We present an ac heterodyne technique in cavity ringdown spectroscopy that permits $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ absorption sensitivity with microwatt-level light power. Two cavity modes, one probing the empty cavity and the other probing intracavity absorption, are excited simultaneously but with their intensities temporally out of phase, with one mode decaying and the other rising. Heterodyne detection between the two modes reveals the dynamic time constants associated with the empty cavity and the additional intracavity gas absorption. The method offers a quick comparison between the on- and off-resonance information, a prerequisite to reaching the fundamental shot-noise limit. This simple and yet important improvement of cavity ringdown spectroscopy should lead to the enhanced performance of a wide range of applications.
Cavity-enhanced absorption spectroscopy is now widely used as an ultrasensitive technique in observing weak spectroscopic absorptions. Photons inside the cavity are reflected back and forth between the mirrors with reflectivities R close to one and thus (on average) exploit an absorption pathlength L that is 1/(1 − R ) longer than a single pass measurement. As suggested by the Beer-Lambert law, this increase in L results in enhanced absorbance A (given by αL with α being the absorption coefficient) which in turn favours the detection of weak absorptions. At the same time, however, only (1 − R ) of the incident light can enter the cavity [assuming that mirror transmission T is equal to (1 − R )], so that the reduction in transmitted light intensity Δ I caused by molecular absorption equates to that would be obtained if in fact no cavity were present . The enhancement in A = Δ I / I , where I is the total transmitted light intensity, achievable from CEAS therefore comes not from an increase in Δ I , but a sharp decrease in I. In this paper, we calculate the magnitudes of these two terms before and after a cavity is introduced, and aim at interpreting the sensitivity improvement offered by cavity-enhanced absorption spectroscopy from this observable-oriented (i.e. Δ I and I ) perspective. It is first shown that photon energy stored in the cavity is at best as intense as the input light source, implying that any absorbing sample within the cavity is exposed to the same or even lower light intensity after the cavity is formed. As a consequence, the intensity of the light absorbed or scattered by the sample, which corresponds to the Δ I term aforementioned, is never greater than would be the case in a single pass measurement. It is then shown that while this “numerator” term is not improved, the “denominator” term, I , is reduced considerably; therefore, the increase in contrast ratio Δ I / I is solely contributed by the attenuation of transmitted background light I and is ultimately down to the suppression of any measurement noise that is associated with it. The noise component that is most effectively suppressed is the type whose magnitude scales linearly with light intensity I , as is typical of noise caused by environmental instabilities, followed by the shot noise which scales as square root of I . No suppression is achievable for noise sources that are independent of I , a notable example being the thermal noise of a detector or of detection electronics. The usefulness of this “noise suppression” argument is that it links the sensitivity gain offered by a cavity with the property of measurement noise present in the system, and clearly suggests that the achievable sensitivity is dependent on how efficient the various noise components are “suppressed” by the cavity.
High sensitivity detection of quantum absorption is demonstrated at a sensitivity of
1times1011 integrated absorption, in 1 sec, using 10 mTorr total gas pressure. Achieving highly sensitive detection relies on simple basic principles: 1) The molecule-generated electric field in the forward direction (the "darkness wave") is most precious, and contains the maximum available information. It is the physical manifestation of the -
alpha∗L term appearing when beer#### absorption law is expanded for low opacity, 2) After generating the molecular signal, the detected unabsorbed light sets the "shotnoise" measurement floor. We use an optical transmission cavity for the gas cell, since the high internal "build-up" field will elicit a strong molecular "darkness wave", for a given transmitted de light on the detector, A more conventional explanation of Gavity Enhancement would be the extension of the effective cell length by the factor finesse
∗2/pi.3) To avoid excess low-frequency noise, such small signals should be measured by ac methods, comparing on-resonant and off-resonant cases in quick succession. 4) By SIMULTANEOUSLY obtaining and subtracting these cases, one provides a siginal channel with NO OUTPUT unless there is a resonance. This is conveniently accomplished by using the FM detection method with the optical heterodyne sidebands and carrier being transmitted through the cavity via adjacent axial orders 5). A remarkable property of this configuration, when the modulation frequency= cavity mode spacing, is the suppression of ANY detection of laser frequency noise with the transmitted light. We can refer to this property as (laser FM-) noise-Immune detection. This enables profitable use of cavity finesse in the range above 10,000, without a nois penalty, Altogether, we refer to this new spectroscopy as Noise-Immune, Cavity-Enhanced, Optical Heterodyne Molecular spectroscopy, i.e. "NICE OHMS". We have measured excellent saturated dispersion signals from HCCH in the band near 790 mm (
nu1+3nu3), and recently, using a Nd:YAG source, from the HCCD P(5) line (
nu2+3nu3) at 1064 mm. The saturation peaks broaden from the transit limit of 270 kHz near zero pressure at the rate 34.7 kHz/m Torr. We observe interesting narrow linwidths 8-fold below the transit limit, basically using optical selection of slow molecules by low power and pressure (2 mW and 2 m Torr). The absolute frequency is measurred to be 281, 635,363,960 MHz
pm45 kHz.
We introduce optical feedback frequency stabilized cavity ring-down spectroscopy (OFFS-CRDS), a near-shot-noise-limited technique that combines kilohertz resolution with an absorption detection sensitivity of 5×10(-13) cm(-1) Hz(-1/2). Its distributed feedback laser source is stabilized to a highly stable V-shaped reference cavity by optical feedback and fine-tuned by means of single-sideband modulation. The stability of this narrow laser is transferred to a ring-down (RD) cavity using a new fibered Pound-Drever-Hall (PDH) locking scheme without a dedicated electro-optic phase modulator, yielding several hundred RD events per second. We demonstrate continuous coverage of more than 7 nm with a baseline noise of 5×10(-12) cm(-1) and a dynamic range spanning six decades. With its resonant intracavity light intensity on the order of 1 kW/cm2, the spectrometer was used for observing a Lamb dip in a transition of carbon dioxide involving four vibrational quanta. Saturating such a weak transition at 160 μW input power, OFFS-CRDS paves the way to Doppler-free molecular overtone spectroscopy for precision measurements of hyperfine structures and pressure shifts.