Coherent Anti-Stokes Raman

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Temperature Measurements in Flames
at 1000 Hz Using Femtosecond
Coherent Anti
-
Stokes Raman
Spectroscopy



Daniel R. Richardson and Robert P. Lucht


Purdue University, West Lafayette, Indiana 47907


Waruna D. Kulatilaka and Sukesh Roy

Spectral Energies, LLC, 2513 Pierce Avenue, Ames, IA 50010


James R. Gord

Air Force Research Laboratory, Propulsion Directorate, Wright
-
Patterson AFB, Ohio 45433


AIAA Aerospace Sciences Meeting

Orlando, FL January 7, 2010





Acknowledgments


Funding for this research was provided by the Air
Force Office of Scientific Research (Dr. Julian
Tishkoff, Program Manager), and by the Air Force
Research Laboratory, Propulsion Directorate,
Wright
-
Patterson Air Force Base, under Contract
No. F33615
-
03
-
D
-
2329, by the National Science
Foundation, Combustion and Plasmas Program
under Award Number 0413623
-
CTS, and by the
U.S. Department of Energy, Division of Chemical
Sciences, Geosciences and Biosciences, under
Grant No. DE
-
FG02
-
03ER15391.



Excellent technical assistance from Kyle Frisch
at WPAFB.

Outline of the Presentation



Introduction and Motivation


Fs CARS Measurements of Temperature in
Flames: Frequency
-
Spread Dephasing Decay of
the Initial Raman Coherence


Impulsive Interaction of the fs Pump and Stokes
Beams to Create Giant Raman Coherence at t=0



Used of Chirped Probe to Map Temporal
Domain into Frequency Domain: Single
-
Shot
Temperature Measurements


Conclusions and Future Work

Ns CARS for Gas
-
Phase Diagnostics


Ns CARS for Gas
-
Phase Diagnostics


Gr
o
u
n
d

E
l
e
c
t
r
o
n
i
c

L
e
v
e
l
v" = 0
, J
v" = 1
, J
v" = 2
F
r
e
q
u
e
n
c
y
Broadband Dye Laser

Spectrum

Single
-
Shot Multiplex
CARS Spectrum


Nonintrusive


Coherent Laser
-
Like Signal


Spatially and Temporally
Resolved


Excellent Gas
-
Temperature
Measurement Technique


Nonresonant Background


Collisional/Linewidth
Effects


Data
-
Acquisition Rates: No
Correlation Between Laser
Shots at 10 Hz


Broadband Dye Laser Mode
Noise

Ns CARS for Gas
-
Phase Diagnostics


Good
Bad

Fs CARS for Gas
-
Phase Diagnostics



Nanosecond CARS using (typically) a Q
-
switched
Nd:YAG laser and broadband dye laser is a well
-
established technique for combustion and plasma
diagnostics


Fs lasers have much higher repetition rates than ns
Q
-
switched Nd:YAG lasers: > 1 kHz versus ~10 Hz

Fsec CARS for Gas
-
Phase Diagnostics



For application as a diagnostic probe for turbulent
flames, signal levels must be high enough to extract
data on a single laser shot from a probe volume with
maximum dimension ~ 1mm.


How effectively can Raman transitions with line
width ~ 0.1 cm
-
1

line width

be excited by the fs pump
and Stokes beams (200 cm
-
1

bandwidth)? Answer:
very

effectively.


How do we extract temperature and concentration
from the measured single
-
shot fs CARS signals?

Ultrafast Laser System for Fs CARS

Optical System for Fs CARS with Mechanically
Scanned Probe

Calculated Time Dependence of CARS Intensity
with Time
-
Delayed Probe Beam

10
-34
10
-33
10
-32
10
-31
10
-30
10
-29
10
-28
10
-27
0
50
100
150
200
CARS Intensity
Time (psec)
T = 300 K
At t = 0 psec, all Raman
transitions oscillate in phase =
giant coherence

At t > 20 psec, Raman
transitions oscillate with
essentially random phases

Calculated Time Dependence of CARS Intensity
with Time
-
Delayed Probe Beam

0.0001
0.001
0.01
0.1
1
10
0
5
10
15
300 K
500 K
1000 K
2000 K
CARS Intensity (arb. units)
Time (psec)
(a)
100
1000
10
4
10
5
10
6
2250
2265
2280
2295
2310
2325
2340
300 K
2000 K (x 100)
CARS Intensity (arb. units)
Raman Shift (cm
-1
)
(b)
Calculated Time Dependence of CARS
Intensity with Time
-
Delayed Probe Beam

0.01
0.1
1
0
0.5
1
1.5
2
2.5
3
300 K
500 K
1000 K
2000 K
CARS Intensity (Norm.)
Time (psec)
(c)
Temperature can
be determined
from the decay of
the initial Raman
coherence due to
frequency
-
spread
dephasing


Raman transitions
oscillate with
different
frequencies.

