U.S. patent application number 09/759729 was filed with the patent office on 2004-04-08 for cavity ringdown spectroscopy system using differential heterodyne detection.
Invention is credited to Hall, John L., Ye, Jun.
Application Number | 20040065816 09/759729 |
Document ID | / |
Family ID | 32045825 |
Filed Date | 2004-04-08 |
United States Patent
Application |
20040065816 |
Kind Code |
A1 |
Ye, Jun ; et al. |
April 8, 2004 |
CAVITY RINGDOWN SPECTROSCOPY SYSTEM USING DIFFERENTIAL HETERODYNE
DETECTION
Abstract
An ac technique for cavity ringdown spectroscopy permits
1.times.10.sup.-10 absorption sensitivity with microwatt light
power. Two cavity modes are provided temporally out of phase such
that when one mode is decaying, the other mode is rising. When one
of the modes probes intra-cavity absorption of a sample gas,
heterodyne detection between the two modes reveals dynamic time
constants associated with the cavity and the cavity plus
intra-cavity absorption. The system and method provides a quick
comparison between on-resonance and off-resonance modes and enables
sensitivities that approach the shot-noise limit.
Inventors: |
Ye, Jun; (Louisville,
CO) ; Hall, John L.; (Boulder, CO) |
Correspondence
Address: |
Charles E. Rohrer, P.C
P.O. Box 20067
Boulder
CO
80308
US
|
Family ID: |
32045825 |
Appl. No.: |
09/759729 |
Filed: |
January 12, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60175956 |
Jan 13, 2000 |
|
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|
60191574 |
Mar 23, 2000 |
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Current U.S.
Class: |
250/227.18 |
Current CPC
Class: |
G01N 21/39 20130101;
G01J 3/42 20130101 |
Class at
Publication: |
250/227.18 |
International
Class: |
G01J 004/00 |
Claims
What is claimed is:
1. A cavity ringdown system capable of providing optical heterodyne
detection of a ringdown signal including: an optical-signal
generator capable of generating an optical beam comprising a
plurality of modes, the modes being chopped out of phase with
respect to a chopping cycle such that no more than one of the
chopped modes is dominant in the output, an optical resonator
optically coupled to the signal generator capable of receiving the
optical beam, the resonator being capable of containing an
intra-cavity absorber onto which at least one of the modes may be
tuned, and a heterodyne detector coupled to the optical resonator,
the heterodyne detector capable of receiving a plurality of the
modes and demodulating a heterodyne-beat waveform between the modes
to produce a heterodyne-beat amplitude, the heterodyne detector
generating a difference signal of the heterodyne-beat amplitude
between adjacent chopping cycles, which contains the information of
intra-cavity absorption.
2. The cavity ringdown system recited in claim 1 wherein the
optical-signal generator includes an intensity-stabilized
continuous-wave laser.
3. The cavity ringdown system recited in claim 1 wherein the
optical-signal generator includes a tunable cw laser.
4. The cavity ringdown system recited in claim 1 wherein the
optical-signal generator includes an electro-optic modulator
capable of providing RF sidebands to the optical beam.
5. The cavity ringdown system recited in claim 1 wherein the
optical-signal generator includes a plurality of acousto-optic
modulators capable of splitting the beam into a plurality of modes
having a relative frequency offset.
6. The cavity ringdown system recited in claim 1 wherein the
optical resonator is characterized by a free-spectral range and the
optical-signal generator is adapted to generate modes having a
frequency offset that is an integer multiple of the free-spectral
range.
7. The cavity ringdown system recited in claim 1 wherein the
optical-signal generator includes a chopping system capable of
chopping the modes out of phase.
8. The cavity ringdown system recited in claim 7 wherein the
chopping system includes a plurality of acousto-optic
modulators.
9. The cavity ringdown system recited in claim 1 further
comprising: a pre-fixed cavity resonance photodetector, a polarized
beam splitter and a quarter-wave plate capable of steering the
entire reflected optical beam from the optical resonator onto the
pre-fixed photodetector, said photodetector optically coupled to
the beam splitter, the photodetector capable of receiving the
reflected optical beam and converting the received beam to an
electrical signal, and a laser-cavity locking loop electrically
coupled to the photophotodetector, the laser-cavity locking loop
capable of receiving the electrical signal and generating a
feedback signal to maintain a lock between the optical-signal
generator and the optical resonator.
10. The cavity ringdown system recited in claim 9 wherein the lock
between the optical-signal generator and the optical resonator is
maintained using the Pound-Drever-Hall technique.
11. The cavity ringdown system recited in claim 9 wherein the
optical-signal generator includes an electro-optic modulator
capable of providing RF sidebands to the optical beam.
12. The cavity ringdown system recited in claim 9 wherein the
optical-signal generator generates an off-resonance continuous mode
that is processed by the laser-cavity locking loop to maintain a
lock between the optical-signal generator and the optical
resonator.
13. The cavity ringdown system recited in claim 12 wherein the
heterodyne photodetector is adapted to filter out contributions of
the continuous mode to the heterodyne-beat waveform.
14. The cavity ringdown system recited in claim 1 wherein the
optical resonator is characterized by a decay time relative to an
empty cavity, and the optical-signal generator chops the modes with
respect to a chopping cycle suitable for the decay time.
15. The cavity ringdown system recited in claim 1 wherein the
optical resonator is a high-finesse cavity.
