Phase-matched scalable THz generation in two-color filamentation
Kiyong Kim
Institute for Research in Electrons and Applied Physics, University of Maryland, College Park, MD 20742
• Background- THz generation via two-color laser mixing- Plasma current model
• THz generation with high-power lasers
• THz phase matching in long filaments
• Summary
Outline:
Lens BBOTHz pulse
Two-color photoionization:
2
plasma
2
BBO crystal
THz generation mechanism:
e- e- e- e- e-
e- e- e-
THz
Current surge THz generation
Directional quasi-DC current
Tunneling ionization:
U(x)
x
-Ui
U(x)
-Ui
x
U(x)
-Ui
x
Multiphoton ionization
Tunneling ionization
Over-the-barrier ionization
The nonlinearity arises from photoionization!
However, single-color photoionization can not effectively generate THz radiation.
I < 1012 W/cm2 I > 1014 W/cm2 I > 1016 W/cm2
Plasma current model I:
K. Y. Kim et al, Opt. Express 15, 4577 (2007)K. Y. Kim et al, IEEE J. Quantum Electron. 48, 797 (2012)
2( ) cos( ) cos(2 )LE t E t E t
: relative phase
Laser field:
-4
-2
0
2
4x 10
18
e- den
sity
, Ne (c
m-3
)
-50 0 50 100
-100
0
100
Cur
rent
, J (a
.u.)
Time (fs)
= 0
Plasma current model II:Tunneling ionization and subsequent classical electron motion in the laser field are considered.
I = 1014 W/cm2, I2 = 2 1013 W/cm2, 50 fs (FWHM)
Strong field approximation; ignored rescattering, collisional processes, plasma oscillations.
-4
-2
0
2
4x 10
18
e- den
sity
, Ne (c
m-3
)
-50 0 50 100-50
0
50
Cur
rent
, J (a
.u.)
Time (fs)
= /2
Quasi-DC current
0 0.2 0.4 0.6 0.8 1 1.2
10-10
10-5
100
Inte
nsity
(a.u
.)
Frequency (PHz)
= /2 = 0 alone
2
THz 3
Radiation spectrum
* Laser field:
* Ionization rate:
* Plasma current:
* THz field:
* f(E) is highly nonlinear, not necessarily quadratic dominant.
The nonlinearity arises from extremely nonlinear tunneling ionization localized near the laser peaks.*
Plasma current model III:
)2cos(cos)( 2 tEtEtEL
)(32exp
)(4)(
tEE
tEEtw
L
a
L
aa
)()()( tvteNtJ e
sin)()(2THz EEf
dttdJE
a
aa
EE
EE
EEEf
3
32exp)(
• Ionization model:Tunneling vs multiphoton ionization
• Plasma current calculation:Semiclassical vs quantum-mechanical calculation
• Additional effects:Plasma oscillations, collisional (electron-ion, electron-neutral) effects, rescattering with parents’ ions
• Propagation effects:Self- and cross-phase modulations, spectral shifting and broadening, Kerr-induced polarization rotation, phase-and group velocity walk-offs
More effects to consider:
Broadband EM generation & control:
1 THz 10 THz 100 THz 1 PHz 10 PHz300 m 30 m 3 m 300 nm 30 nm
Spectral broadening(SPM & blue shift)
rescattering
Plasma current
Plasma oscillation &Collisional effects
Ion current
0 1 2 3
-1
0
1
Time (ns)
B-d
ot s
igna
l (V
) B-dot probe
0 5 10 15 20 25 30 35
10-4
10-3
10-2
10-1
100
Frequency(THz)
Pow
er(a
rb. u
nits
)
EFISHFTIR
5 mJ, 25 fs, 1 kHz Ti:S laser
Laser upgrade @ Kim Lab:
15 mJ, 1 kHz Ti:S laser(Peak power ~0.6 TW)
New cryo-amplifier
New cryogenic amplifier:
Beam profile
Ti:S crystal
Cryo-chamber
15 mJ laser interaction with gaseous targets
10 mm
Filamentation in air
Interaction with Ar cluster gas jets
THz generation with 15 W laser @1 kHz:
2 3 4 5 6 7 8 9 10 110
0.5
1
1.5
2
2.5
3
3.5
4
Laser energy (mJ)
THz
yiel
d (a
.u.)