Theory for Fitting Time
-
Delayed Probe Fs
CARS Data











cos exp
t
res p s i i i
i
i
d
P t E t E t dt N t t
d

 

 
 
 
  
  
 
 
 
 

 
 








nres p s
P t E t E t










2
pr res nres
S I t P t P t dt
 


  
 
 

Input parameters from
spectroscopic database

Fitting parameters

R. P. Lucht et al.,
Appl. Phys. Lett.

89
, 251112 (2006).

Fs CARS Experimental Results:
Flame Temperatures

S. Roy et al.,
Opt. Commun.

281
, 319
-
325 (2008).


Raman Excitation for Fs Pump and
Stokes Pulses


There is a drastic difference in laser
bandwidth (150
-
200 cm
-
1
) and Raman line
width (0.05 cm
-
1
) for 100
-
fs pump and Stokes
laser pulses.


How effectively do the laser couple with the
narrow Raman transitions?


Can single
-
laser
-
shot fs CARS signals be
obtained from flames? (The answer is yes)


Coupling of 70
-
Fs Pump and Stokes Pulses
with the Raman Coherence

Numerical Model of fs CARS in N
2


A model of the CARS process in nitrogen
based on direct numerical integration of the
time
-
dependent density matrix equations has
been developed [Lucht et al., Journal of
Chemical Physics, 127, 044316 (2007)].


Model is nonperturbative and is based on
direct numerical integration of the time
-
dependent density matrix equations.

Single
-
Laser
-
Shot Fs CARS
Measurements


Most significant difference for fs CARS
compared to ns CARS is the potential for
data rates of 1
-
100 kHz as compared to 10
-
30
Hz for ns CARS.

Optical System for Single
-
Pulse fs CARS
with Chirped Probe Pulse

S
t
o
k
e
s
B
e
a
m
-

2
7
8
0
n
m
,
7
0
f
s
e
c
P
u
m
p
B
e
a
m
-

1
6
6
0
n
m
,
7
0
f
s
e
c
P
r
o
b
e
B
e
a
m
-

3
6
6
0
n
m
,
7
0
f
s
e
c
D
e
l
a
y
L
i
n
e
f
o
r
P
r
o
b
e
C
A
R
S
S
i
g
n
a
l
B
e
a
m
-

4
T
u
r
b
u
l
e
n
t
F
l
a
m
e
o
r
G
a
s
C
e
l
l
C
h
i
r
p
e
d
P
r
o
b
e
P
u
l
s
e
2
-
3
p
s
e
c
R
a
m
a
n
C
o
h
e
r
e
n
c
e
t
D
i
s
p
e
r
s
i
v
e
R
o
d
6
0
c
m
S
F
1
1
T
o
S
p
e
c
t
r
o
m
e
t
e
r
a
n
d
E
M
C
C
D
Lang and
Motzkus,
JOSA B
19
,
340
-
344
(2002).

Optical System for Single
-
Pulse fs CARS
with Chirped Probe Pulse

Single
-
Shot CPP fs CARS

10
-5
10
-4
10
-3
10
-2
10
-1
-2
-1
0
1
2
3
4
5
500K
600K
800K
CARS Intensity
Probe Delay Time (ps)
+2 ps Probe Delay

4 Single
-
Shots with Chirped Probe Pulse

Probe
Delay =
+2 ps

300 K

900 K

Theory for CPP fs CARS











cos exp
t
res p s i i i
i
i
d
P t E t E t dt N t t
d

  

 
 
 
  
   
 
 
 
 

 
 








nres p s
P t E t E t










2
pr res nres
S I t P t P t dt
 


  
 
 

Input parameters from spectroscopic database

Fitting parameters







2
0
0
2
0 0 0
exp
cos
pr
pr pr
pr
pr pr pr pr pr
t t
E t E
t
t t t t
  
 
 

 
 
 
 

 
 
 
 
    
 
 
Linear chirp parameter

Envelope function

Theory for CPP fs CARS

Source: Swamp Optics website

Theory for CPP fs CARS













nonres pr nonres
pr p s
E t E t P t
E t E t E t









res pr res
E t E t P t

Calculate time
-
dependent nonresonant signal:

