Analog detection for cavity lifetime spectroscopy

Details Analog detection for cavity lifetime spectroscopy Analog detection for cavity lifetime spectroscopy

1999-03-19

2001-05-15

Font, Frank G. (Department: 2877)

Optics: measuring and testing

For light transmission or absorption

Of fluent material

C356S440000, C250S343000

Reexamination Certificate

active

06233052

ABSTRACT:

FIELD OF THE INVENTION
This invention relates to the field of spectroscopy, and in particular to analog electronics for determination of ring-down and ring-up rates in lifetime cavities, also known as ring-down cavities.
BACKGROUND OF THE INVENTION
Traditional spectroscopic methods are limited in sensitivity to approximately one part per ten thousand (1:10
4
) to one part per hundred thousand (1:10
5
). The sensitivity limitation arises from instabilities in light source intensity that are translated into noise in the absorption signal. For general information on traditional spectroscopy methods see for example Dereniak and Crowe,
Optical Radiation Detectors
, John Wiley & Sons, New York, 1984, and Demtroder,
Laser Spectroscopy
, Springer, Berlin, 1996.
Cavity lifetime spectroscopy, otherwise known as Ring-Down Spectroscopy (CRDS), a technique first described by O'Keefe and Deacon in an article in
Rev. Sci. Instrum
. 59(12):2544-2551 (1988), allows one to make absorption measurements with sensitivities on the order of one part per ten million (1:10
7
) to one part per billion (1:10
9
) or higher. For general information on CRDS see U.S. Pat. No. 5,528,040 by Lehmann, as well as the articles by Romanini and Lehmann in
J. Chem. Phys
. 102(2):633-642 (1995), Meijer et al. in
Chem. Phys. Lett
. 217(1-2):112-116 (1994), Zalicki et al. in
App. Phys. Lett
. 67(1):144-146 (1995), Jongma et al. in
Rev. Sci. Instrum
. 66(4):2821-2828 (1995), and Zalicki and Zare in
J. Chem. Phys
. 102(7):2708-2717 (1995).
In a CRDS system, the sample (absorbing material) is placed in a high-finesse stable optical resonator or ring-down cavity having an input coupling mirror and an output coupling mirror. Light admitted into the ring-down cavity through the input coupler circulates back and forth multiple times setting up standing waves having periodic spatial variations. Light exiting through the output coupler is proportional to the intracavity light intensity.
After the input light source is terminated, the radiant energy stored in the ring-down cavity decreases in time (rings-down). For an empty cavity, the stored energy follows an exponential decay characterized by a ring-down 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 ring-down is accelerated; under suitable conditions, the intracavity energy decays almost perfectly exponentially. An absorption spectrum for the sample is obtained by plotting the ring-down rate R or the reciprocal of the ring-down decay constant 1/&tgr; versus the wavelength &lgr; of the incident light.
In comparison to conventional spectroscopic techniques, CRDS promises to achieve extremely high detection sensitivity because the ring-down rate 1/&tgr; is not a function of the intensity of the incident light. In other words, intensity fluctuations of the incident light are not related to the ring-down rate in the ring-down cavity and thus do not directly affect the CRDS measurement.
In conventional absorption measurements, when light passes through a sample of length l, the ratio of the transmitted and incident intensities, I
t
and I
o
, satisfies Beer's law:
&Dgr;I/I
o
=(I
o
-I
t
)/I
o
=1−e
−&agr;1
,
where &agr; is the absorption coefficient of the sample. Any intensity fluctuations will clearly result in uncertainties in the absorption measured. It is possible to define a minimum detectable absorption (MDAL) based on the intensity noise of the system as follows:
MDAL =&sgr;
l
/l
eff
,
where &sgr;
I
is the root-mean-square (RMS) intensity noise and l
eff
