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Spectroscopy of the instantaneous
all-optical switching nonlinearity
of thin films
F.P.
Strohkendl, R.J. Larsen, L.R. Dalton,
University of Southern California
Z.K. Kafafi
Naval Research Laboratory
“All-optical switching”

“Linear” optical properties are intensity dependent :
n(I)  n0  n2 I
(I)  0  2 I

Nonlinear phase shift:

Hope for
fNL  2 n2 IL
I1sin2(fNLf0)
- fast all-optical switching
L
-”Packet switching”
Nonlinear
Material
I
I
I2 cos2(fNLf0)
Mechanisms contributing to n2
slow

Electronic excitation

Nuclear movement/alignment

Distortion of electronic wave function
“instantaneous, electronic nonlinearity”
n
80
12 0
80
80
0

10 0
20 0
time (fs)
30 0
"integrating"
40
0
0
small
12 0
40
40
large
fast
n
"instantaneous"
n
n
12 0
n2
Relaxation
Heating

0
0
10 0
20 0
time (fs)
30 0
0
10 0
20 0
time (fs)
Short-pulse experiments favor “instantaneous” electronic
nonlinearity
30 0
Phase-mismatched DFWM: Amplitude and phase
of c(3) [F. P. Strohkendl et al., J. Opt. Soc. Am. B 14, 92 (1997)]
Sample
Ls
B
T hin
Film
Sample
2
3
E
Ls / Lfilm  102-103
1
A
Lfilm
|c(3)|2
Observation
Plane
Signal, A
Film, B or E


• Diffraction
Thin Film: Raman-Nath,
Thick Substrate: Bragg
Substrate
Signal addition
48 2
n2  2 Rec 1111( ,  , ,  )
n0 c
DFWM is directly related
to all-optical switching para2 48 2
2 
Imc 1111( ,  , , ) meters
2
c
n0 c
Four-wave mixing signals under
absorptive / non-absorptive conditions
Absorptive, 2500 cm-1
Non-absorptive
A , C6 0 on CaF2
B, C6 0 on CaF2
E, C6 0 on CaF2
A , CaF2
6
4
B,
c
DFWM in C 60 at 690 nm
1.2
1.0
DFWM Signal
four wave mixing sig nal ( relat ive unit s)
8
2
1
0.8
0.6
E
0.4
c
3
A,
c
0.2
2
A: beam
1 delayed
0.0
B: beam 1 delayed
E: beam-500
3 delayed0
-40 0
-20 0
0
2 00
500
1000
1500
Beam Delay (fs)
4 00
beam delay ( f s)
•Femtosecond pulses under absorptive conditions
are NOT sufficient to measure instantaneous response
“Instantaneous,” electronic c(3)
c(432) =
(3)

abc
b
c
a
fabc (23)
g

all states 
4

g
|
r
|
c

c
|
r
|
b

b
|
r
|
a

a
|
r
|
g



Ne




  ...
c(3) ( 4 ,  3 ,  2 , 1 )  F








3




a, b, c 
 cg   3   2   1   i cg  bg   3   2   i bg  ag   3   i ag 

where  a | r | g  Transition dipole moment,

 ag = Transition energy,  ag  Transition linewidth.
Internal transition energies are revealed through multi-photon resonances
– THG : (432)(3) , 1-, 2-, and 3-photon resonances
– DFWM: (432)() , only 1-, and 2-photon resonances
Example: DFWM vs. Third Harmonic
Generation in C60
DFW M, Strohkendl '96
THG
100
• Third Harmonic Generation
9
8
(THG) and DFWM spectra
are unrelated.
•Two-photon resonance
observed with DFWM
remains undetected by
THG.
7
|c |(03 esu)
6
5
4
3
2
10
9
8
7
0.5
1.0
1.5
wavelength (µm)
2.0
2.5
Exploration of the instantaneous
nonlinearity under absorptive conditions

Why? The all-optical switching behavior is determined
once all one- and two-photon resonances are known!
c
two-photon
state b
(3)
a
a,b,c
c
ground
state
Two-Photon Term


