1. Joakim Bood and Andrew McIlroy
Measurement of the Sixth Overtone Band of NO Using Cavity-Enhanced Frequency Modulation Spectroscopy
David Osborn
Joakim Bood and Andrew McIlroy
Combustion Research Facility
Sandia National Laboratories
Livermore, CA
USA
I’d like to thank the organizers for the invitation to speak in this session. I’d like to describe our work on the first measurements of the 6th overtone of nitric oxide using the NICE-OHMS technique, which I will explain in a moment. This research was conducted at the Combustion Research Facility of Sandia National Laboratories in Livermore, CA.

2. Absorption methods provide quantitative measurements
Measures absolute number densities
Unaffected by quenching or predissociation
Enhance absorption signal
Reduce background noise to the quantum limit S N
maximized
Goal:
Of course laser induced fluorescence is also a very sensitive technique for monitoring reactions, but absorption measurements can give absolute number densities and are unaffected by non-radiative processes, and therefore we are pursuing an absorption technique. As with any experiment, the sensitivity will be greatest when we enhance the absorption signal from a sample while reducing the background noise. As we attempt to do this, we need to know the maximum sensitivity possible in order to evaluate our progress.

3. Sensitivity enhancement by an optical cavity
Cavity modes
FSR
FWHM
High reflectivity mirrors (R>99.99%)
High cavity finesse (F>10000)
Large number of passes (>10000)
Long effective pathlengths (>1 km)
Lcav = Total cavity
losses
Now, to enhance the signal, we increase the absorption pathlength drastically by placing the sample in an optical cavity formed by two highly reflective mirrors. The cavity supports longitudinal modes which are separated by the Free Spectral Range of the cavity. The finesse of the cavity, F, equals the ratio between the FSR and the bandpass (FWHM) of the cavity. As the light coupled into the cavity makes many round trips through the sample, the effective absorption length is increased by a factor of 2 F over pi, and the minimum detectable absorption is therefore reduced by 2 F over pi.
The effective absorption length is increased by a factor 2F/p, the minimum detectable absorption is reduced by 2F/p

4. Cavity Ringdown TechniqueL
Trigger
Cavity decay time is a function of the intracavity absorption
Time-domain measurement avoids laser technical noise 
very high sensitivity
So why not use cavity ringdown spectroscopy? Well, of course cavity ringdown is a very powerful technique. While it does provide very long effective pathlengths as I’ve just described, which increases the signal, the noise in the system is usually 3 to 6 orders of magnitude larger than the shot noise limit. While there are many reasons for this excess noise, one universal reason is that the measurements on and off the molecular resonance are separated by a large time delay, usually seconds to minutes, or sometimes even longer, so that low frequency noise, which typically scales as 1/f, dominates.
Large time delay between
Measurements of () and 0

5. Shot-noise limit: the highest possible sensitivity in direct absorption
Shot noise = Noise due to quantum fluctuations of the
photons arriving at the detector
The experiment will have the least noise when this is
the dominant noise source
If Beer’s Law is written as:
Minimum detectable absorption:
The experiment will have the least noise when the dominant noise component is the shot noise of the photons arriving at the detector. For small absorption, i.e., alpha L is much smaller than unity, it follows from Beer-Lambert’s law that the fractional absorption is simply given by alpha L, where alpha is the absorption coefficient and L is the cell pathlength. The minimum fractional absorption, alpha L min, is now given by this simple equation. In order to compare cells of different length and different amounts of signal averaging, we normalize the shot noise limit by cell length and bandwidth to obtain the minimum detectable absorption coefficient with units of per centimeter per root Hertz. This is a well-defined parameter to compare sensitivities in absorption spectroscopy. Unfortunately, in most experiments, technical noise sources, such as vibration of components in the lab, overwhelms the shot noise and degrades the sensitivity, often by many orders of magnitude.
Even when the light level on the detector appears to be ideally steady there are fluctuations on the photocurrent.
L = absorption cell pathlength (cm)
= absorption coefficient (cm-1)
e = electron charge (C)
B = detection bandwidth (Hz)
h = detector responsivity (A/W)
P = photon power at detector (W)
(cm-1 Hz-1/2)