is the effective sample path length (e.g., in a multi-pass absorption measurement cell, the effective sample length can be many times the physical sample path length, since the light beam circulates inside the cell, passing through the sample many times, e.g., up to 500 times or more). Of course, more than one absorption measurement can be taken and the results averaged to reduce the measurement error, however, the fundamental limitation of the system being subject to intensity noise can not be overcome.
In CRDS the measured variable is the decay constant, &tgr;, or the ring-down rate 1/&tgr;, and thus the sensitivity is expressed as:
S
&tgr;
=&sgr;
&tgr;
/(l
eff
{square root over (F)}),
where F is the number of measurements taken per unit time and the units are expressed in cm
−1
Hz
−½
. Clearly, intensity noise does not figure in this equation. In fact, the ultimate limit of CRDS is the fundamental barrier due to shot-noise inherent in the light beam. Shot-noise results from the discrete nature of photons making up the light beam. The photocurrent produced by a laser beam having power P is i=RP where R is the responsivity of the photodetector. For ideal detection, the photocurrent noise will directly reflect the shot noise of the light. The temporal distribution of shot-noise obeys Poisson statistics and can be expressed as:
&sgr;
I,shot-noise
={square root over ((
2
el))},
where e is the electronic charge (1.602×10
−19
C).
Theoretically, if CRDS were only limited by shot-noise, the achievable sensitivity would be in the range of 10
−14
cm
−1
Hz
−½
for a CRDS system having a 50 cm long cavity, a 10 mW continuous-wave (CW) laser with a 10 kHz linewidth and mirrors having losses of 50 ppm.
The actual performance of state-of-the-art CRDS in comparison to other conventional methods is illustrated in Table 1.
TABLE 1
Typical
Spectroscopic Scheme
MDAL (cm
−1
)
Cost
Complexity
Single-pass absorption
10
−6
low
simple
Multi-pass absorption
10
−8
moderate
simple
ICLAS
10
−6
-10
−11
high
difficult
FM
10
−6
-10
−8 
moderate
moderate to difficult
P CRDS
10
−6
-10
−10
moderate
simple
CW CRDS
10
−8
-10
−12
low to
simple to moderate
moderate
ICLAS = intracavity absorption spectroscopy; FM = frequency modulation;
P CRDS = pulsed CRDS; CW CRDS = continuous-wave CRDS
Most experimental CRDS setups have used pulsed laser sources (P CRDS). However, P CRDS has several practical disadvantages, which preclude shot-noise-limited detection, unless significant effort is made to eliminate them. First, most P CRDS arrangements are limited by the detector noise on the signal, unless special photodetectors such as photomultiplier tubes are used. Unfortunately, photomultiplier tubes can operate only in the ultra-violet to near-infrared wavelength ranges, so that P CRDS in the mid-infrared can be extremely limited. This detection noise is a direct consequence of the limited optical throughput of the high-finesse ring-down cavity. The optical throughput is a function of the ratio of the laser and cavity linewidths. Typical throughputs for pulsed lasers do not exceed 0.01%. In other words, this problem relates to the excess noise present on the ring-down signals, which makes the signal much more difficult to fit accurately. The greater this excess detector noise, the larger the error in the decay rate fit, and hence the greater the error in the absorption loss measurement.
Second, P CRDS is limited by the quality of the mode-matching between the laser beam transverse profile and the ring-down cavity modes. Ideally, only a single transverse and longitudinal cavity mode—the fundamental TEM
00
mode—is excited in the ring-down cavity. However, because most pulsed laser linewidths tend to be large, multiple longitudinal modes can be excited if the ring-down cavity length is sufficiently large. Moreover, because it is difficult to accurately match the transverse profile of pulsed laser beams to the ring-down cavity mode geometry, multiple transverse modes become excited. Excitation of higher order modes, each having a distinct resonance frequency, can impose a sinusoidal beating which is superposed on the ring-down signal intensity exiting the ring-down cavity, unless all modes are perfectly collected onto

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