-
a,b
a
b
ground
state
One-Photon Term
Problem: DFWM signal under resonant conditions is
dominated by (non-instantaneous) sample excitation !
Solution: Two-color FWM.
Nearly degenerate four-wave mixing (nDFWM)
suppresses non-instantaneous response
• Amplitude of excited state
Kg = | K1-K2 |
population rating is reduced due to
moving grating by
N 
N0
 Pulse
Moving
Grating
 K1
,  Pulse   Exci tation
•Example
  0.1eV, P ul se 100 fs
  Integration  7 fs
K2


Doppler
shifted Signal
(3)
cinstantaneous
( ,, , )  c (3)[(  ), , ,(  )] for  << 
 = transition linewidth
nDFWM Geometry
B
2
Thin Film
Sample
E
3
 A  1   2   3
 B  1   2   3
1
A
Observation
Plane
•3-beam signals at A, B, and E
•Measure thin film at B, and thick
fused silica reference at A
•Fused Silica: n2 = 3.0 x 10-16 cm2/W
Comparison of nDFWM/DFWM in C60
4
ps DFWM, Flom 92
2
DFWM/ NDFWM in C
(absorptive conditions)
1.2
6
nDFWM
fs DFWM
fs DFWM
es u)
4
0.8
0.6
0.4
2
-13
c1111 (10
DFWM Signal
8
at 690 nm
non-instantaneous
instantaneous x 20
1.0
1000
60
fs DFWM, Rosker 92
100
8
6
17000 cm
4
0.2
0.0
-1
2500 cm
-1
-500
0
500
1000
1500
Beam Delay (fs)
2
•DFWM signal under absorptive conditions
10
8
is unrelated to instantaneous response
6
4
0.50
0.60
0.70
0.80
wavelength (µm)
0.90
1.00
Exploring the Absorption Spectrum?
Absorption Spectrum of C60
80x10
3
2.5
Film Thickness: O.16 µm
60
absorption (cm
-1
)
2.0
1.5
1.0
40
20
0.5
0
0.0
200
400
600
800
400
500
600
wavelength (nm)
Full UV-Vis Spectrum
Explored Region
700
800
Conclusion

1- and 2-photon resonances determine the “instantaneous”
all-optical switching parameters (n2, 2) of a material.

DFWM / nDFWM are uniquely suited to explore the unknown
2-photon spectrum.

Used nDFWM successfully to suppress non instantaneous
response ( < 14000 cm-1).

Implemented new method for two-color femtosecond-pulse
generation.
Tunable femtosecond light source: 0.45-3.2 µm
Nd:YAG Pump
Femtosecond Oscillator
Mira 900 by Coherent
Ti:Sapphire
76 MHz, 10 nJ,
100-180 fs, 720-980 nm
Ar-ion
Pump
Laser
Grating Stretcher
grating:1800 l/mm
100fs -> 100ps
Two Stage Optical
Parametric Amplifier
0.45 - 3.2 µm, 60 µJ ±2% rms
50 - 120fs
Second
Harmonic
Generator
Continuum
Generator
Prism
Compressor
idler
signal
DFWM
Experiment
Regenerative Amplifier
Ti:Sapphire, 20 Hz
740-880 nm
2 mJ ±0.4% rms
Grating Compressor
1800 l/mm, 100ps ->
100fs, 0.8 mJ
sech2 transform limited
Automated femtosecond optical
parametric generator/amplifier
0.45-3.2 µm
Group velocity dispersion
0.4 mm
BBO
BBO,OPA
Fused
Silica
Dispersive
delay
BBO, OPA
0.7 mJ±0.4% rms
0.79µm
BBO,SHG
£ 60µJ Signal+Idler
±2% rms
0.45-0.75µm
0.85-3.2µm
Dual color generation for nDFWM in a single
femtosecond Optical Parametric Amplifier
Group velocity dispersion
0.4 mm

x
BBO
Input
0.8 mJ
790 nm
from Regen
395 nm
SHG
Continuum
Output
-7 µJ per color
- 0.1eV
BBO 1


BBO 2
Dispersive
Delay Line