Purdue University Femtosecond CARS Spectroscopy of Gas-Phase Transitions: Theory and Experiments Prof. Robert P. Lucht School of Mechanical Engineering.

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Femtosecond CARS Spectroscopy of Gas-Phase Transitions: Theory

and Experiments

Femtosecond CARS Spectroscopy of Gas-Phase Transitions: Theory

and Experiments

Prof. Robert P. Lucht

School of Mechanical Engineering

Purdue University

and

The Institute for Quantum Studies

Texas A&M University

TAMU/Princeton Summer School on Quantum Optics and Molecular Spectroscopy

Casper, Wyoming July 16, 2007

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AcknowledgmentsAcknowledgments

• Sukesh Roy, Innovative Scientific Solutions, Inc., Dayton, Ohio

• Terrence Meyer, Iowa State University

• Jim Gord, Air Force Research Laboratory, Wright-Patterson AFB

• Paul Kinnius, PhD Student, Purdue

• Funding Support from NSF, AFOSR, DOE/BES

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Fsec CARS for Gas-Phase Diagnostics Fsec CARS for Gas-Phase Diagnostics

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

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

• But can we obtain a sufficient signal on a single laser shot to make measurements in turbulent environments? And how do we extract temperature and concentration from the signal?

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Fsec CARS for Gas-Phase Diagnostics Fsec CARS for Gas-Phase Diagnostics

• Fsec CARS for H2 and N2 has been demonstrated

by Motzkus, Beaud, Knopp and colleagues primarily as a spectroscopic tool.

• For application as a diagnostic in 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 fsec pump and Stokes beams (200 cm-1 bandwidth)?

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Potential Advantages of Fsec CARSPotential Advantages of Fsec CARS

• Data rate of 1-10 kHz (yet to be demonstrated) would allow true time resolution, study of turbulent fluctuations

• Data rate of 1-10 kHz as opposed to 10 Hz would decrease test time considerably

• Fsec CARS, unlike nsec CARS, is insensitive to collision rates even up to pressure > 10 bars

• Fsec CARS signal increases with square of pressure

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Laser System for Fsec CARSLaser System for Fsec CARS

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Optical System for Fsec CARSOptical System for Fsec CARS

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

CA

RS

Inte

nsity

Time (psec)

T = 300 K

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

CA

RS

Inte

nsity

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 random phases

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Calculated Time Dependence of CARS Intensity with Time-Delayed Probe BeamCalculated 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 K500 K

1000 K2000 K

CA

RS

Inte

nsi

ty (

arb

. un

its)

Time (psec)

(a)100

1000

104

105

106

2250 2265 2280 2295 2310 2325 2340

300 K

2000 K (x 100)

CA

RS

Int

ensi

ty (

arb.

un

its)

Raman Shift (cm-1)

(b)

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

CA

RS

Int

ensi

ty (

Nor

m.)

Time (psec)

(c)

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Fs CARS Experimental Results: Flame Temperatures

Fs CARS Experimental Results: Flame Temperatures

0.1

1

10

100

-1 0 1 2 3 4 5 6 7

=0.5=0.6=0.7=0.8=0.9=1.0

CA

RS

Sig

nal (

arb

. units

)

Probe Delay (ps)

Equivalence ratio is a measure of the actual fuel-air ratio to the stoichiometric fuel-air ratio.

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Fs CARS Experimental Results: Flame Temperatures

Fs CARS Experimental Results: Flame Temperatures

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Theory for Fitting Time-Delayed Probe Fs CARS Data

Theory for Fitting Time-Delayed Probe Fs CARS Data

cos expt

res p s i i ii i

dP t E t E t dt N t t

d

nres p sP t E t E t

2

pr res nresS I t P t P t dt

Input parameters from spectroscopic databaseFitting parameters

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Fs CARS Experimental Results: Flame Temperatures

Fs CARS Experimental Results: Flame Temperatures

Fit temperatures are in excellent agreement with calculated adiabatic equilibrium temperatures.

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Fs CARS Experimental Results: Concentration Effects

Fs CARS Experimental Results: Concentration Effects

Nonresonant peak allows in-situ calibration of resonant CARS signal.

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

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

Stokes Beam - 2780 nm, 70 fsec

Pump Beam - 1660 nm, 70 fsec

Probe Beam - 3660 nm, 70 fsec

Delay Linefor Probe

CARS Signal Beam - 4Turbulent Flame

or Gas Cell

Chirped Probe Pulse2-3 psec

Raman Coherence

t

DispersiveRod

60 cm SF11

To Spectrometerand EMCCD

Lang and Motzkus, 2002

•Sukesh Roy (ISSI): High-Repetition Rate Gas-Phase Temperature Measurements in Reacting Flows Using Femtosecond CARS Spectroscopy (21:30)

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Numerical Model of Fs CARS in N2Numerical Model of Fs CARS in N2

• A model of the CARS process in nitrogen based on direct numerical integration of the time-dependent density matrix equations has been developed.

