Intense Terahertz Generation and
Spectroscopy of Warm Dense Plasmas
Kiyong Kim
University of Maryland, College Park
Collaborators:
Kishore Yellampalle
George Rodriguez
Toni Taylor
Jim Glownia
LOS ALAMOS NATIONAL LABORATORY
Outline:
• Background:
- Terahertz (TH) science.
• Intense THz generation:
- Two-color photoionization.
• THz spectroscopy:
- Warm dense plasmas.
Phenomena at terahertz (THz) frequencies:
1 THz = 1012 Hz =1 ps = 300 m = 0.004 eV = 33.3 cm-1
molecules
Rydberg
atoms
Gaseous and solid-state
plasmas
Semiconductor
nanostructures
Figure courtesy of Klaas Wynne
Biomolecules & proteins
Strong THz sources:
Large facility THz sources*
FEL
Linacs
Photo courtesy: DESY
Stanford, UCSB, FELIX
Free electron lasing
SLAC, JLab,BNL
synchrotron radiation
Synchrotrons
Photo courtesy: ALS
ALS (BNL)
Coherent synchrotron
radiation
* M. S. Sherwin et al., DOE-NSF-NIH Workshop on Opportunities in THz Science
Intense THz generation:
Two-color photoionization
Two-color photoionization:
Four-wave mixing *
 THz =  +  - 2


2
plasma
Lens
SHG
But the third order nonlinearity originating from
bound electrons of ions ((3)ions) and free
electrons ((3)free-electrons) via ponderomotive or
thermal effects is too small to explain the
measurements.
(3)plasma = (3)ions + (3)free-electrons
THz pulse
* M. Kress et al, Opt. Lett. 29, 1120 (2004);
T. Bartel et al, Opt. Lett. 30, 2805 (2005);
X. Xie et al, Phys. Rev. Lett. 96, 075005 (2006).
THz generation mechanism:
e-
e-
THz
eDirectional quasiDC current
e- e- e- e- e-

2

BBO crystal
Current surge
 THz generation
THz energy measurement:
1000
THz energy vs laser energy
Kr
800
Ar
600
N2
Air
400
200
He
0
0
200
400
600
Pressure (torr)
S i filte r
800
P yro e le ctric sig n a l (m V )
Pyroelectric signal (a.u.)
THz energy vs pressure
600
400
S i + P .E . filte r
200
S i + T e flo n filte r
0
0
5
10
15
20
L a se r e n e rg y (m J)
• ETHz ~ 5 J/pulse with Kr (C.E. > 10-4)
K. Y. Kim et al., Nature Photonics doi:2008.153 (2008).
THz spectrum measurement:
1 .0
(a)
Fourier-transform spectra
A r 1 0 to rr
S p e c tra l p o w e r
(n o rm .)
P yroelectric signal
(norm .)
Field autocorrelations
0 .5
(b)
A r 1 0 0 to rr
S p e c tra l p o w e r
(n o rm .)
P yroelectric signal
(norm .)
P yroelectric signal
(norm .)
1 .0
0 .5
(b´)
A r 1 0 0 to rr
1
0
0 .0
0 .5
0 .0
A r 1 0 to rr
1
0
0 .0
1 .0
(a´)
(c)
S p e c tra l p o w e r
(n o rm .)
A ir 5 8 0 to rr
(c´)
A ir 5 8 0 to rr
1
0
0 .3
0 .6
T im e d e la y (p s)
0 .9
0
20
40
60
F re q u e n c y (T H z )
THz generation up to 75 THz (= 4 m)
THz spectroscopy:
Warm Dense Matter
Electrical conductivity measurements of WDM:
Drude model
r
Optical probe
WDM
(THz)
From the reflectivity, one can measure the
electrical conductivity at the probe frequency.
H. M. Milchberg et al., Phys. Rev. Lett. 61, 2364 (1988).
A. Ng et al., Phys. Rev. Lett. 72, 3351 (1994).
A. N. Mostovych et al., Phys. Rev. Lett. 79, 5094 (1997).
0
(1    )
2
2
0
Optical pump
pulse
Measure probe
reflectivity
 r ( ) 
AC (0)
THz
0