16. The cavity ringdown system recited in claim 1 wherein the
optical resonator is adapted to contain an intra-cavity sample
gas.
17. The cavity ringdown system recited in claim 1 wherein the
cavity reflection photodetector includes a p-i-n diode in a
resonant matching circuit.
18. The cavity ringdown system recited in claim 1 wherein the
heterodyne photodetector includes a suitable detector, such as an
avalanche photodiode, resonant matched p-i-n photodiode or
photomultiplier.
19. The cavity ringdown system recited in claim 1 wherein the
heterodyne photodetection system includes an RF demodulation
component.
20. The cavity ringdown system recited in claim 1 wherein the
optical signal generator includes an adjustable power system
capable of being responsive to increased intra-cavity absorption in
the optical resonator for increasing power of the optical beam.
21. The cavity ringdown system recited in claim 1 wherein the
optical signal generator includes an adjustable chopping system
capable of being responsive to increased intra-cavity absorption in
the optical resonator by decreasing duration of the chopping
cycle.
22. A cavity ringdown system capable of providing optical
heterodyne detection of a ringdown signal including: an optical
source capable of generating an optical beam with a plurality of
modes having a predetermined relative frequency offset between the
modes, a high-finesse optical cavity capable of receiving the
modes, a chopping system for chopping the modes out of phase such
that only one dominant mode is coupled into the cavity at any time,
and a heterodyne detector optically coupled to the cavity capable
of Il detecting an optical signal coupled out of the cavity, the
optical signal including the modes, which modes overlap to produce
a heterodyne-beat waveform, the heterodyne detector including: a
demodulation unit capable of demodulating the waveform to produce a
heterodyne-beat amplitude, and a difference-signal analyzer coupled
to the demodulator, the difference-signal analyzer capable of
generating a difference signal from adjacent chopping cycles of the
heterodyne-beat amplitude.
23. The cavity ringdown system recited in claim 22 wherein the
optical source includes an intensity-stabilized continuous-wave
laser.
24. The cavity ringdown system recited in claim 22 wherein the
optical source includes a tunable cw laser.
25. The cavity ringdown system recited in claim 22 wherein the
optical source includes an electro-optic modulator capable of
providing RF sidebands to the optical beam.
26. The cavity ringdown system recited in claim 22 wherein the
optical source includes a plurality of acousto-optic modulator s
capable of splitting the beam into a plurality of modes having a
relative frequency offset.
27. The cavity ringdown system recited in claim 22 wherein the
optical cavity is characterized by a free-spectral range and the
optical source is adapted to generate modes having frequency
offsets that are related to the free-spectral range.
28. The cavity ringdown system recited in claim 22 wherein the
chopping system includes a plurality of acousto-optic
modulators.
29. The cavity ringdown system recited in claim 22 further
comprising: a cavity resonance photodetector, a polarized beam
splitter and a quarter-wave plate capable of steering the entire
reflected optical beam from the optical resonator onto the cavity
resonance photodetector, said photodetector optically coupled to
the beam splitter, the photodetector capable of receiving the
reflected optical beam and converting the received beam to an
electrical signal, and a laser-cavity locking loop electrically
coupled to the photodetector, the laser-cavity locking loop capable
of receiving the electrical signal and generating a feedback signal
to maintain a lock between the optical-signal generator and the
optical resonator.
30. The cavity ringdown system recited in claim 29 wherein the lock
between the optical source and the optical cavity is maintained
using the Pound-Drever-Hall technique.
31. The cavity ringdown system recited in claim 29 wherein the
optical source includes an electro-optic modulator capable of
providing RF sidebands to the optical beam.
32. The cavity ringdown system recited in claim 29 wherein the
optical source generates an additional off-resonance continuous
mode that is processed by the laser-cavity locking loop to maintain
a lock between the optical source and the optical cavity.
33. The cavity ringdown system recited in claim 32 wherein the
heterodyne detector is adapted to filter out contributions of the
continuous mode to the heterodyne-beat waveform.
34. The cavity ringdown system recited in claim 22 wherein the
chopping system chops the modes with respect to a chopping cycle
that is suitable for the decay time characterizing the optical
cavity when empty.
35. The cavity ringdown system recited in claim 22 wherein the
optical cavity is adapted to contain a sample gas.
36. The cavity ringdown system recited in claim 22 wherein the
cavity reflection photodetector includes a p-i-n diode in a
resonant matching circuit.
37. The cavity ringdown system recited in claim 22 wherein the
heterodyne photodetector includes a suitable detector, such as an
photodiode, resonant matched p-i-n photodiode or
photomultiplier.
38. The cavity ringdown system recited in claim 22 wherein the
heterodyne photodetection system includes an RF demodulation
component.
39. The cavity ringdown system recited in claim 22 wherein the
optical source includes an adjustable power system capable of being
responsive to increased intra-cavity absorption in the optical
cavity for increasing power of the optical beam.
40. The cavity ringdown system recited in claim 22 wherein the
chopping system is an adjustable chopping system capable of being
responsive to increased intra-cavity absorption in the optical
cavity by decreasing the duration of the chopping cycle.