6. Basic Principle and Setup for FM spectroscopy
c-m c
c+m
Sample
c-m c c
c+m
Laser
EOM PD
RF Source
Mixer
RF amp.
Phase shifter
Signal
Very briefly, frequency modulation, or FM spectroscopy, works by frequency moldulating a narrowband laser beam, in our case using an electro-optic modulator, at a high frequency, denoted by omega m, which is typically hundreds of MHz. This modulation of the input light, called the carrier, puts sidebands on the laser at the frequencies omega c plus omega m and omega c minus omega m. If there are no absorbing molecules in the cell, each of the two sidebands forms a beat signal with the carrier and the two beat signals are exactly equal in amplitude and 180 degrees out of phase, so that they cancel and, ideally, no RF amplitude modulation is observed. Now imagine there is a molecular absorption centered on the right sideband. This sideband will now be slightly attenuated. This leads to imperfect cancellation of the two beat signals and, thus, to an amplitude modulation of the laser beam. When this signal is demodulated at frequency omega m, we obtain the difference in absorption at the left versus the right sideband. This is how FM spectroscopy allows on and off resonance measurements to be made simultaneously. The advantage is that we are only subject to the noise near the frequency omega m, and this noise is typically just the shot noise.
(Because nothing is ever free in this world, there is a penalty to pay when using FM spectroscopy. The minimum detectable absorption coefficient is now larger by about a factor of four due to the fact that the signal is contained in only one sideband, but the shot noise comes from all three components of the light. But generally this price is well worth paying because the total noise is now dominated by the shot noise, not the technical noise, which is many orders of magnitude higher.)
So the challenge is to combine a high finesse cavity with FM spectroscopy.
Low-pass
filter
Simultaneous comparison between
on-resonant and off-resonant cases

7. Cavity Enhancement + Frequency Modulation
High modulation frequency (to decrease N)
High finesse (to increase S)
No modulation
Low modulation frequency
Technical noise
(1/f-noise)
High modulation frequency
No signal!
FM to AM
conversion
Now back to our efforts. We want a high modulation frequency to decrease noise, and a high cavity finesse to increase the signal. You’ll now see an apparent dilemma. First, the linewidth of a high-finesse cavity is narrow, making it a sharp discriminator for any frequency noise. Frequency noise between the laser and the cavity is converted to amplitude noise with a huge gain. In order to get the carrier and the sidebands through the cavity, we have to choose a very low modulation frequency where there is still substantial technical noise. If we choose a high modulation frequency, as we would like, the sidebands are not transmitted through the cavity, which defeats the purpose of FM spectroscopy.
Apparent dilemma:
The modulation frequency is limited by the cavity linewidth

8. The NICE-OHMS* solution
Noise-Immune Cavity-Enhanced Optical Heterodyne Molecular Spectroscopy
D = FSR
Detection at D
Laser
EOM (D)
FSR
Empty cavity (FSR = D)
Transmission is pure FM
Zero background
Frequency noise immune D
Molecular
dispersion
One mode shifted by molecules
FM unbalanced and signal appears
(due to differential change of modes)
The solution to this problem was found a few years ago by Jun Ye and Jan Hall at JILA, University of Colorado at Boulder. It’s rather simple in principle. One simply chooses the modulation frequency to match the free spectral range of the cavity, so that the carrier and sidebands are transmitted on adjacent longitudinal modes of the cavity. An important bonus of this idea is that moderate frequency noise between the laser and the cavity does not generate noise on the signal because the carrier and sidebands, which are derived from one laser, jitter in exactly the same pattern. Since the FM technique is detecting the difference between the two sidebands, there is no noise introduced by a moderately noisy laser. This “noise immune” feature led to the rather long acronym of NICE-OHMS, which, again, stands for noise-immune cavity-enhanced optical heterodyne molecular spectroscopy. I’ll use the term NICE-OHMS interchangeably with cavity enhanced FM spectroscopy. They mean the same thing.
Now let’s briefly look at the experimental setup.
*J. Ye, L. S. Ma, and J. L. Hall,
Opt. Lett. 21, 1000 (1996).