Calculate time
-
dependent resonant signal:

















cos
sin
real nonres res
imag nonres res
E E t E t t dt
E E t E t t dt
 
 




 
 
 
 
 
 








2 2
real imag
S E E
  
 
Theory for CPP fs CARS

Fourier transform time
-
dependent CARS signal:

CPP fs CARS Spectrum in Room Temp
Air

0
5 10
2
1 10
3
1.5 10
3
2 10
3
2.5 10
3
3 10
3
3.5 10
3
4 10
3
0
5 10
11
1 10
12
1.5 10
12
16920
17040
17160
17280
17400
Experiment
Theory
N
2
CARS Signal (arb. units)
N
2
CARS Signal (arb. units)
CARS Signal Frequency (cm
-1
)
CPP fs CARS Spectrum at +2 ps Delay for
500 K

0
2 10
2
4 10
2
6 10
2
8 10
2
1 10
3
1.2 10
3
0
2 10
11
4 10
11
6 10
11
8 10
11
1 10
12
1.2 10
12
1.4 10
12
16920
17040
17160
17280
17400
Experiment
Theory
N
2
CARS Signal (arb. units)
N
2
CARS Signal (arb. units)
CARS Signal Frequency (cm
-1
)
Theoretical fit parameters same as for
300 K spectra

CPP fs CARS Spectrum at +2 ps Delay for
700 K

Theoretical fit parameters same as for
300 K spectra

0
2 10
2
4 10
2
6 10
2
8 10
2
1 10
3
1.2 10
3
0
2 10
11
4 10
11
6 10
11
8 10
11
1 10
12
1.2 10
12
16920
17040
17160
17280
17400
Experiment
Theory
N
2
CARS Signal (arb. units)
N
2
CARS Signal (arb. units)
CARS Signal Frequency (cm
-1
)
CPP fs CARS Spectrum at +2 ps Delay for
900 K

Theoretical fit parameters same as for
300 K spectra

0
2 10
2
4 10
2
6 10
2
8 10
2
1 10
3
1.2 10
3
0
2 10
11
4 10
11
6 10
11
8 10
11
1 10
12
16920
17040
17160
17280
17400
Experiment
Theory
N
2
CARS Signal (arb. units)
N
2
CARS Signal (arb. units)
CARS Signal Frequency (cm
-1
)
CPP fs CARS Spectra at +2 ps Delay

0
5 10
11
1 10
12
1.5 10
12
16950
17100
17250
17400
300 K
500 K
700 K
900 K
S(

) (arb. units)
Signal Frequency (cm
-1
)
Chirped Probe Delay Time = +2 ps
Temperature Histograms from Single
-
Shot fs CARS

Temperature Histograms from Single
-
Shot fs CARS from Flames

1 kHz Temperature Data from Flame with
a 10 Hz Driven Pulsation

1 kHz Temperature Data from Flame with
a 10 Hz Driven Pulsation

1 kHz Temperature Data from Flame with
a 10 Hz Driven Pulsation

1 kHz Temperature Excursion Data from
Flame with a 10 Hz Driven Pulsation

0
100
200
300
400
500
600
700
50
100
150
200
363-1670K
365-1620K
366-1568K
368-1545K
369-1601K
370-1674K
377-1772K
CARS Signal (a.u.)
Pixel
Laser Shot Number - Fit Temperature (K)
1 kHz Temperature Excursion Data from
Flame with a 10 Hz Driven Pulsation

0
100
200
300
400
500
600
700
50
100
150
200
363-1670K
365-1620K
366-1568K
368-1545K
369-1601K
370-1674K
377-1772K
CARS Signal (a.u.)
Pixel
Laser Shot Number - Fit Temperature (K)
1 kHz Temperature Excursion Data from a
Turbulent Bunsen Burner Flame

0
400
800
1200
1600
2000
2400
2800
3200
100
200
300
400
500
600
100
101
102
103
104
CARS Signal (a.u.)
Pixel
Laser Shot Number
1 kHz Temperature Excursion Data from a
Turbulent Bunsen Burner Flame

0
0.2
0.4
0.6
0.8
1
100
200
300
400
500
600
100
101
102
103
104
CARS Signal (a.u.)
Pixel
Laser Shot Number
Conclusions


Single
-
shot fs CARS spectra from N
2

recorded
at 1000 Hz from atmospheric pressure air at
temperatures of 300, 500, 700, and 900 K, and
from laminar, unsteady, and turbulent flames.


Signals are very strong and reproducible from
shot to shot. Precision and accuracy
comparble to best single
-
shot ns CARS.