41. A method of cavity ringdown spectroscopy including: providing
for generation of an optical beam, providing for generation of a
plurality of modes from the optical beam, the modes having a
predetermined relative frequency offset, providing for out-of-phase
chopping of the modes with respect to a chopping cycle such that
the optical beam consists of only one dominant mode when incident
upon an optical resonant cavity, providing for resonating of the
modes in the cavity, and providing for heterodyne detection of an
optical signal coupled out of the cavity, the optical signal
including the modes, which modes overlap to produce a
heterodyne-beat waveform, the heterodyne detection including:
providing for demodulation of the waveform to produce a
heterodyne-beat amplitude, and providing for generation of a
difference signal from adjacent chopping cycles of the
heterodyne-beat amplitude.
42. The cavity ringdown spectroscopy method recited in claim 41
wherein providing for generation of an optical beam includes
generating an intensity-stabilized continuous-wave laser beam.
43. The cavity ringdown spectroscopy method recited in claim 41
wherein providing for generation of an optical beam includes
generation of an optical beam by a cw tunable laser.
44. The cavity ringdown spectroscopy method recited in claim 41
wherein providing for generation of an optical beam includes
electro-optic modulation of the beam for providing RF sidebands to
the optical beam.
45. The cavity ringdown spectroscopy method recited in claim 41
wherein providing for generation of a plurality of modes includes
acousto-optic modulation of the beam into a plurality of modes
having a relative frequency offset.
46. The cavity ringdown spectroscopy method recited in claim 41
wherein providing for generation of a plurality of modes includes
providing a frequency offset to the modes that is related to the
free-spectral range that characterizes the cavity.
47. The cavity ringdown spectroscopy method recited in claim 41
further comprising: providing for coupling the reflected optical
beam from the cavity to a transducer for providing an electrical
signal in response to the reflected beam, and providing for locking
between the optical-beam generation and the mode resonance.
48. The cavity ringdown spectroscopy method recited in claim 47
wherein providing for locking is performed using the
Pound-Drever-Hall technique.
49. The cavity ringdown spectroscopy method recited in claim 47
wherein providing for generation of a plurality of modes includes
generating an off-resonance continuous mode that is processed by
the locking step.
50. The cavity ringdown spectroscopy method recited in claim 49
wherein the providing for heterodyne detection is adapted to filter
out contributions of the continuous mode to the heterodyne-beat
waveform.
51. The cavity ringdown spectroscopy method recited in claim 41
wherein the chopping cycle providing for out-of-phase chopping of
the modes is suitable for the cavity decay time.
52. The cavity ringdown spectroscopy method recited in claim 41
wherein providing for resonating of the modes includes coupling the
beam into a high-finesse cavity.
53. The cavity ringdown spectroscopy method recited in claim 41
wherein providing for resonating of the modes includes providing an
intra-cavity sample gas having an absorption line to which at east
one of the modes is tuned.
54. The cavity ringdown spectroscopy method recited in claim 41
wherein providing for heterodyne detection includes RF
demodulation.
55. The cavity ringdown spectroscopy method recited in claim 41
wherein providing for generation of the beam includes increasing
power to the beam in response to increased intra-cavity absorption
in the cavity.
56. The cavity ringdown spectroscopy method recited in claim 41
wherein providing for out-of-phase chopping of the modes includes
decreasing duration of the chopping cycle in response to increased
intra-cavity absorption in the cavity.
Description
[0001] This application claims the benefit of U.S. Provisional
Applications No. 60/175,956 filed Jan. 13, 2000 and No. 60/191,574
filed Mar. 23, 2000.
FIELD OF THE INVENTION
[0002] This invention relates to the field of absorption
spectroscopy and, in particular, to a cavity-ringdown system for
the determination of ringdown rates by optical heterodyne
detection.
BACKGROUND OF THE INVENTION
[0003] Traditional spectroscopic methods are limited in sensitivity
to approximately one part per ten thousand (1:10.sup.4) to one part
per hundred thousand (1:10.sup.5). The sensitivity limitation
arises from instabilities in light-source intensity translated into
noise in the absorption signal.
[0004] The use of optical resonators for enhancing absorption
contrast is described by Kastler ("Atomes l'Intrieur d'un
Interfromtre Perot-Fabry," Appl. Opt. 1, 1 (1962) pp 17-24) and
implemented by Cerez et, al. ("He--Ne Lasers Stabilized by
Saturated Absorption in Iodine at 612 nm," IEEE Trans. Instrum.
& Meas. 29, 4 (1980) pp 352-354) and Ma et. al. ("Optical
Heterodyne Spectroscopy Enhanced by an External Optical Cavity:
Toward Improved Working Standards," IEEE J. Quan. Electron. 26, 11
(1990) pp 2006-2012). Cavity Ring-Down Spectroscopy (CRDS), first
described by O'Keefe and Deacon in "Cavity ring-down optical
spectrometer for absorption measurements using pulsed laser
sources," in Rev. Sci. Instrum. 59, 12 (1988): pp 2544-2551, allows
absorption sensitivities of 1.times.10.sup.-7. The applications of
CRDS include measurement of ultra-slow reflector velocities,
atmospheric sensing, detection of trace species in gasphase
environments, absolute determination of absorption-band strength
and/or species concentration, analysis of combustion and plasma
dynamics, study of chemical kinetics (such as radical reactions and
internal vibration redistribution), and characterization of optical
cavities and high-reflectivity mirror coatings. Recently, CRDS has
been applied to surface and condensed matter (Pipino,
"Ultrasensitive Surface Spectroscopy with a Miniature Optical
Resonator," Phys. Rev. Lett. 83, 15 (Oct. 11, 1999) pp 3093-3096),
thus permitting a wide range of novel fundamental
investigations.