With THz probing, one can measure
quasi-DC conductivity directly.
THz conductivity measurements of WDM:
THz probe
D ~ 1 mm
Pump pulse
Target
(Aluminum)
To single-shot THz
diagnostic
The quasi-DC electrical conductivity can be directly
determined from THz probe reflectivity measurements.
Experimental results I:
THz reflectivity ratio, R'p/Rp
THz reflectivity for various pump energies
1.6
Al, 3 mJ
Al, 4 mJ
Al, 5 mJ
Al, 9 mJ
Al, 10 mJ
2
GaAs, 5 J/cm
-1
GaAs (x10 +0.8)
1.4
1.2
Al
1.0
0.8
0.5
1.0
1.5
Frequency (THz)
Breakdown of
Drude model
Possible pseudogap formation at the Fermi energy ???
K. Y. Kim et al., Phys. Rev. Lett. 100, 135002 (2008).
Experimental results II:
THz reflectivity vs delay
17
10
0.0
16
10
15
10
-0.1
-1
0.1
Reflectivity, R/R
2
Conductivity r (s )
13
Simulation, 10 W/cm
19
13
2 10
Simulation, 1.5 x 10 W/cm
Reflectivity
18
10
Conductivity r
14
10
-0.2
13
-20
0
20
40
60
80
100 120
10
Delay (ps)
Conductor-to-insulator-like
transition
Room temp. Al: r = 4.1  107 -1m-1 = 3.7 1017 s-1
[-1m-1] = 1.1  10-10 [s-1]
Experimental results III:
THz reflectivity vs intensity
0.02
17
Reflectivity, R/R
-1
Reflectivity
0.00
Conductivity r
-0.02
16
10
-0.04
15
10
-0.06
-0.08
14
0.2
0.4
0.6
0.8
13
Conductivity r (s )
10
1.0
10
2
Peak intensity (10 W/cm )
Resistivity
saturation
Summaries:
• THz generation via two-color photoionization:
– Generated intense (>5 J), super-broadband TH radiation (>75 THz).
– Developed a transient photocurrent model.
– Potential application for nonlinear THz optics and spectroscopy.
• THz spectroscopy for WDM:
– Directly measured the quasi-DC electrical conductivity of warm dense
aluminum.
– Complements optical and x-ray diagnostics for WDM studies.
Backup slides:
Experimental setup:
B-dot probe & 3
measurement
Pyroelectric
detector
BBO
d
P.D.
B-dot
probe
3
filter
P.D.
THz pulse
Si
window
BBO
Plasma
THz energy
measurement
P.D.
THz spectrum
measurement
Strong THz field science*:
THz pump experiments
• THz pumping of metals, insulators, and
correlated electron materials.
• Coherent band-gap distortion & phase
transition.
• THz-pump optical-probe experiments.
ETHz
• THz coherent control
Rapid THz imaging
• Biomedical and security
imaging
> 1 MV/cm
Strong THz sources
Nonlinear THz Optics
• THz 2nd, 3rd nonlinear effects.
• Extreme nonlinearity with
ponderomotive energy > photon energy
• THz-optical nonlinear mixing
Photo courtesy: the Star Tiger
High magnetic field effects
• 1 MV/cm  0.3 T
• Pulsed electron spin resonance
• THz spintronics
* M. S. Sherwin et al., DOE-NSF-NIH Workshop on Opportunities in THz Science
Plasma current model I:
=0
 = /2
E L ( t )  E 1 cos(  t   )  E 2 cos[ 2 ( t   )   ]
2 field
 field
 : relative phase
0
-10
20
0
-20
-
 : photoionization phase
10
(b)
e displacement
(nm)
Laser field
Laser field
8
(10 V/cm)
(a)
0
3
d 
eE 1
m e
sin  
eE 2
2 m e
sin( 2   )
-
Electron drift velocity
e drift velocity
8
(10 cm/s)
(c)
intensity of I = 1015 W/cm2 and I2 = 2  1014 W/cm2
(assuming 20% efficiency of frequency doubling)
9
0
3
6
9
Time (fs)
10
0
EL
EL
-10
e
e
-2
 ( = 800 nm) and 2 ( = 400 nm) lasers with relative
6
Time (fs)
0
2
Phase  (rad)
-3
0
Phase  (rad)
K. Y. Kim et al., Opt. Express 15, 4577 (2007).
3
Plasma current model II:
The nonlinearity arises from extremely nonlinear tunneling ionization localized
near the laser peaks.*
* Laser field:
* Ionization rate:
E L ( t )  E  cos  t  E 2  cos( 2 t   )
 Ea 
 exp
w ( t )  4  a 