9. Experimental Design 541 MHz PID1 Laser OI PID 4 PID2 PID3 4 MHz
Electrical
541 MHz
PID1
Optical
Lock-in
NICE-OHMS
signal
BD2
Linewidth 1 x 10-7 cm-1
Laser
PD2 BS
High-finesse cavity OI
l/4
BD1
PD1
AOM1 BS
AOM2
PID 4
PBS
l/2
PID2
EOM1 ML
AOM3
Reference etalon
PID3
4 MHz
EOM2 BS
PBS2
EOM3 BS
Wavemeter
l/2
PBS1

10. Empty Cavity Parameters
Free spectral range (FSR)
541 MHz
Finesse (F)
20000
Cavity FWHM
27 kHz
Cavity transmission
15%
Effective path length
3.5 km
Here I’ve listed the most important parameters corresponding to our cavity.

11. Balanced detection reduces residual amplitude modulation
Imperfections in EOM
Accidental etalons
 Residual amplitude modulation (RAM)  background signal
Balanced
detector
Scans over an NO line
I1-I2 2
ND filter disc BS
Beam 1 1
Beam 2
In the ideal world the laser beam coming out from the electro-optic modulator should be purely frequency modulated. However, in reality, due to imperfections in the electro-optic crystal, there is also a weaker amplitude modulation. This residual amplitude modulation (RAM) appears as a signal at the modulation frequency in the absence of sample absorption. Thus, RAM results in a background contribution in the demodulated signal and therefore limits the sensitivity. In addition, as clearly visible in the upper diagram, the intensity of the background signal varies with laser frequency. In order to suppress this background interference we recently implemented a balanced detector to our setup. A fraction of the laser intensity is split off by a beam splitter and forms a reference beam, while the remaining light goes through the cavity just like previously. The output signal of the detector is now the difference between the photocurrents produced at detector 1 and 2. If the detector is carefully balanced we obtain a common mode rejection ratio of about 25 dB, and as you can see in the two diagrams, both the DC-level as well as the background slope is significantly reduced.
Now let’s take a look at some spectroscopic results from two stable molecules.
Accidental etalon
Requirements for efficient suppression of RAM:
Equal amplitudes at the two detectors (balanced)
The two signals must be in phase

12. Calibration measurement in C2H2
Transition: P(11) in the (11 + 33) band
T = 296 K
P = 77 mTorr
Cavity-enhanced
direct absorption
p = 1.80(7)10-5 cm‑1torr‑1
at 296 K
NICE-OHMS
= 210-11 cm-1Hz-1/2
= 610-13 cm-1Hz-1/2
First, we studied an overtone of acetylene. Here is the P(11) transition in the 1 nu1 + 3 nu3 band. The pressure of acetylene is 77 mTorr, and you can see this is a fairly weak line from it’s literature absorption coefficient of 10^ -5 per cm per Torr. We can observe both the direct absorption signal, which is the simple cavity-enhanced signal, and also the NICE-OHMS signal, which adds frequency modulation. It’s clear that the signal-to-noise is substantially increased in the NICE-OHMS signal. From the observed signal to noise we find our minimum detectable absorption coefficient is 2 x per cm per root Hz.

13. Spectrum of NO(7n), 2P1/2 - 2P1/2 sub-band
Line positions predicted
from C. Amiot and
J. Verges, J. Mol. Spec.
81, 424 (1980)
The two strongest line in the P-branch of the experimental spectrum (which are here truncated and thus they are actually even stronger than they appear in this figure) are water lines. To avoid, or at least significantly reduce, the water interference, we intend to repeat these measurements in a weak flow of NO (the present data was recorded in a static cell).

14. R(7.5) in the 2P1/2 - 2P1/2 sub-band
NO(7  0) spectrum
R(7.5) in the 2P1/2 - 2P1/2 sub-band
Cavity-enhanced
direct absorption
T = 296 K
P = 67 Torr
Line Intensity
Sensitivity ~ 1 ppt
NICE-OHMS
(parts per ten)
S = 1.24(37) x cm/molecule
 = 5.2 x cm2/molecule
This viewgraph shows a blow-up of the R(7.5) transition. As you can see, the cavity-enhanced direct absorption signal is now almost lost in the noise, but the NICE-OHMS signal still has exceptional signal to noise, and the expected lineshape is recovered in a fit to the data. The fit was based on a pure Doppler-broadened line shape.
So far we have analyzed three lines of NO quantitatively.