[0005] In a CRDS system, a sample (absorbing material) is placed in
a high-finesse stable optical resonator or ringdown cavity. The
light completes many roundtrips through the intra-cavity absorber,
effectively increasing the interaction length by
2.multidot.Finesse/.pi.. Light admitted into the ringdown cavity
circulates back and forth multiple times setting up standing waves
having periodic spatial variations. Light exiting the ringdown
cavity is proportional to the intra-cavity light intensity.
[0006] The radiant energy stored in the ringdown cavity decreases
in time (rings down). For an empty cavity, the stored energy
follows an exponential decay characterized by a ringdown rate that
depends only on the reflectivity of the mirrors, the separation
between the mirrors and the speed of light in the cavity. If a
sample is placed in the resonator, the ringdown is accelerated.
Information about intra-cavity gas absorption is obtained by
measuring the change of decay associated with the cavity field. An
unknown absorption coefficient is compared to known mirror losses.
The mirror losses may have a magnitude similar to the unknown
absorption coefficient in order to reduce background detection,
thus enhancing contrast between the unknown absorption coefficient
and the background (i.e., mirror losses). An absorption spectrum
for the sample is obtained by plotting the reciprocal of the
ringdown time X or the decay constant 1/.tau. versus the wavelength
.lambda. of the incident light.
[0007] U.S. Pat. No. 5,528,040 describes a CRDS system in which the
decay rate of the ringdown cavity cell is calculated from a signal
produced by a photodetector that is responsive to radiation
resonated by the cell. The calculated decay rate is used to
determine the level of trace species in the sample gas. The method
measures cavity ringdown using a continuous wave laser. The cavity
transmitted power is used to monitor the intra-cavity absorption.
Lacking an efficient differential comparison mechanism, intensity
noise of the diode laser used in the method places substantial
limit on the achievable absorption sensitivity.
[0008] U.S. Pat. Nos. 5,986,768 and 5,835,231 describe elegant
setups of high finesse optical resonators that permit measurement
of absorption using evanescent waves to provide spatial resolution.
However, the technique employed is the commonly used single beam
cavity ringdown.
[0009] In CRDS, a pulsed operation produces an abrupt termination
of the cavity input field, which permits a measurement of the
exponential decay curve of the cavity-transmitted power. Intensity
fluctuations of the incident light are not related to the ringdown
rate in the ringdown cavity and thus, they do not directly affect
the CRDS measurement. Thus, this cavity ringdown method avoids the
noise in the light source. However, residual fluctuations in the
apparent cavity loss prevent this method from achieving the
performance suggested by fundamental noise limits. For example, if
CRDS were only limited by shot-noise inherent in any light beam due
to the quantum nature of the photons constituting the light beam,
the achievable sensitivity would be in the range of 10.sup.-14
cm.sup.-1 Hz.sup.-1/2.
[0010] Various improvements to CRDS are well known. For example,
U.S. Pat. No. 5,528,040 describes a laser-diode source for CRDS.
The diode laser is optically locked using controlled optical
feedback from a reference cavity to improve the coupling of light
into the ringdown cavity. U.S. Pat. No. 6,084,682 describes a CRDS
system that uses separate sampling and locking light beams. The
sampling and locking beams are provided with different wavelengths.
U.S. Pat. No. 5,912,740 describes a ring resonant cavity that
eliminates feedback into the light source. The absence of feedback
to the light source leads to reduced frequency fluctuations,
improved light-cavity coupling, reduced baseline noise, and
increased absolute sensitivity. U.S. Pat. No. 5,815,277 describes
an acousto-optic modulator used to couple light into a CRDS
resonant cavity. U.S. Pat. Nos. 6,097,555 and 5,973,864 describe
utilizing Brewster's angle prism retro-reflectors.
[0011] There are two basic limitations to conventional CRDS. One of
these limitations is due to the DC nature of CRDS. For example, two
decay-time measurements are made, one for an empty cavity and the
other for a cavity containing a sample. The difference between the
two measurements contains useful information. However, when there
is a large time difference between the two measurements, slow drift
and various noise factors contaminate the data.
[0012] Another limitation of CRDS is the requirement that a CRDS
detector have a large dynamic range to record data. Typically, a
lower portion of the exponential CRDS decay curve is masked by
instrument noise because insufficient power is available for the
decay curve to be distinguishable from electronic noise.
[0013] Accurate measurements of small signal changes with a varying
background signal can be achieved with a precise signal-extraction
method and averaging. Modulation techniques are typically employed
to distinguish decay-time measurements from background signals so
that any drifts and noise in the background can be removed. In
"Ultrasensitive detections in atomic and molecular physics:
demonstration in molecular overtone spectroscopy," J. Opt. Soc. Am.
B 15, 1, pp 6-15 (1998), which is hereby incorporated by reference,
a frequency-modulation technique enables shot noise limited
absorption sensitivity in sub-Doppler resolution. On-resonance and
off-resonance information are compared at a radio-frequency (RF)
rate, which is located away from the laser-intensity noise
spectrum.
