Transcript DLong_ElecQuad_OSU2009_ver1.ppt

Calculations and first quantitative laboratory
measurements of O2 A-band electric quadrupole line
intensities and positions
0.482
16
P
-27
0.481
-6
-1
S = 2.87x10 cm molec.
-1
12934.5516 cm
-1
(10 cm ) [c]
-1
b1 - X1 Q(11) magnetic dipole, O2
16O
2
b(1) ← X (1) PQ(11) magnetic dipole hot band line
-27quadrupole
-1
electric
S=2.87×10
cm molecline
0.480
0.482
-30
-1
S = 3.74x10 -1 cm molec.
cm
 =12934.5516
12934.74895 cm
-1
-6
-1
S = 2.87x10 cm molec.
-1
12934.5516 cm
0.478
0.480
16O NO(21)
2
electric quadrupole line
-30 cm molec-1
S=3.70×10
electric quadrupole
line
quadrupole abs. peak/RMS = 16:1
-30
-1
S = 3.74x10 cm =12934.7490
molec.
cm-1
-1
12934.74895 cm

-5
4.0x10
0.0
0.479
-5
-4.0x10
0.478
(obs. - calc.)
16
-27
-1
(obs. - calc.
) cm ) [c]
(10
-1
P
b1 - X1 Q(11) magnetic dipole, O2
0.479
0.481
-5
4.0x10
0
2
4
quadrupole abs. peak/RMS = 16:1
6
8
detuning (GHz)
0.0
-5
-4.0x10
David
A. 2Long, Mitchio
Okumura,
0
4
6
8 Caltech
detuning (GHz)
Charles E. Miller, Herbert M. Pickett, JPL
Daniel K. Havey, Joseph T. Hodges, NIST, Gaithersburg
The O2 A-band: b 1  g ← X 3 g (0,0)
|Δ J |= 2
N+3
PP P
Q
N+1
N-1
RR R Q
RR R Q T S
PP P P
Q O RS
NO
J=N+3
TS
PO R
S
J=N+1
NO
J = N -1
J=N+3
++1
J1 
=N
1
g

+
g
J = N -1
|Δ J |= 0,1
80
PP,PQ
P
RR,RQ
P
R
P, Q
60
-25
-1
|Δ J |= 0,1
intensity (10
) -1)
cmcm
molec.
(10-25
molec.
intensity
100
R
R, Q
Sband, MD~2.23×10-22 cm molec.-1
40
20
HITRAN 2008
0
12900
13000
13100
13200
wave number (cm
•N must be odd for
3J
J=N
J=N+1
J=N–1
J=N
J=N+1
J=N–1
16O
2
and
J=N+2
= -N + 3
J
=gN + 1
18O
2
•We will use the notation ΔNΔJ (N ΄΄)
3

-
g
-30
-1
-30 cm molec.
intensity
intensity (10 cm
molec. )-1)
N
J=N+2
J=N+3
J=N+1
-1
)
P
120
N+2
13300
O
PO
100
|Δ J |= 2
RR
SS
80
Sband, EQ~1.8×10-27 cm molec.-1
60
40
N
20
T
O
S
TS
NO
0
12900
13000
13100
13200
wave number (cm
-1
)
13300
Electric quadrupole transitions in the O2 A-band
Overlap with MD transitions
•
•
Present study has quantitatively measured
nine transitions.
Eight have not previously been observed.
P
120
O
R
-1
transitions first observed in the solar
spectra of Brault (JMS, 1980).
TS(9) line was observed in the laboratory by
Naus et al (PRA, 1997).
-30
•
TS
molec.-1
intensity
intensity
(10(10-30
))
cmcm
molec.
•
S
100
80
60
40
N
T
O
S
*
20 this work
Brault
Brault
0
12900
12900
13000
13000
13100
13100
13200
13200
-1
wave
(cm-1))
wavenumber
number (cm
13300
13300
Why should we care about such weak transitions?
•
A-band is widely utilized to determine optical pathlength and surface pressure via
remote sensing
– EQ transitions have been observed in solar spectra.
• Can reach 1% absorbance.
• Can bias A-band remote sensing retrievals.