15. Fitting Intensity Data
Constants
F(m) = 1 + am + bm2
Herman-Wallis factor
Boltzmann
fraction
Honl-
London
factor ~
vibrational transition
dipole moment
Line intensity
(cm/molecule)
|m70| = 3.09(47) x 10-6 Debye
a = (26)
b = (45)

16. Extracting the Dipole Moment Function
(r - re) = M0 + M1(r-re) + M2(r-re)2 + M3(r-re)3 +…
 = 0
 = 7
 = 21
DW = M. Drabbels and A. M. Wodtke, J. Chem. Phys. 106, 3024 (1997).
LBP = S. R. Langhoff, C. W. Bauschlicher, and H. Partridge, Chem.
Phys. Lett. 223, 416 (1994).

17. Extracting the Dipole Moment Function
(r - re) = M0 + M1(r-re) + M2(r-re)2 + M3(r-re)3 +…

18. Monitor complete time evolution of reactant or product
Transient NICE-OHMS
NICE-OHMS is a cw technique
Monitor complete time evolution of reactant or product
Probe
laser
Demod.
EOM
Pump laser dissociates precursor
Probe laser tuned to an absorption
line of the species to study
I should point out that unlike cavity ringdown spectroscopy, NICE-OHMS is a cw technique, which will allow us to obtain the full time course of a reaction in one experiment. Here we see a principle experimental scheme for transient NICE-OHMS measurements. The general scheme is the same, except that a photolysis laser will dissociate a precursor to produce a transient species that we want to probe with the NICE-OHMS technique.
Pump
laser

19. The First Transient NICE-OHMS Signal Monitored NH2 transition
Cavity-enhanced direct absorption
Monitored NH2 transition
X2B1(170  000) 3313  3422
cm-1
NICE-OHMS signal
(Single-shot signal)
PNH3=10 mTorr, T = 296 K
I will now show some very preliminary data from our first NH2 measurements. We monitored a X-state vibronic transition for detection of the NH2 radical. The upper level is located close to the excited A-state so the transition gains oscillator strength from this state. In the lower diagram, illustrating the time-resolved NICE-OHMS signal we observe a decay curve reflecting the decrease in NH2 concentration in the probe volume. In the upper diagram, showing the corresponding cavity-enhanced direct absorption signal, we can’t extract any information about the NH2 decay. There is no sign of unlocking during, or immediately after, the photolysis pulse has been fired. Now, let’s take a look at a signal recorded at a much higher pressure.

20. NH2 signals at higher pressures
Monitored NH2 transition
X2B1(170  000) 3313  3422
cm-1
PNH3=150 mTorr, T = 296 K
These curves were recorded with 150 mTorr of NH3. The NH2 concentration is now presumably 15 times higher. Again, these are preliminary results and we have not yet analyzed the data. We notice that there is a sharp spike at time zero on both curves. This spike also appears in the laser-to-cavity error signal, and indicates that the servo-loop is now put to the severe test, and it has to work much harder now to maintain lock. Still, we don’t loose lock, and the NICE-OHMS signal shows a nice decay curve. Thus, our laser-to-cavity lock loop is robust enough to perform this type of experiments. In the near future we will optimize our experiment by choosing the strongest possible transition and optimize the overlap between the pump and probe beams. Then we will study the reaction of NH2 + NO, which is a key step in thermal De-NOx chemistry. There is a spread in the literature rate coefficients of about a factor of two, and we hope the high signal to noise of our experiment will allow for an extremely good characterization of the NH2 decay, and hence the rate coefficient.