[0014] Ye et al. ("Ultrasensitive Detection in Atomic and Molecular
Physics: Demonstration in Molecular Overtone Spectroscopy", Journal
of the Optical Society of America B, 15, 1, (January 1998), pp.
6-15) teaches a heterodyne technique building on spectroscopic
techniques employing frequency modulation (FM) detection.
[0015] Levenson et. al. ("Optical heterodyne detection in cavity
ring-down spectroscopy," Chem. Phys. Lett. 290 (1998) pp 335-340)
describes a heterodyne technique used to superimpose a large
local-oscillator field onto a decay field so that the resultant
beat frequency is only light-noise limited.
[0016] U.S. Pat. No. 6,094,267 describes an optical heterodyne
detection technique that improves the detection sensitivity of a
CRDS system such that the sensitivity approaches the shot-noise
limit. A local-oscillator signal and a signal wave are coupled into
a ringdown cavity containing a sample. The local-oscillator signal
and the signal wave have different frequencies. To perform the
ring-down measurement, the signal wave is interrupted, such as by
chopping the wave or changing the signal frequency. An
exponentially decaying ringdown signal output from the cavity is
combined with the uninterrupted local-oscillator signal to produce
a heterodyne beat frequency. However, this technique does not offer
the possibility of a quick comparison of on-resonance and
off-resonance information, which is key to achieve Quantum noise
limited sensitivity. Also, this technique still requires recording
the entire ringdown decay curve, which needs a substantial dynamic
range to record accurately the decay curve.
[0017] Unfortunately, the above adaptations are not well designed
to measure exponentially decaying waveforms. In particular, these
techniques do not work well for signal detection in CRDS. It is
desirable to employ a single technique that simultaneously
addresses the two basic limitations of CRDS.
[0018] It is also desirable to provide a method that approaches the
fundamental quantum-noise limit in cavity-enhanced linear
spectroscopy.
SUMMARY OF THE INVENTION
[0019] An object of the present invention is to provide a CRDS
system that is substantially immune to slow drift and various noise
factors that typically contaminate data, and therefore enable a
true quantum noise limited detection sensitivity.
[0020] Another object of the invention is to provide a CRDS system
that reduces the dynamic range of a CRDS detector required to
accurately record data.
[0021] The present invention compares two slightly different time
constants. One time constant is associated with an empty cavity.
The other time constant is associated with cavity loss plus an
additional loss. Using cavity filtering and an intensity-stabilized
laser, it is possible to approach (within a of four) the
fundamental quantum-noise limit in cavity-enhanced linear
spectroscopy.
[0022] The invention uses heterodyne detection of two modes having
a relative frequency offset that are chopped out of phase and
coupled into a resonating cavity. One of the modes may be tuned to
an absorption line of a sample gas in the cavity. In a first
half-cycle, a heterodyne-beat signal results from one mode that is
coupled into the cavity (and thus, rising exponentially in
intensity) beating against a second mode that has been switched off
(and thus, is diminishing exponentially in intensity). In a second
half-cycle, the first mode is switched off and the second mode is
switched on. Absorption of one of the modes by the sample gas is
easily detected by observing the difference between adjacent
half-cycles of the heterodyne beat signal.
BRIEF DESCRIPTION OF THE DRAWINGS
[0023] FIG. 1 shows one embodiment for a chopped heterodyne CRDS
system. Two acousto-optic modulators provide a frequency offset
between two modes that are chopped out of phase such that at any
time, only one mode enters a cavity containing a sample gas. The
laser can be locked onto the cavity, since there is always one mode
entering the cavity. A heterodyne beat between the two modes at a
cavity output is demodulated with respect to the known frequency
offset to produce a decay signal. One of the two modes interacts
with the intra-cavity molecules while the other one is tuned off
resonance.
[0024] FIG. 2A shows a demodulated ringdown curve for a first mode
in an empty cavity.
[0025] FIG. 2B shows a demodulated ringdown curve for a second mode
in the empty cavity.
[0026] FIG. 2C shows a heterodyne-beat amplitude of the first and
second modes measured at the output of the empty cavity.
[0027] FIG. 2D shows a difference signal, which is a difference of
the heterodyne-beat signal between adjacent half chopping cycles.
In the absence of differential absorption between the two modes,
the difference signal is zero.
[0028] FIG. 2E shows a demodulated ringdown curve for a first mode,
which is tuned to an off-resonance of a sample gas in the
cavity.
[0029] FIG. 2F shows a demodulated ringdown curve for a second
mode, which is tuned to a molecular resonance of the sample gas in
the cavity.
[0030] FIG. 2G shows a heterodyne-beat amplitude of the first and
second modes measured at the output of the cavity containing the
sample gas.
[0031] FIG. 2H shows a difference signal, which is a difference of
the heterodyne-beat signal between adjacent chopping cycles. The
difference signal is non-zero because the second mode experiences
absorption due to the gas whereas the first mode does not.
[0032] FIG. 3 shows a trace of a chopped ringdown curve for an
empty cavity. The trace was obtained from a video output of an RF
spectrum analyzer. A theoretical fit and the fit residual are also
shown.
[0033] FIG. 4 shows five heterodyne-beat amplitudes (left column)
that occur between two chopped cavity modes. Each of the
heterodyne-beat amplitudes corresponds to a different intra-cavity
absorption that affects one of the modes. Five absorption signals
(right column) are also shown. Each of the absorption signals is a
difference in beat amplitude of neighboring half cycles shown in
the corresponding heterodyne-beat amplitudes.