•
High-resolution MD lineshape studies.
•
A benchmark for ultra-sensitive techniques.
•
Computational models.
Figure from Yang et al. JQSRT, 2005
Frequency-stabilized cavity ring-down spectroscopy
(FS-CRDS)
cw probe laser
optical resonator
pzt
decay signal
R~99.997%
F~105,000
frequency-stabilized
reference laser
)
time
Leff~25 km
cavity stabilization servo
absorption spectrum
200 MHz
stabilized comb of
resonant frequencies
)
FSR = c/2L = 200MHz
frequency
TEM00
TEM01
frequency
Spectral scans (mode jumping)
dq
1. lock to local mode
2. acquire ring-down data
3. unlock laser
4. tune to next mode
detuning
Electric quadrupole line position calculations:
uncertainties less than 3 MHz
•Positions based on simultaneous fit to ground (X 3 g ) and excited state (b 1  g ).
•Utilized a fit to an ensemble of literature positions for the ν=0 and ν=1 levels of the ground state
to determine lower state parameters:
 Raman: Rouillé et al. JMS, 1992; Millot et al. JMS, 1996; Brodersen et al. JMS, 2003; Brown et
al., JMS, 2000. Microwave: Yu et al. JMS, 2005; Golubiatnikov et al. JMS, 2003; Endo et al. Jpn. J.
Appl. Phys., 1982; Park et al. JQSRT, 1996. Far-infrared: Zink et al., JMS, 1987.
•FS-CRDS A-band MD positions of Robichaud et al. (JMS, 2008) used to determine upper state
parameters. Positions were tied to 39K D1 and D2 transitions; uncertainties < 1MHz.
Precise knowledge of EQ positions and probe laser frequency allowed us unambiguously
locate EQ transitions and average over narrow spectral windows.
Short-term measurement statistics:
ring-down time averaging
-9
After 5s averaging,
rms baseline=1.1×10-10 cm-1
/(c )
2
-1
Relative standard deviation in the ringdown time, στ/τ, <0.2%, facq~10 Hz →
εNEA~2.5×10-10 cm-1 Hz -1/2
Allan deviation (cm )
10
-10
10
Δtacq
u() = /[(c )(facq tav) ]
2
1/2
-11
10
0.1
1
10
100
tav = nd/facq (s)
1000
Long-term measurement statistics:
averaging of complete spectra
•Long-term averaging led to a reduction in
detection limit by a factor of 10.
Minimum rms baseline ~ 1.8×10-11 cm-1
→ detection limit ~ 2.5×10-31 cm molec.-1.
u(<>) = min,acq ns
-1
root-mean-square baseline (cm )
•After 10 h of averaging, observe steady
reduction in baseline noise with an ns-1/2
dependence.
-1/2
-10
10
-
u(<>) = Afit ns
μ=0.46
9.7 h duration
-11
10
1
10
number of spectra, ns
100
Increase in signal-to-noise ratio with spectra averaging
s =
ns =n20
-1
[c] (10 cm )
0.486
=5
-6
ns = 5
ns
20
0.485
-1
ns = 1
ns = 1
0.484
12955.1
12955.2
12955.3
12955.4
-1
wave number (cm )
N.B. Middle and
top spectra are
offset vertically.
NO(19)
EQ transition
S = 6.36×10-30 cm molec.-1
Spectra averaging with FS-CRDS does not lead to
non-physical lineshapes
1.25
SNR=18,000:1
[c]
-1
1.00
•Measured Doppler width agreed with
calculated value to within 143 kHz (1/6000)
on average with a standard deviation of 379
kHz.
0.75
-6
-1
(10 cm )
0.50
•Center frequency agreed to 200 kHz.
-4
5x10
[obs.-calc.
•Measured PP(21) MD line near the Doppler
limit.