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

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Numerical Model of N2 CARSNumerical Model of N2 CARS

CARS process is modeled using a fictitious electronic level as the intermediate level in the Raman process. The transition strengths are adjusted to give the correct Raman cross section.

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Time-Dependent Density Matrix Equations for the Laser Interaction

Time-Dependent Density Matrix Equations for the Laser Interaction

Rate of change of population of state j:

Time development of coherence between states i and j:

Coupling of laser radiation and dipole moment for states j and m:

1 2 3, , , ,jm jm jmV E r t E r t E r t E r t

( )jjjm mj jm mj j jj mj mm

m m

iV V

t

( ) ( )ijij ij ij im mj im mj

m

ii V V

t

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1 4exp expkg kg kgt t i t t i t

2 3exp expke ke ket t i t t i t

1 2expeg egt t i t

Time-Dependent Density Matrix Equations for the Laser Interaction

Time-Dependent Density Matrix Equations for the Laser Interaction

The off-diagonal density matrix elements are written in terms of slowly varying amplitude functions and a term that oscillates at the frequency or frequencies of interest for each term:

The envelope functions and polarizations for the pump, Stokes, and probe beams are specified.

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Calculation of the Raman CoherenceCalculation of the Raman Coherence

Time-dependent density matrix equations for coherence amplitudes (after application of the rotating wave approximation):

The two-photon Raman coherence operates through intermediate states k. States e and g are not single-photon coupled.

2 3 11 2eg eg eg eg ek kg ek kg ek kg

k

ii V V V

11 1 1 2 2 2 3 3 32

1 2 31 2 3

ˆ ˆ ˆexp exp exp

exp exp exp

kg kg

kg kg kg

V e A i t e A i t e A i t

V i t V i t V i t

The laser interactions terms are defined by the following and similar equations:

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Numerical Results for 100 Fs PulseNumerical Results for 100 Fs Pulse

Je = Jg = 8

Raman = 0.05 cm-1 Stokes Irrad = 10xPump Irrad

10-5

10-4

10-3

10-2

0

1 1016

2 1016

3 1016

4 1016

5 1016

0 100 200 300 400 500 600

Co

here

nce

and

Po

pula

tion

De

nsity

Ma

trix

Ele

me

nts

Pu

mp

Lase

r Irradia

nce (W

/m2)

t (fsec)

ee

/gg

0

|eg

|/gg

0

Ipump

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Numerical Results for 70 Fs PulseNumerical Results for 70 Fs Pulse

Je = Jg = 5

Raman = 0.05 cm-1 Stokes Irrad = Pump Irrad

-0.1

0.0

0.1

0.2

0.3

0

1 1017

2 1017

3 1017

4 1017

5 1017

0 500 1000 1500 2000 2500 3000Co

he

ren

ce D

en

sity

Ma

trix

Ele

men

tsP

um

p La

ser Irradia

nce

(W/m

2)

t (fs)

(b) Q(5)

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0

1 1018

2 1018

0 100 200 300 400 500 600

(EG

)r/(GG

)0

(EG

)i/(GG

)0

|EG

|/(GG

)0

I1(W/m2)

Co

he

ren

ce D

en

sity

Ma

trix

Ele

men

tsP

um

p La

ser Irradia

nce

(W/m

2)

t (fs)

(a)

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Comparison of Raman Excitation for 70 Fs Pulses, Peak Irradiance 2x1018 W/m2

Comparison of Raman Excitation for 70 Fs Pulses, Peak Irradiance 2x1018 W/m2

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0

1 1018

2 1018

0 100 200 300 400 500 600

(EG

)r/(GG

)0

(EG

)i/(GG

)0

|EG

|/(GG

)0

I1(W/m2)

Co

he

ren

ce D

en

sity

Ma

trix

Ele

men

ts

Pu

mp

Laser Irrad

ian

ce (W

/m2)

t (fs)

(a)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0

1 1018

2 1018

0 100 200 300 400 500 600

EE

/(GG

)0I1(W/m2)

No

rma

lize

d E

xcite

d L

eve

l Po

pu

latio

n

Pu

mp

Laser Irrad

iance

(W/m

2)

t (fs)

(c)

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0

1 1018

2 1018

0 100 200 300 400 500 600

(EG

)r/(GG

)0

(EG

)i/(GG

)0

|EG

|/(GG

)0

I1(W/m2)

Co

he

ren

ce D

en

sity

Ma

trix

Ele

men

ts

Pu

mp

Laser Irrad

ian

ce (W

/m2)

t (fs)