[0034] FIG. 5A shows a pair of curves representing signal-contrast
versus intra-cavity molecular absorption. A solid line curve
includes a change of cavity input coupling efficiency. A dotted
line curve indicates no inclusion of a change of cavity input
coupling efficiency.
[0035] FIG. 5B shows a plot of signal contrast relative to
intra-cavity absorption for experimental data and theory. The
experimental data (taken from FIG. 4) shows signal saturation
occurring when molecular absorption approached the empty-cavity
loss, which in this case is 35.times.10.sup.-6 for a single
pass.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0036] FIG. 1 is an illustration of an apparatus of the present
invention. An intensity-stabilized continuous-wave (cw) laser 101
generates a beam that is provided with RF sidebands by an
electro-optic modulator (EOM) 103. The beam is then split by a pair
of acousto-optic modulators (AOM) 105 and 107. The AOMs 105 and 107
provide a 1.3-GHz relative frequency offset between the pair of
split beams. The offset is preferably selected so that both beams
can resonate within a high-finesse cavity, ref. no. 115. In this
case, the cavity 115 has a free-spectral range of 318.34 MHz. Thus,
the 1.3-GHz offset corresponds to a separation of four mode orders.
The cavity 115 has a finesse of approximately 90,000.
[0037] The beams are combined at a beam splitter 109 and coupled
into the cavity. However, the AOMs 105 and 107 chop the intensities
of the beams out of phase such that only one beam is coupled into
the cavity at any time. Although the beams are switched
periodically at the cavity input, a detector 112 that monitors the
cavity reflection uses the Pound-Drever-Hall technique (such as
described in "Laser phase and frequency stabilization using an
optical resonator," Appl. Phys. B 31, 97 (1983)) to maintain the
laser/cavity lock using the RF sidebands generated by the EOM 103.
This is possible because there is always one beam that is in
resonance with the cavity. A polarized beam splitter 111 and a
quarter-wave plate 117 are used to steer the reflected beam onto
the photodetector 112 that provides a feedback signal to a
laser-cavity locking loop 114.
[0038] The beam coupled into the cavity 115 produces a rising mode
that rises exponentially while the previously coupled beam decays
exponentially within the time scale of the cavity ringdown. The
transmitted signal from the cavity 115 has a heterodyne beat
waveform occurring between the rising and decaying modes inside the
cavity 115. This output signal is detected by an avalanche
photodiode 119. A demodulation unit 121 accepts an electrical
signal from the avalanche photodiode 119 and the 1.3 GHz
frequency-offset signal from the AOMs 105 and 107. Demodulating or
otherwise downconverting the known carrier frequency (1.3 GHz) of
the beat waveform to baseband reveals the heterodyne beat
amplitude. The beat amplitude contains information about the
dynamic variation between the modes, and thus the intra-cavity
absorption signal.
[0039] FIG. 2A and FIG. 2B show relative variations of the two
modes in an empty cavity. In the first chopping cycle shown, mode 1
is switched into the cavity 115 and thus, rises exponentially. At
the same time, mode 2 is switched off and thus, decays
exponentially. At the second chopping cycle, mode 1 is switched off
(and thus, decays exponentially) while mode 2 is switched into the
cavity 115 (and thus, rises exponentially).
[0040] FIG. 2C shows a heterodyne-beat amplitude of the modes
measured at the output of the empty cavity. A heterodyne-beat
waveform that occurs between mode 1 and mode 2 is demodulated
relative to the 1.3-GHz frequency offset to produce the
heterodyne-beat amplitude. The heterodyne-beat amplitude contains
information about the dynamic variation of the modes. In an empty
cavity, the heterodyne-amplitude waveform remains unchanged for
adjacent chopping cycles. FIG. 2D shows a difference signal for the
heterodyne amplitude between adjacent chopping cycles.
[0041] FIG. 2E and FIG. 2F show relative variations of the two
modes in a cavity containing a sample gas. Mode 1 is not absorbed
by the gas. However, mode 2 is tuned to a molecular resonance of
the gas and is absorbed. The system exhibits two slightly different
time constants associated with the two modes. The rise and decay
curves shown in FIG. 2E are similar to the curves shown in FIG. 2A.
In FIG. 2F, the absorption affects both the rise and decay
curves.
[0042] The heterodyne amplitude shown in FIG. 2G is slightly
different between adjacent chopping cycles. This difference is
related to the intra-cavity absorption. A non-zero difference
signal resulting from the asymmetric heterodyne amplitude shown in
FIG. 2G is shown in FIG. 2H.
[0043] In a preferred embodiment, the period of the chopping cycle
may be selected to approximately match the decay time 1/e of the
empty cavity. This embodiment enables a quick comparison of
on-resonance and off-resonance information and suppresses technical
noises associated with the light and the cavity. Since each
ringdown waveform is processed within one chopping period (which is
on the order of 1/e decay time), this reduces the dynamic range
needed to record the signal by several decades. Thus, the present
invention makes full use of the resolution of the digitization
process. characteristic time constant .tau..sub.cav (i.e., the
1/e-decay time) associated with the mode dynamics of a field
applied to an empty cavity can be expressed by a round-trip loss
L.sub.cav and a round-trip time t.sub.roundtrip of the light: 1 cav
= 2 t roundtrip L cav ( 1 )
[0044] This time constant expression for an empty cavity is
equivalent to an expression for a cavity mode that is far detuned
from the medium resonance.