21. Summary
Laser
Phase
modulator
Demod.
NICE-OHMS
NICE-OHMS combines FM spectroscopy and cavity enhancement into a single spectrometer that provides ultrahigh sensitivity (210-11 cm-1Hz-1/2 demonstrated).
Balanced detection techniques reduce residual amplitude modulation.
We have made the first measurements of the (7  0) vibrational band of NO, and determined a new electric dipole moment function.
A transient species (NH2) has been measured for the first time using NICE-OHMS. These initial results indicate the potential for NICE-OHMS as
a powerful chemical diagnostic technique.

22. Outline
Motivation
Basic concept of cavity-enhanced frequency modulation spectroscopy (NICE-OHMS)
Experimental arrangement
Measurement of the 6th overtone of NO
Recent results and future projects
- Transient measurement of NH2
- Flame diagnostics
Summary
After discussing the motivation for this work, I will explain the basic principles of cavity-enhanced frequency modulation spectroscopy and briefly go over the experimental setup. Then I’ll discuss our first application of the technique, which was to measure the extremely weak 6th overtone spectrum of nitric oxide. Following this I will discuss recently started work on detection of a transient species. Before wrapping up with a summary I will also talk a little bit about an upcoming flame experiment.

23. Motivations for ultrasensitive spectroscopy
To probe weak transitions: Molecular spectroscopy
Overtone/combination bands can be explored
Fundamental tests: forbidden transitions, perturbations, etc.
To measure low concentrations
Trace gas monitoring
Medical diagnostics
Chemical kinetics
Flame chemistry
Example: A• + RH  AH + R (1) Rate = k1[A•][RH] 1st order in [A•]
A• + A•  products (2) Rate = k2[A•]2 2nd order in [A•] k1 k2
There are many interesting applications for ultrasensitive absorption techniques. From a spectroscopic point of view ultrasensitive detection allows us, for example, to study spectra of weak overtones and combination bands, and also to learn more about forbidden transitions, perturbations, et.c. Techniques with high sensitivity enable measurements of very low concentrations. Typical applications are: detection of trace species in gas-phase environment, atmospheric sensing, medical diagnostics based on measurement of gas emissions in exhaled human breath, and of course combustion chemistry, which is the focus of our research.
Let me illustrate how chemical kinetics benefits from high sensitivity with an example: whenever the reaction of A + RH occurs, the radical self reaction will always compete, often with a much larger rate coefficient. The second reaction is second order in A, and can be discriminated against by lowering A. High sensitivity will allow us to drastically decrease A while still having sufficient signal-to noise.

24. Division of Chemical Sciences, Geosciences, and Biosciences,
Acknowledgments
Dr. Joakim Bood and Dr. Andrew McIlroy
Mr. Paul Fugazzi
Mr. Gary Wilke
Dr. Ray Bambha
Dr. Jun Ye (JILA, University of Colorado, and NIST, Boulder)
Dr. Richard Fox (NIST, Boulder)
Let me start by thanking the many people who have contributed to the efforts in this program over the past two years, and I want to thank the Basic Energy Sciences program for financial support.
Financial Support:
Division of Chemical Sciences, Geosciences, and Biosciences,
the Office of Basic Energy Sciences of the United States Department of Energy.

25. Cavity Ringdown in Flames
Cavity ringdown provides quantitative measurements
Problems
Large time delay between on and
off-resonant measurements
Need large dynamic range to monitor intensity decay
Low frequency (1/f)
noise dominates
Background
noise
For combustion applications two of the limiting noise sources are scattering and beam steering due to thermal gradient fluctuations. This type of noise affects all wavelengths of light equally on the scale of a CRDS spectrum. What we need is a way to make the on and off resonance measurements in rapid succession, or even better, simultaneously, so that this type of noise could be subtracted exactly. Frequency modulation spectroscopy does just this.
POSSIBLE DELETE
Differential measurement
Monitor E field, not intensity
Detect at high frequency
Thoman Jr, J.W., McIlroy A., J. Phys. Chem. A 104, 4953 (2000)

26. First test of Transient NICE-OHMS: Detection of NH2
Flash photolysis using Excimer laser (193 nm):
NH3  H + NH2
Time-resolved FTIR spectrum
NH2 A  X
current mirrors
The first transient we want to detect is NH2. I’ve shown a portion of the X to A spectrum obtained via time-resolved FTIR in this plot (measured by David Osborn). Our current cavity mirrors cover this range, where there are many transitions.
POSSIBLE DELETE