SiHDPE x2Teflon x15
Gas jetLaser pulse
BBO
THz
e–
e–
Lens Pyroelectric detector
THz generation with 20 TW laser
In vacuumMonomers or clusters
20 TW laser
Parabolodal mirror
0
1
2
3
4
5
0 100 200 300 400 500 600
pressure (psi)py
ro s
igna
l (V)
N2
Ar
• Several microjoule THz radiation per pulse.
• THz energy saturation.
• Clusters provides less THz output.
Experimental Result:THz energy vs pressureTHz energy vs laser energy
0
0.5
1
1.5
0 50 100 150
Pyr
o s
ign
al (
V)
Laser energy (mJ)
Phase matching in THz generation:
Microscopic source
Macroscopic phase
matching
2
e-e-e-e-e-
e- e- e-
Directional current surge
2
THz
2
2
Gaseous medium
Dephasing between and 2:This occurs due to different refractive indices at and 2in air and plasma
BBO
022,,12,, /])()[( cLnnLnn filamentfilamentairair
filament
THz
l = P3 – (P1 + P2) = (m + 1/2)
cos 1 – /(2ld)
Phase matching in a long filament:
Condition for constructive interference:
THz phase matching:
THz far field:
' ' ',Ω , sin ( ') exp Ω ,g THzP r A r z in k z i t
Source:
''3 '
,( ,Ω)
'
THzi k r r
V
P r eE r d r
r r
22 2 222 ' 2 2 11 2 1 2 02
2 β ( ), ,Ω , 2 cos 2Ja lE r A r
r
THz intensity:
1,21,2
1,2
sin( )
1,2 cos
2 2THz
gd
k l nl
2 sina
cos 12p
dl
angle(degree)
angl
e(de
gree
)
-10 -5 0 5 10
-10
-5
0
5
10
angle(degree)
angl
e(de
gree
)
-10 -5 0 5 10
-10
-5
0
5
10
angle(degree)
angl
e(de
gree
)
-10 -5 0 5 10
-10
-5
0
5
10
angle(degree)
angl
e(de
gree
)
-10 -5 0 5 10
-10
-5
0
5
10
Simulated THz profiles:
Ne ~ 3 1016 cm-3
0.1 ~ 1 THz 1 ~ 30 THz
Short (~1 cm) plasma
Long (~3 cm) plasma
THz radiation profile measurement:
Pyroelectric detector
BBO
THz
Lens
FilamentRaster
scanning
Laser pulse
Teflon & Si filtersor
Ge filter
horizontal ()
verti
cal ()
-5 0 5
-4
0
4
0.1
0.2
0.3
0.4
0.5
horizontal ()
verti
cal ( )
-5 0 5
-4
0
4
0
0.2
0.4
0.6
0.8
horizontal ()
verti
cal ( )
-5 0 5
-5
0
50.5
1
1.5
2
2.5
horizontal ()
verti
cal ( )
-5 0 5
-5
0
5 2
4
6
8
10
12
14
16
18
Low THz High THz
Short (<1 cm) plasma
Long (>3 cm) plasma
Measured THz profiles:
Measured optical and THz profiles:
~700 nm
(blue-shifted 800 nm)400 nm + 800 nm
THz focusing issue:
Focused THz profiles
~6 mm long filament
THz yield vs filament length:
BBO
lfaperture
THz yield vs filament length:
THz output increases almost linearly with the plasma length
• THz generation via two-color laser mixing:– Ideal for broadband intense THz spectroscopy
• High-energy THz generation:– Used 15 W, 1 kHz and 20 TW, 10 Hz lasers
– Produced several J THz radiation but observed saturation
• Scalable THz generation:– Demonstrated THz phase matching in long filaments
– THz output energy increases with the filament length
Summaries:
Acknowledgements:
Yong Sing You
Taek Il Oh
Luke Johnson
Yungjun Yoo
Jeffrey Magill
Tomas Antonsen
UINVERSITY OF MARYLAND