[0045] The time constant for a mode that is tuned to an absorption
peak of the medium can be expressed by: 2 abs = 2 t roundtrip L cav
+ A ( 2 )
[0046] where A is the round-trip absorption of the intra-cavity
medium.
[0047] In the intensity-chopping scenario described with reference
to FIG. 1 and FIGS. 2A to 2H, mode 1 corresponds to an empty-cavity
or off-resonance mode and mode 2 corresponds to an on-resonance
mode that experiences intra-cavity absorption. During a first
half-period [0, .alpha.t/2], mode 1 is switched on and mode 2 is
switched off. Field amplitudes E.sub.1 and E.sub.2 for modes 1 and
2, respectively, are expressed by:
E.sub.1=c.sub.1[1+exp(-.DELTA.t/2.DELTA..tau..sub.cav)-exp(-t/.tau..sub.ca-
v)]; (3)
E.sub.2=c.sub.2exp(-t/.tau..sub.abs);
[0048] where c.sub.1 and c.sub.2 are amplitude coefficients.
[0049] During a second half-period [.DELTA.t/2, .DELTA.t], mode 1
is switched off and mode 2 is switched on. The demodulated
heterodyne-beat waveform is expressed by the product of the field
amplitudes E.sub.1 and E.sub.2. A comparison of the heterodyne-beat
amplitudes for two neighboring half-cycles can be expressed by a
difference equation: 3 ( E 1 E 2 ) [ 0 , t / 2 ] - ( E 1 E 2 ) [ 0
, t / 2 ] = c 1 c 2 [ ( 1 + - t 2 cav ) - t abs - ( 1 + - t 2 abs )
- t cav ] ( 4 )
[0050] In FIGS. 2A to 2H, the chopping period .DELTA.t is selected
to be 4.tau..sub.cav and the time axes are normalized to
.tau..sub.cav. In an empty cavity, the switched waveforms of mode 1
and mode 2 are symmetric, resulting in a uniform heterodyne-beat
amplitude between neighboring half-cycles. When mode 1 and mode 2
experience different cavity losses, the resulting heterodyne-beat
amplitude is asymmetric with respect to neighboring half-cycles.
Differences between neighboring half-cycles indicate the amount of
additional absorption.
[0051] The sensitivity of the method of the invention can be
expressed with respect to equations (3) and (4). The difference
signal shown in equation (4) can be expressed by: 4 i signal 2 2 P
0 [ - t abs - - t cav ] = - 2 P 0 t cav [ 1 - - t ( 1 abs - 1 cav )
] = - 2 P 0 ( 1 abs - 1 cav ) t - t t cav ( 5 )
[0052] In equations (3 & 4), c.sub.1=c.sub.2={square
root}P.sub.0, and light is converted to a photo current according
to i=.eta..multidot.P. where .eta. is the detector responsivity
(A/W). The demodulation beat current is
.eta..multidot.2E.sub.1E.sub.2/{square root}2. In this case the
small absorption limit .tau..sub.cav.apprxeq..tau..sub.abs is
provided and .DELTA.t/.tau..sub.cav.gtoreq.10. Since the beat
amplitude is maximum when E.sub.1=E.sub.2, then
exp(-t/.tau..sub.cav).apprxeq.1/2 and t=.tau..sub.cav.sub.ln 2.
Thus, i.sub.signal can be expressed by: 5 i signal = - 2 P 0 cav ln
2 2 A 2 t roundtrip = - P 0 ln 2 2 A L cav . ( 6 )
[0053] The shot noise produced by the DC photo current, 6 i DC = 2
( P 0 2 ) 2 = P 0 / 2 , is i noise = 2 eB P 0 / 2 ,
[0054] where e is the electron charge and B is the detection
bandwidth. The resutant signal-to-noise ratio (S/N) is: 7 i signal
i noise shot noise = P 0 eB ln 2 2 A L cav . ( 7 )
[0055] In terms of noise-equivalent sensitivity of single-pass
integrated absorption, we set S/N=1 and: 8 ( A 2 ) min = 2 ln 2 eB
P 0 L cav 2 = 2 ln2 eB P 0 Finesse . ( 8 )
[0056] The sensitivity expression of equation (8) is similar to
equation (3) in "Ultrasensitive detections in atomic and molecular
physics: demonstration in molecular overtone spectroscopy," Ye et.
al., J. Opt. Soc. Am. B, 15, 1 (1998) pp 6-15, except for a factor
of approximately 2. This similarity is expected because both
techniques are shot-noise limited. The difference is due to some of
the carrier power being converted to the sidebands in
cavity-enhanced frequency-modulation spectroscopy. This conversion
leads to a slight loss of sensitivity for a fixed total power.
[0057] In one embodiment of the present invention, a Yb:YAG laser
is used to probe acetylene gas inside a high-finesse cavity having
a length of 46.9 cm. An intra-cavity gas pressure of a few mTorr
may be used. A probing mode is tuned to a vibration overtone line
C.sub.2H.sub.2(3v.sub.3)R(29) having a wavelength of 1031.6528 nm
and an absorption coefficient of
4.times.10.sup.-6/Torr.multidot.cm. This system and its operation
are described by Ye, et. al. in "High-resolution frequency standard
at 1030 nm for Yb:YAG solid-state lasers," J. Opt. Soc. Am. B, 17,
6 (2000) pp 927-931, which is hereby included by reference.