27. Challenges of Transient NICE-OHMS
All cavity fringes will be shifted due to change in refractive index upon photodissociation.
Instantaneous (sub-ps) number density increase as NH3  H + NH2
Slower temperature rise as excess energy equilibrates with bath gas Temperature rise (at constant pressure) lowers density
FSR
before photolysis
after photolysis
There are several challenges of implimenting NICE-OHMS on transient species. The creation of new molecules will cause the optical pathlength inside the cell to change abruptly, and consequently all the cavity fringes will move to a new position. The challenge is that the laser, which is locked to the cavity, must follow this change in order for the experiment to continue.
POSSIBLE DELETE
DnP = -800 Hz
DnT = 13 kHz
0.5 mTorr NH3, 193 nm
1.6 x 1011 molecules/cm3 NH2 

28. Experimental Design NICE-OHMS signal Laser-to-cavity lock D = 540 MHz
Function
Generator 1
D = 540 MHz
Phase trim. BP
To laser’s
Ref. cavity
PD4
Freq.
servo To
EOM3
l/2
Etalon (FSR = 300 MHz) LP
To AOM
Driver (VCO)
PD1
EOM 1 Z
EOM 2
FSR tracking
CW 532 Nd:YAG
3 PZTs
EOM 3
I can discuss the experimental details later at our poster if anyone is interested, but the key features are the cw Ti Sapphire single mode laser, the electro-optic modulator (EOM1) that frequency modulates the light at the free spectral range frequency, and the high finesse cavity where the sample is located. The method requires that the laser frequency is locked to a longitudinal cavity mode. We use the Pound-Drever-Hall stabilization scheme to accomplish this lock. Electro-optic modulator 2 and 3, as well as the electronics outlined in the yellow box are all involved in the locking system. When the laser frequency are to be scanned we scan the cavity length by moving the entrance mirror using three piezo-electric actuators. Because the laser is locked to the cavity with a servo loop the laser frequency will follow the cavity. With the current PZTs we can scan the laser about 6 GHz. Now, changing the cavity length leads to a change in the cavity’s free spectral range. Since the noise-immune property relies on a perfect match between the modulation frequency and the free spectral range, the modulation frequency has to be continuously adjusted during the scan. Another servo loop, shown in the blue box, takes care of this. I don’t have time to explain how the servo loops work, but I’ll be happy to talk about it at the poster.
Remember that the end goal is to look at kinetics of free radical reactions, and the cell was designed to allow photolysis of a precursor molecule perpendicular to the probe axis. However, to get the experiment running we looked at two stable molecules.
PD3
Lock-in
AOM driver
AOM
l/4 BS
error CW
Ti:Sapphire
servo
controller
Dither
PD2
Intensity
servo
Opt. Isol.
Phase trimmer
AOM
Function gen. 2, d = 4 MHz
Function gen.

29. Challenges of NICE-OHMS
for flame diagnostics
Laser-to-cavity locking is a big issue
Heat from the flame will introduce thermal motion to the flame chamber
The cavity mirror mounts have to be decoupled from the motion
of the flame chamber  external stabilization of the mirror mounts is needed
Laser lock must withstand refractive index changes
Mirrors of lower reflectivity and cavity locked to laser (instead of vice versa)
Cavity twice as long as the previously used cavity
Sidebands have to be lined up with cavity modes located
two modes apart from the central mode
To implement NICE-OHMS for measurements in flat low-pressure flames will be really challenging. The biggest difficulty will most likely be the thermal motion of the flame chamber due to the heat generated by the flame. Currently we are designing an experimental setup where an invar rod will be used to stabilize the cavity mirrors.