 E L (t ) 
 2 Ea 


 3 E (t ) 
L


Ea: atomic field
* Plasma current: J ( t )  eN e ( t ) v ( t )
* THz field:
E THz 
dJ ( t )
dt
f (E ) 
 f ( E  )  E 2   sin 
Ea
E
 2 Ea
E 
exp  
 3  
Ea 
 3 E
for Ea > E >> E2 and Ng >> Ne
* The function f(E) is highly nonlinear, not necessarily quadratic dominant.
Simulation results I:
ADK tunneling ionization and subsequent classical electron
motion in the laser field are considered.
Electron current
(a.u.)
-0.2
2
-0.2
2
0
0
-2
-2
-20
0
20
40
60
80
Time (fs)
(ii)
-40
-20
0
20
40
60
Time (fs)
I = 1015 W/cm2, I2 = 2  1014 W/cm2, 50 fs (FWHM)
Quasi-DC current
Assumptions: No rescattering effect, No electron-ion or
electron-neutral collisional processes, No space charge
effect, No electron transport.
80
-3
6
4
2
0
0.0
(ii)
-40
(i)
19
0.0
0.2
Ne (10 cm )
6
4
2
0
-3
(i)
19
0.2
Simulation with  =  /2
Ne (10 cm )
Laser field
(E/Eat)
Simulation with  = 0
Experimental setup I:
Electro-optic THz detection
Balanced
detector
Laser pulse
WP
QWP
ZnTe
CCD
or
P
ZnTe
P
Pellicle
THz imaging
THz pulse
BBO
(Type I)
Si window
4.4 mm
Air plasma
Max. 8% conversion efficiency
with
polarization
An amplified Ti:sapphire laser system
delivering 815 nm, 50 fs, 25 mJ pulses at a
10 Hz repetition rate was used.
Experimental result I:
THz spectrum
THz waveform
4
S p e ctra l in te n sity a( .u .)
T H z fie ld a( .u .)
6
3
0
-3
-6
0
2
4
T im e p( s)
Strong THz absorption by
water vapor in air
6
3
2
1
0
0
1
2
F re q u e n cy T( H z)
Detection bandwidth is limited
by dispersion and absorption in
our 1-mm thick ZnTe crystal.
Experimental result II:
To check the validity of our plasma current model, we studied
 dependence of THz yield
E L ( t )  E 1 cos(  t )  E 2 cos[ 2  t   ]
T H z yield (a.u.)
BBO

60
d
40
20
0
0
2
4
6
8
D istance ( d ) (cm )
0

As d  0, THz yield  0
Current model :
 = (nn2)d/c
Four-wave mixing :
10
12
3 measurements:
Simulation
Experiment
SHG
THG
THz
90
120
60
90
120
180
30
150
30
150
60
180
0
0
2 polarization angle
Spectral Power (a.u.)
Anti-correlation of THz and THG
 = 0,
 = /2,
 alone
-1
10
-5
10
-9
10

10
0.0
0.2
0.4
3
2
-13
0.6
0.8
1.0
1.2
Frequency (PHz)
K. Y. Kim et al., Nature Photonics (submitted).
Warm Dense Matter (WDM):
WDM: warm (0.1~100 eV) dense (0.1~10 times the solid density) matter which
is a strongly coupled (e  kBT) and Fermi degenerate (F ~ kBT) plasma.
Brown dwarfs
NASA
Jupiter
Laser-heated solids
NASA
WDM lies between a solid state and an
ideal plasma state. It is too hot to be
described by solid-state physics and too
dense to be depicted by the classical
plasma theory.
WDM
Single-shot THz detection:
Chirped spectral
interferometric technique *
Spectrometer
Chirped optical pulse
CCD
Electro-optic crystal
(ex. ZnTe)
Polarizer
THz field
Polarizer
ETHz (t)
Pellicle beam combiner
THz pulse
Optical
pulse
Delay (time)
* K. Y. Kim et al., Appl. Phys. Lett. 88, 041123 (2006); Z. Jiang et al., Appl. Phys. Lett. 72, 1945 (1998);
Experimental setup:
(b)
0.2
Chirped optical
probe
THz generation pulse
0
Spectrum (a.u.)
Difference spectrum (a.u.)
(a)
-0.2
800
820
2
(c)
1
0
0
Polarizer
1
2
Freq (THz)
840
ZnTe
Wavelength (nm)
Optical pump
CCD
Teflon
Al
target
Imaging
spectrometer
Polarizer ZnTe
Experimental setup:
Al disk
Laser-ablated spots
Gratings
ZnTe
Sample
Pellicle
Experimental result IV:
THz generation from ablation
Aluminum
Transient current
+
+
+
eee-
Optical pump pulse
Coherent THz generation from a current
surge in the laser-produced plasma
Difference spectrum (a.u.)
THz waveform
0
-0.2
-0.4
1 ps
-0.6
800
810
820
830
Wavelength (nm)
840
THz propagation simulation:
To determine the THz skin depth, we solve the Helmholtz equation.
2
1
( d  dx )( dB dx )  k (   sin  ) B  0
2
2
3
1.5
(a)
1.0
3
Te at 1 ps
Te at 10 ps
 at 1 ps
 at 10 ps
0.5
2
1
-
e temperature Te (eV)
2
0.0
THz intensity
Mass density  (g/cm )
d B dx  
0
(b)
1.0
Te ~ 0.9 eV,  ~ 2.6 g/cm3,
r ~ 1016 s-1
ITHz at 1 ps
ITHz at 10 ps
0.5
0.0
-100
At 1ps:
At 10 ps:
-50
0
50
100
Distance (nm)
150
200
Te ~ 0.6 eV,  ~ 1.6 g/cm3,
r ~1015 s-1
K. Y. Kim et al., Phys. Rev. Lett. 100, 135002 (2008).