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.
In this work, we analyze the possibility of exploiting the recently demonstrated super-resonant intracavity coherent absorption effect for quantitative sensing applications. The method relies on a system of two nested resonators (ring and Fabry-Perot) which allows to increase the radiation-matter interaction pathlength by a factor proportional to the product of the two resonator’s individual finesse coefficients. In this way, it is possible to dramatically increase the interaction of intracavity radiation with a weakly absorbing sample without need of an ultra-high finesse optical cavity. Here, we propose a measurement strategy that allows to exploit the super-resonant enhancement provided by the nested-resonators system and cancel out the noise connected with the radiation source at the same time, and compare it to a conventional cavity-enhanced absorption measurement.
We present a cavity-enhanced optical absorption measurement technique based on high-bandwidth Pound-Drever-Hall (PDH) sideband locking, which naturally provides a real-time, resonant amplitude quadrature readout that can be mapped onto the cavity’s internal loss rate. Cavity-enhancement is widely used in the detection of small signals -- an optical cavity traps photons between two highly reflective mirrors, thereby enhancing the effective path length through the absorber [Romanini et al., 2014]. Most of the available techniques, however, probe transmission signals and/or do not provide the stability required for the detection of fast signals.To ensure optimal enhancement of absorption sensitivity, probe light must be locked on resonance with the cavity. PDH locking relies on phase modulation of a laser beam, creating two sidebands on the original carrier frequency [Black, 2001]. Upon reflection from a cavity, this modulated light produces a heterodyne signal (beat note) that can be detected and demodulated. We use the phase quadrature of the beat note to lock the cavity on resonance with one of the sidebands, achieving a locking bandwidth in the MHz range that keeps cavity and probe light resonant for hours [Reinhardt et al., 2017]. Simultaneously, we monitor the amplitude quadrature, which provides a continuous, real-time, heterodyne-amplified readout of the cavity’s internal absorption. Our PDH sideband cavity-enhanced absorption readout technique (SideCAR) ensures high sensitivity without reaching saturation limits in the intracavity medium by keeping a relatively low intracavity power, since only one of the sidebands is allowed to enter the cavity, but the signal is boosted above the detector noise by heterodyne detection (using the carrier as a local oscillator).This thesis presents the theoretical formulation of the sensing technique together with the expressions for the sensitivity limit (ultimately given by the laser quantum noise), and the experimental results from a test cavity setup. Probing a proof-of-concept 5-cm-long Fabry-Perot cavity with a coupled power of 160 uW, we measure an absorption sensitivity of 7*10^(-11) cm^(-1)/sqrt(Hz) at 100 kHz (roughly the cavity bandwidth), a factor of 11 from the shot-noise limit. This technique allows the detection of small, transient signals against absorptive backgrounds with sensitivity close to the shot noise limit using a reflection-based measurement in a fairly simple setup, opening the possibility of developing new microscopic single-port real-world sensors for transients, for example using micron-scale optical fiber cavities
This paper presents a theoretical analysis of the optical properties of an optical cavity with both one- and two-photon intracavity absorption loss, without saturation. The cavity two-photon absorption loss per pass is assumed to be small, but otherwise the analysis is general. Analytical results for the cavity transmission as a function of cavity parameters, linear and two-photon intracavity loss, and detuning from resonance are derived and limiting cases discussed. Extraction of the two-photon loss from both cavity ring-down and cavity-enhanced absorption spectroscopy methods is analyzed and the predicted shot-noise limited sensitivities derived and compared. Numerical results are computed using the parameters of a recent experimental intracavity measurement of two-photon absorption of nitrous oxide. The results will be useful in the design and interpretation of cavity-enhanced, two-photon absorption spectroscopy.
Optical quantum sensing strategies that utilise features of quantum states of light have implications for precision measurement in areas as wide ranging as such as gravitational wave sensing [1] and biological imaging [2]. Optical absorption estimation is the task of estimating the transmission parameter η which is defined by the ratio of input, Iin, to output, Iout, intensity of light from a sample of interest (Iout= ηIιη). The optimal quantum strategy provides a quantum advantage (per incident photon) of 1/(1-η) over the best classical strategy [3]. This technique has been demonstrated experimentally in single parameter estimation and imaging scenarios [4,5].
Quantum light, such as entangled photon pairs, is a special state of light that cannot be described by classical electrodynamics. Owing to its exotic nonclassical properties, the use of quantum light can open up a new possibility for spectroscopy that cannot be realized by a classical light source. Recently, using entangled photon pairs as the light source, we demonstrated ultrasensitive absorption spectroscopy with quantum-enhanced sensitivity [1]. This novel approach allows us to obtain absorption spectra with a noise level suppressed below the shot-noise limit, which is a fundamental and unavoidable limit in conventional absorption spectroscopy. In this presentation, we will discuss two applications of this sub-shot-noise absorption spectroscopy.