30. Low-pressure flame experiment
Mirror mount
Bellow
Mirror mount
Here you can see our plan for a flame experiment. The long blue cylinder is a used invar rod from a Coherent 699 ring laser. Currently parts are being machined. The idea is that the two mirror mounts should be very stable thanks to the low thermal expansion of the invar rod. Unfortunately the mirror mounts cannot be totally decoupled from the flame chamber, because we need to have vacuum inside the entire cavity. In order to keep any flame chamber vibrations away from the mirror mounts we will use two welded bellows between the flame chamber and each mirror mount.
Invar rod

31. FM Spectroscopy Applications
FM Spectroscopy demonstrated for detection of stable molecules
Bjorklund, G. C., Opt. Lett. 5, 15 (1980)
Gas-phase kinetics using time-resolved FM spectroscopy
North et al., Int. J. Chem. Kinet. 29, 127 (1997)
Quantitative concentration measurements in shock tube kinetic experiments
Votsmeier et al., Int. J. Chem. Kinet. 31, 323 (1999)
Votsmeier et al., Int. J. Chem. Kinet. 31, 445 (1999)
Friedrichs et al., J. Chem. Phys. 4, 5778 (2002)
Deppe et al., Ber. Bunsenges. Phys. Chem. 102, 1474 (1998)
Friedrichs and Wagner, Z. Phys. Chem. 214, 1723 (2000)
Chemical kinetics using flash photolysis/CW FM spectroscopy
Pilgrim et al., J. Phys. Chem. A 101, 1873 (1997)
The FM technique was first introduced by Bjorklund for the detection of stable molecules in the early eighties. Since the pioneering work by Bjorklund in the early eighties, it took a while until the method was applied for chemical kinetics measurements. Greg Hall’s group at Brookhaven made the first demonstration of time-resolved chemical kinetics measurements using FM spectroscopy. More recently, a number of excellent papers on FM spectroscopy in shock tubes have been published by Professor Hanson’s group at Stanford and Professor Wagner’s group in Goettingen. Craig Taatjes’ group at Sandia has applied Infrared FM spectroscopy to study combustion kinetics. Particularly, the production of the HO2 radical in reactions between alkyl radicals and molecular oxygen has been extensively investigated.
Flame measurements using Intra-Cavity Laser Absorption Spectroscopy
Cheskis, S., J. Chem. Phys. 102, 1851 (1995)

32. Vibrational transition dipole moment for various overtones
We can compare the transition dipole moment for this overtone, shown as the black data point, with the other overtones available in the literature. While a linear fit to the lowest three data points would be reasonable, there is significant curvature in the plot due to anharmonicity at higher vibrational levels. We will use this information in the future to extract the electric dipole moment function of NO.

33. Basic Principle and Setup for FM spectroscopy
c-m
c-m c c
c+m c
c+m
Laser
EOM
Sample PD
RF Source
Mixer
RF amp.
Phase shifter
Signal
Very briefly, frequency modulation, or FM spectroscopy, works by frequency moldulating a narrowband laser beam, in our case using an electro-optic modulator, at a high frequency, denoted by omega m, which is typically hundreds of MHz. This modulation of the input light, called the carrier, puts sidebands on the laser at the frequencies omega c plus omega m and omega c minus omega m. If there are no absorbing molecules in the cell, each of the two sidebands forms a beat signal with the carrier and the two beat signals are exactly equal in amplitude and 180 degrees out of phase, so that they cancel and, ideally, no RF amplitude modulation is observed. Now imagine there is a molecular absorption centered on the right sideband. This sideband will now be slightly attenuated. This leads to imperfect cancellation of the two beat signals and, thus, to an amplitude modulation of the laser beam. When this signal is demodulated at frequency omega m, we obtain the difference in absorption at the left versus the right sideband. This is how FM spectroscopy allows on and off resonance measurements to be made simultaneously. The advantage is that we are only subject to the noise near the frequency omega m, and this noise is typically just the shot noise.
(Because nothing is ever free in this world, there is a penalty to pay when using FM spectroscopy. The minimum detectable absorption coefficient is now larger by about a factor of four due to the fact that the signal is contained in only one sideband, but the shot noise comes from all three components of the light. But generally this price is well worth paying because the total noise is now dominated by the shot noise, not the technical noise, which is many orders of magnitude higher.)
So the challenge is to combine a high finesse cavity with FM spectroscopy.
Low-pass
filter
Simultaneous comparison between
on-resonant and off-resonant cases