support: DoE, NSF, JHU-APL

2. Some applications of filaments directed energy triggering and guiding of lightening remote detection: LIDAR, LIBS directed, remote THz generation

3. High power, femtosecond laser beams propagating through air form extremely long filaments due to nonlinear self-focusing (  (3) ) dynamically balanced by ionization and defocusing. Introduction to Filamentation n eff = n 0 +  n gas +  n plasma  0 P cr ~ 2 /8n 0 n 2

4. Filament images at increasing power (P cr occurs at 1.25 mJ for a 130fs pulse) What does a filament look like? 5 mm 0.8P cr 1.3P cr 1.8P cr 2.3P cr 2.8P cr 3.5 mJ

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

6. 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

7. Field alignment and “revivals” 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 Rotational wavepacket eigenstate

8. 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

9. A pump pulse generates transient refractive index  n (r, t) Extract  probe (x, t) to obtain n(x, t). medium Probe Ref. Pump pulse x y z Probe and Ref. Temporally stretched (chirp) for long temporal field of view (~ 2 ps). ~100 nm bandwidth supercontinuum gives ~10 fs resolution. CCD Imaging spectrometer Probe Ref. Imaging lens Single-shot Supercontinuum Spectral Interferometry (SSSI) – Imagine a streak camera with 10fs resolution!

10. Experimental setup and sample interferogram Chen, Varma, York and Milchberg, Opt. Express 15, 11341 (2007) 0 ps~ 2 ps 723nm652nm 250  m N 2 O gas Sample interferogram

11. Rotational wavepacket of D 2 and H 2 molecules P=7.8 atm I=4.4x10 13 W/cm 2 room temperature

12. SSSI measurement showing alignment and anti-alignment “wake” traveling at the group velocity of the pump pulse. Rotational quantum “wakes” in air Vg pump v g pump T N2, ¾T O2

13. Pump-probe filament experiment Polarizing beamsplitter Object plane 2m filament CCD f/300 focusing

14. 5 mm 8.0 8.4 8.8 (ps) B A C D 8.0 8.4 8.8 Filaments are trapped/enhanced or destroyed T N2, ¾T O2

15. Trapped filaments are ENHANCED White light generation, filament length and spectral broadening are enhanced. Aligning filament (left) and probing filament (right), misaligned Both beams collinear, probe filament coincident with alignment wake of N 2 and O 2 in air CCD camera saturation

16. Conclusions SSSI enables us to probe refractive index transients with ~10fs resolution over 2ps in a single shot, allowing us to observe room-temperature molecular alignment. A high intensity laser filament propagating in the quantum wake of molecular alignment can be controllably and stably trapped and enhanced, or destroyed. Applications: directed energy, remote sensing, etc...

17. Response near t=0 (ps) Increasing aligning pulse energy 0.68P cr 1.12P cr 1.72P cr 2.20P cr 2.60P cr 3.72P cr Pump power scan (probe=3.4P cr ) A A laser

18. Spectral broadening The spatio-temporally varying refractive index of the wake of molecular alignment causes predictable spectral modulation and broadening of the probe filament. Alignment v. delay A B C D E Filament spectrum v. delay A B C D E

19. Molecular rotational wavepacket revivals mode-locking analogy: coherent sum of longitudinal modes pulse width ≈ (round trip time) / (# of modes) typ. spectrum Example: N 2 Example: N 2 peak width ≈ T / j max (j max +1) ~ 40 fs for N 2 ps T/ 4 T =8.2ps nitrogen T/ 2 3 T/ 4 modes

20. 1D spatially resolved temporal evolution of O 2 alignment x (  m) (ps) (fs) x (  m) 00 0.25  0.5  0.75  11 1.25  pump peak intensity: 2.7x10 13 W/cm 2 5.1 atm O 2 at room temperature  =11.6 ps

21. High power, femtosecond laser beams that propagate through air form extremely long filaments due to nonlinear self-focusing (  (3) ) dynamically balanced by ionization and defocusing. Filaments can propagate through air up to 100s of meters, and are useful for remote excitation, ionization and sensing. Introduction to Filamentation

22. Rotational wavepacket of H 2 molecules at room temperature Fourier transform =61.8 cm  1  =270 fs  ØThe pump intensity bandwidth (~2.5x10 13 s -1 ) is even less adequate than in D 2 to populate j=2 and j=0 states. ØWeaker rotational wavepacket amplitude. P=7.8 atm I=4.4x10 13 W/cm 2 0.30  10 -24 cm 3 Experiment: Lineout at x=0 Calculation:

23. Charge density wave in N 2 at 1 atm Filament ionization fraction ~10 -3  2x10 16 cm  3 ~0.5% ponderomotive charge separation at enhanced intensity ~5x10 14 W/cm 2 over 50- 100 fs alignment transient   N e ~ 10 14 cm -3  E~ 0.75 MV/cm Many meters of propagation Quantum beat index bucket vgvg “probe” pulse -- +

24. Experimental setup and sample interferogram xenon gas cell 1 kHz Ti:Sapphire regenerative amplifier 110 fs Michelson interferometer P: pinhole BS: beamsplitter HWP: /2 plate SF4: dispersive material supercontinuum (SC) ~300  J (up to ~8 atm) (1-2 atm) 0 ps~ 2 ps 723nm652nm 250  m N 2 O gas  Optical Kerr effect (  (3) ) and the molecular rotational response in the gas induce spectral phase shift and amplitude modulation on the interferogram. ØBoth spectral phase and amplitude information are required to extract the temporal phase (refractive index). high pressure exp gas cell Sample interferogram

25. Experimental setup and sample interferogram xenon gas cell 1 kHz Ti:Sapphire regenerative amplifier 110 fs Michelson interferometer P: pinhole BS: beamsplitter HWP: /2 plate SF4: dispersive material supercontinuum (SC) ~300  J (up to ~8 atm) (1-2 atm) 0 ps~ 2 ps 723nm652nm 250  m N 2 O gas  Optical Kerr effect (  (3) ) and the molecular rotational response in the gas induce spectral phase shift and amplitude modulation on the interferogram. ØBoth spectral phase and amplitude information are required to extract the temporal phase (refractive index). high pressure exp gas cell Sample interferogram