(a)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0

1 1018

2 1018

0 100 200 300 400 500 600

EE

/(GG

)0I1(W/m2)

No

rmal

ize

d E

xcite

d L

eve

l Po

pu

latio

n

Pu

mp

Laser Irrad

iance

(W/m

2)

t (fs)

(c)

Je = Jg = 5

Raman = 0.05 cm-1Stokes Irrad = Pump Irrad

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Comparison of Raman Excitation for 70 Fs Pulses, Peak Irradiance 1019 W/m2

Comparison of Raman Excitation for 70 Fs Pulses, Peak Irradiance 1019 W/m2

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0

1 1018

2 1018

0 100 200 300 400 500 600

(EG

)r/(GG

)0

(EG

)i/(GG

)0

|EG

|/(GG

)0

I1(W/m2)

Co

he

ren

ce D

en

sity

Ma

trix

Ele

men

ts

Pu

mp

Laser Irrad

ian

ce (W

/m2)

t (fs)

(a)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0

1 1018

2 1018

0 100 200 300 400 500 600

EE

/(GG

)0I1(W/m2)

No

rma

lize

d E

xcite

d L

eve

l Po

pu

latio

n

Pu

mp

Laser Irrad

iance

(W/m

2)

t (fs)

(c)

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0

5 1018

1 1019

0 100 200 300 400 500 600Co

he

ren

ce D

en

sity

Ma

trix

Ele

me

nts P

um

p La

ser Irradia

nce (W

/m2)

t (fs)

(b)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0

5 1018

1 1019

0 100 200 300 400 500 600No

rma

lize

d E

xcite

d L

eve

l Po

pul

atio

n

Pu

mp

Laser Irrad

ian

ce (W

/m2)

t (fs)

(d)

Je = Jg = 5

Raman = 0.05 cm-1 Stokes Irrad = Pump Irrad

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Comparison of CARS Signal for 70 Fs PulsesComparison of CARS Signal for 70 Fs Pulses

Stokes Irrad = Pump Irrad = 1019 W/m2

Stokes Irrad = Pump Irrad = 5x1017 W/m2

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Raman Excitation for 70 Fs PulsesRaman Excitation for 70 Fs Pulses

• Despite the drastic difference in laser bandwidth (200 cm-1) and Raman line width (0.05 cm-1), the 70-fsec laser pulse excites the Raman transition very effectively.

• The 70-fsec pulse couples very effectively with the Raman transition because the Raman coherence is established by a two-photon process.

• The Q-branch transitions are excited to the same extent with the same initial phase

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

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

Stokes Beam780 nm, 200 cm-1

Pump Pulse660 nm, 200 cm-1

Optical Frequency

1-2 =2300 cm-1

1-2 =2300 cm-1

1-2 =2300 cm-1

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Phase of the Raman Coherence for Different Transitions

Phase of the Raman Coherence for Different Transitions

Stokes Irrad = Pump Irrad

1 2eg

is different for each of the different Q-branch transitions.

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

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

Stokes Irrad = Pump Irrad

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Simultaneous Fs CARS for CO (2145 cm-1) and N2 (2330 cm-1)

Simultaneous Fs CARS for CO (2145 cm-1) and N2 (2330 cm-1)

0.1

1

10

-1 0 1 2 3 4 5 6

N2 1atm Pump = 675 nm

75% N2 25% CO 1atm

Pump = 675nm

CA

RS

Sig

na

l (a

rb. u

nits

)

Probe Delay (ps)

The 180 fs spacing of the modulation in the probe delay scan corresponds to the 185 cm-1 frequency difference in the N2 and CO Raman

bands.

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Simultaneous Fs CARS for CO (2145 cm-1) and N2 (2330 cm-1)

Simultaneous Fs CARS for CO (2145 cm-1) and N2 (2330 cm-1)

The pump wavelengths for Raman resonance for N2 and CO are

675 nm and 682 nm, respectively.

0.1

1

10

-1 0 1 2 3 4 5 6 7

N2 5 atm Pump = 675 nm

50% N2 50% CO 5atm

Pump = 679nm

CA

RS

Sig

na

l (a

rb. u

nits

)

Probe Delay (ps)

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ConclusionsConclusions

• Initial fs CARS measurements show that temperature and concentration can be determined from temporal dependence of CARS signal in the first few fsec after “impulsive” pump-Stokes excitation. Measured flame temperatures appear to be very accurate.

• Fsec CARS offers some distinct (potential) advantages compared to nsec CARS

1 kHz data rate or greater Impulsive excitation, strong coherence at short

time delays No effect of collisions for short time delays You can see the fsec CARS signal from room air