[0058] The system operates with a beam-chopping frequency of 1.4
kHz (.DELTA.t=714 .mu.s). The cavity transmission is received by an
avalanche photodiode that couples a beat signal to an RF spectrum
analyzer for demodulation.
[0059] Empty-cavity finesse is measured by tuning both mode 1 and
mode 2 out of the molecular resonance of the gas. FIG. 3 is a plot
of a measured demodulated heterodyne-beat ringdown waveform along
with a theoretical fit corresponding to the mathematical model
derived previously herein. The mathematical model provides an
excellent fit to the measured data and produces an estimated cavity
ringdown (1/e) time of 90 .mu.s. This results in a cavity linewidth
of 3.5 kHz (FWHM) and a finesse of 90,000. Within a detection
bandwidth of 173 kHz (resolution bandwidth of 300 kHz and video
bandwidth of 100 kHz), the recovered signal-to-noise ratio is 150.
The recovered signal-to-noise ratio is approximately two times
smaller than the expected value, partly due to ringing noise of the
spectrum analyzer's RF filter function, which is optimized for
frequency-domain analysis. Smaller analyzer bandwidths were
observed to increase distortion of the ringdown signal.
[0060] When mode 2 is tuned to the center of the acetylene
resonance, the ringdown waveform becomes asymmetric for adjacent
half-cycles. FIG. 4 illustrates a set of ringdown beat waveforms
corresponding to a set of different intra-cavity absorption levels,
which are related to different intra-cavity gas pressures. Five
different gas pressures were provided, including a zero pressure
(i.e., empty cavity). FIG. 4 also shows a set of absorption
waveforms derived from the ringdown beat waveforms. The absorption
signals are generated by a difference between each ringdown beat
waveform and a copy of the waveform that is shifted in time by a
half chopping cycle.
[0061] In a single-pass absorption of 1.7.times.10.sup.-6, the
acquired signal to noise is 10 with a bandwidth of 173 kHz. The
absorption sensitivity normalized to 1-s averaging time is
1.6.times.10.sup.6. At a steady state (i.e., no chopping), each
mode has 3 .mu.W (P.sub.0 ) in the cavity transmission. The value
of .eta. of the avalanche photodiode is 0.3 A/W. The shot noise
limited sensitivity of equation (8) is then approximately
1.2.times.10.sup.-11 at 1-second averaging. However, since the
avalanche photodiode has an excess noise factor of three, the
expected minimum absorption sensitivity should be approximately
4.times.10.sup.-11, which is a factor of four lower than this
experimental result.
[0062] In FIG. 4, the absorption-signal amplitude does not increase
linearly with respect to cavity absorption. FIG. 5A shows signal
contrast against intra-cavity absorption normalized to the
empty-cavity loss. The dotted line curve is calculated based on an
assumption that the coupling power to mode 2 (the absorbing mode)
is constant. However, since there is additional loss inside the
cavity, the power coupling efficiency to the cavity changes and the
available power for mode 2 decreases. Thus, for a fixed incident
power, signal saturation occurs sooner, as shown by the solid line
shown in FIG. 5A.
[0063] FIG. 5B illustrates saturation of the experimental data
shown in FIG. 4. The model illustrated by FIG. 5A is used to fit
the data plotted in FIG. 5B. A solution to the problem of
saturation may include increasing the power input to the cavity as
intra-cavity absorption increases. Another means for addressing the
problem of saturation is to use faster chopping cycles.
[0064] The application of the present invention to CRDS enables
shot noise limited detection for linear absorption measurements.
There is excellent agreement between the experimental ringdown
waveform and the theoretical models. Measurements made in the
presence of 1.times.10.sup.-6 intra-cavity absorption indicate a
detection sensitivity of 1.6.times.10.sup.-10 at a 1-s averaging
time. Particular applications of the present invention include, but
are not limited to, spectrum measurements made under conditions of
Doppler or atmospheric-pressure broadening.
[0065] Although particular embodiments are described, improvements
and adaptations to the embodiments may be provided without
departing from the scope of the invention. Improvements may include
basic operational changes, such as using faster chopping cycles.
Improvements may include component changes, such as replacing the
avalanche photodiode with a sensitive p-i-n diode in a resonant
matching circuit. Adaptations may include stabilizing the laser on
the cavity with a third mode that is off resonance and independent
of the other two modes. The third mode can be left on continuously
to maintain a lock while the first two modes are switched. The
heterodyne-detection process can be adapted to filter out
contributions from the third mode.
[0066] The foregoing discussion and the claims that follow describe
the particular embodiments of the present invention discussed
herein. Particularly with respect to the claims, it should be
understood that changes may be made in particular embodiments
without departing from the essence of the invention. In this
regard, it is intended that such changes would still within the
scope of the claimed invention. To the extent such revisions
utilize the essence of the present invention, each naturally falls
within the breadth of protection encompassed by this patent. This
is particularly true for the present invention, since its basic
concepts and understandings are fundamental in nature and can be
broadly applied.
* * * * *