Slide 1

Transcript Slide 1

UNIVERSITY OF MARYLAND AT COLLEGE PARK

Trapping and destruction of long range high intensity optical/plasma filaments by molecular quantum wakes

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

HEDLP - 2008 Support: DoE, NSF, JHU-APL

Some applications of filaments

• directed energy • triggering and guiding of lightening • remote detection: LIDAR, LIBS • directed, remote THz generation

Introduction to Filamentation

• High power, femtosecond laser beams propagating through air form extremely long filaments due to nonlinear self-focusing (  (3) ) dynamically balanced by ionization and defocusing.

 0

eff =

0 + 

gas + 

plasma P cr ~  2 /8n 0 n 2

What does a filament look like?

0.8P

cr 1.3P

cr 1.8P

cr 2.3P

cr 2.8P

cr 3.5 mJ

Filament images at increasing power (P cr occurs at 1.25 mJ for a 130fs pulse)

5 mm

“prompt” and “delayed” optical response of air constituents

Prompt electronic response Delayed inertial response

+ + + + + -

Atoms: 1% argon

+ + + + + + + + + + -

Molecules: 78% nitrogen, 21% oxygen

Laser field alignment of linear gas molecules

Classical picture E p



induced dipole moment p / /

molecular axis -

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 (~10 13 W/cm 2 ) random orientation

cos 2   1/ 3

E “some” alignment



time-dependent refractive index shift

 2 

 

0  cos 2   

1 3

degree of alignment

cos 2   1/ 3

< > t : time-dependent ensemble average

0 =

( random orientation )

Field alignment and “revivals” of rotational wavepacket

Quantum description of rigid rotor

exp( 



j t

) eigenstate where 

B j

 

E j h

(8  /  2π (

even

 1) 2

)  1 (j: ≥0 integer) (“rotational constant”)

: moment of inertia

Rotational wavepacket

  

exp( 



j t

) An intense fs laser pulse “locks” the relative phases of the rotational states in the wavepacket

Quantum revival of rotational response

The time-delayed nonlinear response is composed of many quantized rotational excitations which coherently beat.

t = 0

We can expect the index of refraction to be maximally disturbed at each beat.

t = T

beat

Single-shot Supercontinuum Spectral Interferometry (SSSI) – Imagine a streak camera with 10fs resolution!

A pump pulse generates transient refractive index 

(

) x Pump pulse Imaging lens Probe Ref. medium y

Probe and Ref.

• Temporally stretched (chirp) for long temporal field of view (~ 2 ps).

• ~100 nm bandwidth supercontinuum gives ~10 fs resolution.

Probe Ref. CCD Imaging spectrometer Extract  probe (

) to obtain

(

Experimental setup and sample interferogram

0 ps N 2 O gas Sample interferogram ~ 2 ps 652nm 723nm Chen, Varma, York and Milchberg, Opt. Express 15, 11341 (2007)

Rotational wavepacket of D 2 and H 2 molecules P=7.8 atm I=4.4x10

13 W/cm 2 room temperature

Rotational quantum “wakes” in air

T N2 , ¾T O2 Vg pump v g pump SSSI measurement showing alignment and anti alignment “wake” traveling at the group velocity of the pump pulse.

Pump-probe filament experiment

f/300 focusing

2m filament Object plane Polarizing beamsplitter CCD

Filaments are trapped/enhanced or destroyed

T N2 , ¾T O2 A B 8.0

8.0

C D 8.8

8.8

(ps)

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

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...

Response near t=0

laser

A A (ps) Pump power scan

(probe=3.4P

cr ) 0.68P

cr 1.12P

cr 1.72P

cr 2.20P

cr 2.60P

cr 3.72P

(ps)

Spectral broadening

The spatio-temporally varying refractive index of the wake of molecular alignment causes predictable spectral modulation and broadening of the probe filament.

Filament spectrum v. delay

Alignment v. delay

A C D E A B C D E

Molecular rotational wavepacket revivals

mode-locking analogy: coherent sum of longitudinal modes

typ. spectrum modes

Example: N 2

pulse width ≈ (round trip time) / (# of modes) T/ 2 T/ 4 3 T/ 4 T =8.2ps

nitrogen

peak width ≈ T ps / j max (j max +1) ~ 40 fs for N 2

x ( m m) 0 T 1D spatially resolved temporal evolution of O 2 alignment 0.25

T 0.5

T • pump peak intensity: 2.7x10

13 W/cm 2 • 5.1 atm O 2 at room temperature • T =11.6 ps (fs) 0.75

T 1 T 1.25

T x ( m m) (ps)

Introduction to Filamentation

• 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.

Rotational wavepacket of H 2 molecules at room temperature

Experiment:

Fourier transform

H 2 =61.8 cm  1 T =270 fs Lineout at x=0

Calculation:

 The pump intensity bandwidth (~2.5x10

13 is even less adequate s -1 ) than in D 2 to populate j=2 and j=0 states.

 Weaker rotational wavepacket amplitude.

P=7.8 atm I=4.4x10

13 W/cm 2   H 2  0.30

 10 -24 cm 3 T

Charge density wave in N

at 1 atm

• Filament ionization fraction ~10 -3 cm  3  2x10 16 v g

Quantum beat index bucket

• ~0.5% ponderomotive charge separation at enhanced intensity ~ 5x10 14 100 fs alignment transient  W/cm 2 over 50  N e ~ 10 14 cm -3 E~ 0.75 MV/cm  • Many meters of propagation

110 fs 1 kHz Ti:Sapphire regenerative amplifier ~300 m J xenon gas cell (1-2 atm)

supercontinuum (SC) 0 ps N 2 O gas

Michelson interferometer Sample interferogram

652nm

Experimental setup and sample interferogram high pressure exp gas cell (up to ~8 atm) P: pinhole BS: beamsplitter HWP:  /2 plate SF4: dispersive material

~ 2 ps

 Optical Kerr effect (  (3) ) and the molecular rotational response in the gas induce

spectral phase shift

and

amplitude modulation

on the interferogram.



Both

spectral phase and amplitude information are required to extract the temporal phase (refractive index).

723nm