Theoretical model developed to fit CPP fs CARS
spectra temperature. Agreement is excellent for
+2 ps probe delay at all temperatures. Other
probe delays also show promise.

Future Work: fs CARS


Analyze recent single
-
shot data acquired in a
turbulent flame at a data rate of 1 kHz. Signals
were excellent but data has a long tail to the
high
-
frequency side due to probe spectrum,
complicating data analysis.



Implement better characterization/phase control
of the laser beams.

Pulse shaping/control for the
pump and Stokes beams may also be quite
useful for suppressing nonresonant
background.



Develop strategies for optimal strategies for
temperature and concentration measurements.


Future Work: fs CARS


New laser system from Coherent ordered
(AFOSR DURIP Program).



Laser rep rate of either 5 kHz with 3 mJ per
pulse or 10 kHz with 1.2 mJ per pulse.



Nominal pulse durations of either 90 fs or 40 fs.


Pulse shaper integrated into the system
between the oscillator and amplifier.


Potential Advantages of fs CARS


Data rate of 1
-
100 kHz would allow true time
resolution, study of turbulent fluctuations and of
transient combustion events.


Data rate of 1
-
100 kHz as opposed to 10 Hz
would decrease test time considerably in
practical applications.


Fs CARS, unlike ns CARS, is insensitive to
collision rates even up to pressure > 10 bars (fs
CARS signal increases with square of pressure).

Potential Advantages of fs CARS


Fs laser pulses are near
-
Fourier
-
transform
limited, noise decreased significantly for single
-
shot measurements.


Because collisions do not influence the
spectrum, no Raman linewidths are needed for
temperature fitting code.


Chirped Probe Pulse Cross
-
Correlation
with Fundamental Beam

Single
-
Shot CPP fs CARS

10
-5
10
-4
10
-3
10
-2
10
-1
-2
-1
0
1
2
3
4
5
500K
600K
800K
CARS Intensity
Probe Delay Time (ps)
+2 ps Probe Delay

Conclusions


Single
-
shot fs CARS spectra from N
2

recorded at 1000 Hz from atmospheric
pressure air at temperatures of 300, 500,
700, and 900 K, and from flames. Signals
are very strong and reproducible from
shot to shot.


Theoretical model developed to calculate
synthetic CPP fs CARS spectra for
comparison with experiment. Agreement
is excellent for latest set of data at +2 ps
probe delay at all temperatures.

Future Work: fs CARS


Implement least
-
squares fitting routine to
obtain quantitative agreement between
theory and experiment.


Implement better characterization/phase
control of the laser beams.


Develop strategies for optimal strategies
for temperature and concentration
measurements.

Future Work: fs CARS


Fs lasers with mJ output and rep rates of up to
100 kHz will be available soon, use of these fs
laser systems has the potential to revolutionize
diagnostic measurements in reacting flows


data rate increase of 2
-
3 orders of magnitude.


New methods will be required for signal
generation and analysis. Pulse shaping/control
for the pump and Stokes beams may be quite
useful for suppressing nonresonant
background. Pulse shaping/control for the
probe beam may be useful for extracting
temperatures and concentrations.

Potential Advantages of fs CARS


Data rate of 1
-
100 kHz would allow true time
resolution, study of turbulent fluctuations and of
transient combustion events


Data rate of 1
-
100 kHz as opposed to 10 Hz would
decrease test time considerably in practical
applications


Fs CARS, unlike ns CARS, is insensitive to collision
rates even up to pressure > 10 bars (fs CARS signal
increases with square of pressure)


Fs laser pulses are near
-
Fourier
-
transform limited,
noise may be decreased significantly for single
-
shot
measurements


Chirped Probe Pulse (CPP) fs CARS in Argon

-
2 ps Probe Delay

+5 ps Probe Delay

0 ps Probe Delay

-3
-2
-1
0
1
2
3
4
5
[E
Pu
(t) E
St
(t)]
2
Probe Delay Time (ps)
Temperature Measurements in Flames

0
2 10
11
4 10
11
6 10
11
8 10
11
1 10
12
1.2 10
12
1.4 10
12
16950
17100
17250
17400
500 K
1000 K
1500 K
2000 K
S(

) (arb. units)
Signal Frequency (cm-1)
Chirped Probe Delay Time = 2 ps
Temperature Measurements in Flames

10
9
10
10
10
11
10
12
10
13
16950
17100
17250
17400
500 K
1000 K
1500 K
2000 K
S(

) (arb. units)
Signal Frequency (cm-1)
Chirped Probe Delay Time = 2 ps