0
ns=1
ns=28
-4
-5x10
-4
-2
0
2
frequency detuning (GHz)
4
Examples of final electric quadrupole spectra:
can resolve ultraweak lines in the wings of strong features
16O18O PP(11)
16O TS(5)
2
MD line
S=1.54×10-26 cm molec.-1
 =13088.3092 cm-1
EQ line
S=2.05×10-29 cm molec.-1
 =13179.9239 cm-1
measurement
fit
0.9
0.5170
P
P(11)
16
18
O O
0.5165
0.8
2x10
-3
0.7
1x10
-3
-1
[c] (10 cm )
-6
-1
[1/(c)] (10 cm )
P
data - fit to P(11) line
N
fit to O(5) quadrupole line
-6
0.5160
-1
0.5155
-4
-2
0
detuning (GHz)
2
4
16O NO(5)
2
0.6
0
13088.10
13088.25
EQ line
S=2.12×10-29 cm molec.-1
 =13088.1529 cm-1
0.5
13088.10
13088.25
-1
wave number (cm )
Lorentzian width utilized in Voigt profiles
•SNR of EQ spectra too low to retrieve wL.
•Set wL = 2γp.
•Utilized empirical J-dependent correlation of Yang et al. (JQSTR, 2005):
  A
B
1  c1 J   c2 J 2  c3 J 4
with experimental FS-CRDS MD parameters of Robichaud et al. (JMS, 2008).
Observed linearity between peak area and O2
number density
4
line
J(N")
NO(13) N
O(5)
N
O(13)
N
O(15)
NO(15) N
O(17)
N
O(19)
NO(17) N
O(21)
-9
-1
peak area (10 GHz cm )
NO(5)
N
2
NO(19)
NO(21)
0
0
18
2x10
18
4x10
18
6x10
-3
number density (molec. cm )
Solid lines are: Ai ,calc  n Si c
(not a linear fit)
Uncertainty analysis
•
Three dominant sources of uncertainty:
1) lineshape (self-broadening coefficient (γ) and use of Voigt profile)
2) ring-down cavity’s base losses
3) total losses (base plus absorption)
•
•
•
Systematic uncertainties: 2.8-4.9%
Random uncertainties: 2.3-9.9%
Total uncertainties: 4.1-11%
•
Observables which should not contribute: measurements of the cavity FSR,
spectra’s frequency axes, sample temperature, pressure, and number density.
Electric quadrupole line intensity calculations
•
Matrix elements of the transitions moments were derived using spherical tensor
relations with Hund’s case (b) basis
•
The three transition moments (M1, Q1, Q3) were then determined through a
simultaneous fit to FS-CRDS MD and EQ measurements
Transition Moments
M1
Q1
Q3
0.06868(8) Bohr-magnetons
0.0124(4) Debye Å
0.00783(23) Debye Å
Band Intensities
Sband, MD=2.25(2)×10-22 cm molec.-1
and
Sband, EQ=1.8(1)×10-27 cm molec.-1
Electric quadrupole line intensity calculations:
comparison to present measurements
1.3
NO
SExp/SCalc
1.2
PO RS
1.1
TS
1
0.9
0.8
12900
12950
13000
13050
13100
13150
13200
wave number (cm-1)
•MAD(Present,Calc) = 5% which is within our average uncertainty
•Indicates that our measurements show the expected J and branch dependences
Electric quadrupole line intensity calculations:
comparison to Brault
1.2
NO
TS
SExp/SCalc
1.1
1
Present
0.9
0.8
Brault
PO RS
0.7
0.6
0.5
12900
13000
13100
13200
13300
wave number (cm-1)
Brault, JMS 1980.
•MAD(Brault,Calc) = 15% consistent with quadrature sum of uncertainties.
•Brault’s measurements are systematically low relative to calculations.
Take home points
•
Frequency-stabilized cavity ring-down spectroscopy was utilized to
quantitatively measure nine electric quadrupole transitions in the O2 A-band.
–
–
–
–
•
Eight of these transitions have never before been measured
Intensities ranged from S ~ 3×10-30 to 2×10-29 cm molec.-1
Uncertainty in S = 4.1-11%
Detection limit of 2.5×10-31 cm-1 molec.-1
This level of sensitivity was possible due to:
–
–
–
–
High reflectivity mirrors (R = 99.997%)
Precise knowledge of EQ line positions
Long-term averaging of entire spectra
Long-timescale frequency stability
Funding
• D. A. Long:
• D. K. Havey:
• Research Funding: