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Abstract
Two-photon absorption spectra are difficult to observe using direct absorption spectroscopy especially in the near-infrared region. Cavity ring-down spectroscopy is a promising absorption spectroscopy technique which has been widely applied to linear and saturated single-photon absorption spectra. In the present study, we report the observation of a possible two-photon absorption in the near-infrared using cavity ring-down spectroscopy, namely a two-photon resonance of methane. Using an optical frequency comb, the single-photon wavenumber of the double-quantum transition has been determined to be 182 207 682.645 MHz with a standard deviation of 75 kHz.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The multi-photon transition is a process whereby two or more photons are simultaneously absorbed by an atom or a molecule. It has many applications, such as two-photon fluorescence microscopy [1], three-dimensional microfabrication [2], optical data storage [3], charge-parity-time reversal symmetry tests [4] and proton-size measurement [5]. However, infrared absorption cross sections are generally smaller than those associated with electronic transitions, so new infrared techniques with substantially greater sensitivity are required [6]. The analysis of the sensitivity limits for two-photon cavity ring-down spectroscopy predicts a theoretical detection limit of 32 ppq (10−15) Hz−1/2 for 12C16O2, a higher sensitivity than any achieved using one-photon absorption [7]. Most recently, using cavity ring-down spectroscopy Zhao et al. observed a two-photon absorption of 14N216O at 4.53 µm [6] in the mid-infrared region. But near-infrared absorption cross sections are smaller than those in the mid-infrared region [6]. As far as we know, there is no literature for two-photon cavity ring-down spectroscopy in the near-infrared region.
Cavity ring-down spectroscopy is a promising laser-based absorption spectroscopy technique with higher absorption sensitivity and frequency resolution compared with traditional absorption spectroscopy techniques. It has found many applications in linear single-photon absorption spectra [8,9], including atmospheric remote sensing [10], gas concentration metrology [11,12], molecular collision theory [12]. In addition to applications of linear single-photon absorption, saturated single-quantum absorption, namely Lamb-dip spectra, was also implemented by cavity ring-down spectroscopy about twenty years ago [13]. Lamb-dip spectroscopy is a powerful Doppler-free technique for measuring transition frequencies and distinguishing overlapped spectra [14,15]. However, another well-known optical Doppler-free technique, multi-photon absorption, has proved difficult to implement using cavity ring-down spectroscopy even though it is theoretically feasible [7,13,16,17].
Given that the probabilities of n-photon absorption depend on the nth power of the light intensity, respectively, the higher optical intensity, the higher possibility of observing a multi-photon absorption. To increase the optical intensity in units of W/cm−2, cavity ring-down spectroscopy uses as the gas sample cell a Fabry-Perot resonator formed by a pair of high reflectivity mirrors [18] or optical cavities, formed by 3 or more mirrors, with a traveling-wave geometry. Only in the 2-mirror standing-wave configuration, Doppler-free two-photon absorption is possible; three-photon absorption would be Doppler broadened. Four-photon absorption would also be Doppler free but is highly improbable. In 1999, Romanini et al. made the first attempt to observe two-photon absorption by cavity ring-down spectroscopy, namely in NO2 near 796 nm [13]. The estimated the intracavity optical intensity at the beginning of a ring-down event was about 1 MW/cm2. Such a high optical intensity might have been sufficient for observation of two-photon fluorescence spectra but the minimum detectable absorption coefficient achieved was ∼1×10−10 cm−1, higher than that achievable in modern instruments, which might be the main reason for the failure to detect two-photon absorption by cavity ring-down spectroscopy [7].
In this study, we present direct observations of two-photon absorptions in the near-infrared region by cavity ring-down spectroscopy. We report the direct observations of a possible two-photon absorption of methane (CH4) by using a cavity ring-down spectroscopy apparatus of the minimum detectable absorption coefficient of 5.8×10−12 cm−1 in the near-infrared region.
2. Experimental apparatus
Cavity ring-down spectroscopy [18] obtains gas absorption coefficients by measuring the ring-down (exponential decay) time of an optical field confined within the cavity. Ring-down times are dominated by the extinction of the gas and the losses of the two cavity mirrors. A schematic of our cavity ring-down spectrometry apparatus, inspired by the designs of Hodges et al. [20,21] and Lin et al. [22], is shown in Fig. 1. The main body of the ring-down cavity (sample cell) is a hollow invar cylinder (length 1.3 m, internal diameter 12 mm and external diameter 60 mm). The linear thermal expansion coefficient of Invar is about 5×10−7 K−1. Two plano-concave mirrors (radius of curvature of 1 m, reflectivity R = 99.998%, transmission T ≈ 0.0015% and absorption A ≈ 0.0005% at 1.65 µm given by the manufacturer) are mounted in custom-designed Invar flexture mounts, enabling precise and stable alignment. The cavity is sealed at both ends with anti-reflection coated windows. Sample gases are injected into the cavity through a flexible stainless-steel tube welded to the cavity. The gas pressure is monitored using a differential pressure gauge (MKS, model 698A11TRC) of range of 0-1333 Pa and accuracy of ±0.12% of reading. The gas temperature is measured with three calibrated 100 Ω capsule platinum resistance thermometers (Hart Scientific, model 5686) located in the middle and at the ends on the surface of the main body.
Fig. 1. The sketch of the cavity ring-down spectroscopy apparatus [19]. Key: BOA: booster optical amplifier; DAQ: data acquisition cards; DG1, DG2: digital gate and delay generators for ring-down signal and probe laser frequency lock; ECDL: extended-cavity diode laser, OFC: optical frequency comb generator; OSC: oscilloscope; WM: wavemeter; Iso: optical isolator; HR Mirror; high reflectivity mirror.
An extended cavity diode laser (ECDL) (Sacher, model LION), a booster optical amplifier (BOA) (Thorlabs, model BOA1082P), and two digital gate and delay generators (SRS, model DG645) are used to produce ring-down events [20–22]. The ECDL, fine-tuned by using a PZT-actuated grating and coarse-tuned by a motor, emits a laser beam of 10 mW in a widely tunable spectral range (1579∼1751 nm). The linewidth of the laser beam is 100 kHz for an averaging time of 0.1 s. The typical output power of the BOA is 20 mW for 1 mW input power. The typical extinction rate of the BOA is about 70 dB. The residual power enters the cavity after the BOA has been switched off was measured to be about 2 nW. The BOA is driven by a laser diode driver (Stanford Research Systems, model LDC502) with an integrated temperature controller. The working temperature and current for the BOA was 293.15 K and 600 mA, respectively. An InGaAs photodetector (PD) (New Focus, model 2053-FS) with an amplifier is used for detecting the optical power transmitted by the ring-down cavity. In the gain setting of 35 V/mW and the frequency response range (3 dB) setting from d. c. to 6 MHz, the output voltage noise is approximate 37 µVrms calculated using the noise equivalent power of 0.34 pW·Hz−1/2. Ring-down signals were digitalized with a 16-bit analog-to-digital converter (Gage, model CSE1622) of a sampling rate of 5 MHz. The relative uncertainty in the sampling rate is 1 ppm (10−6). The ring-down signal triggered simultaneously two digital gate and delay generators (DG1 and DG2). DG1 with a threshold voltage Vtrig = 2.5 V was used to shut the current of the BOA and to trigger the digitizer for sampling ring-down signals. We verified that the actual turn-off time of our system is below 0.5 µs. The digital gate and delay generator (DG2) with a threshold voltage of 1.5 V was used to lock the probe laser frequency to a resonance frequency of the cavity. Probe laser frequency locking was implemented by maximizing the rate of the DG2 trigger events by the slow triangular-wave modulation of the probe laser frequency around the cavity resonance frequency [20,21]. The ring-down time was determined by a fast exponential fitting procedure using the Levenberg-Marquardt algorithm [23]. More details about the temperature-scanning cavity ring-down spectroscopy apparatus can be found in Refs. [19,24,25]. In this experiment, as mentioned above, the gain κ of the PD in our experiment was set to be 35 V/mW. The intra-cavity optical intensity at the beginning of a ring-down event can be calculated via I0=Vtrig/[κTπr2] where r is the cavity waist radius and T is the mirror transmission. Then the estimated maximal intracavity optical intensity was above 487 W/cm2 for r = 483 µm [26]. Ring-down curves were fitted by an exponential model with a baseline. The ring-down time of the vacuum cavity was 236 µs with a typical sample rate being 200 Hz. Figure 2 shows an Allan deviation plot for empty cavity absorption coefficients. The minimum detectable absorption coefficient of an empty cavity was 5.8×10−12 cm−1 at the average time of 3.5 s. The noise equivalent absorption (NEA) realized is 7.8×10−12 cm−1·Hz−1/2 calculated using the Eq. (2) in Ref. [27]. The NEA realized is two order of magnitudes higher than the shot-noise dominated detection limit of 3.3×10−14 cm−1·Hz−1/2 which calculated using the Eq. (7) in Ref. [28].
The absolute frequency of the laser is measured by the beat note between the frequency of the probe laser and that of an optical frequency comb (Menlo Systems GmbH, model FC1500-250-WG). The beat note signals are measured using an oscilloscope (Agilent, model DSO-X3024A) with a sample rate of 500 MHz and converted into the frequency domain by the Fourier transform function of the oscilloscope trace. The resolution of the Fourier transform function is 1.91 kHz. A computer program reads the frequency spectrum and then locates the frequency value of the maximum amplitude as the beat frequency fbeat. A 10 MHz GPS time base (Beijing Time & Frequency, model HJ5410A) with a relative uncertainty below 1×10−11 provides the time reference for the optical frequency comb. The absolute frequency is calculated by fa=±fceo+mfrep±fbeat where m is a positive integer. The symbols fceo and frep denote the offset frequency and the repetition frequency, respectively, of the optical frequency comb. The sign of the fbeat is determined by the frequency value measured by the wavelength meter (WM, Bristol, model 621A) of absolute accuracy 26 MHz at 1.6 µm.
Once the laser frequency has been locked to that of a cavity mode, we finely scan the laser frequency by changing the cavity length. To increase the length, a 9 m long heating tape of 900 W and a constant current source of 2 mA (rms) noise are used to heat the cavity; to decrease it, we let it cool. In order to provide a stable temperature environment for the cavity, a cylinder thermostat, insultated with polyurethane foam sealing agent, was used. Temperature-controlled ethanol at 293.15 K flows through the inner wall of the thermostat. The ring-down cavity is placed unfixed on a table in the thermostat to allow free thermal expansion and contraction. To reduce heat exchange, two 1-cm-thick aerogel pads are placed between the angle plates and the table in a thermostatic enclosure. In the present work, the temperature of the cavity was scanned from 295 to 297 K by an approximate quasi-triangular wave. The typical temperature variation rates of the cavity during the heating phase (the heating tape current = 200 mA) and cooling phase (the heating tape current = 0 mA) were about 580 µK/s and −253 µK/s, respectively [24].
3. Two-photon absorption and Lamb dip
The searched spectral regions are given in Table 1. Actually, we stumbled across the proposed two-photon absorption when searching saturated one-photon absorption lines in our previous work [19]. We didn’t observe other two-photon absorption features in those intervals. To explore the two-photon absorption, we measured the two-photon absorption again at the pressure of 5 Pa and a temperature of 296 K in 2 April 2018. During the spectral measurement, we averaged 50 ring-down events for each spectral point. Figure 3 shows the observed spectrum of methane at 6077.794 cm−1. A Lamb dip (saturated one-photon absorption) at 6077.7965983 cm−1 [19] near the proposed two-photon transition was also observed. As shown in the Fig. 3, contrary to saturated single-photon absorption, two-photon absorption increases absorption of the methane sample.
Fig. 3. Two-photon absorption and saturated single-photon absorption (Lamb dip) spectra near 6077.794 cm−1. The symbol c is the speed of light in vacuum. The energy level diagram of transitions is shown in the inset. The symbol Eg denotes the ground state of one-photon absorption, Eg$^\prime$ the ground state of two-photon absorption, Eo the excited state of the saturated one-photon transition, Ev the virtual intermediate state of the proposed two-photon transition, and Et the excited state of the proposed two-photon transition.
Table 1. Searched spectral regions of this work.
Figure 4(a) shows the cavity decay transient on and off of the two photon absorption and empty cavity decay transient. Figure 4(b) shows the exponential fitting residuals (Experiment − Fit) for the decay signals of the empty cavity. There are no visible systematic deviations of experimental data from a perfect exponential curve. Figure 4(c) shows the exponential fitting residuals (Experiment − Fit) for the decay signals on and off of the two photon absorption. The obtained decay time was 104.57 µs and 104.62 µs on and off of the two photon absorption, respectively. The ring-down curves are non-exponential as a result of nonlinear relaxation processes induced by both the saturated one-photon absorption and the two-photon absorption. In this case, saturated single-photon absorption was the main cause of non-exponentiality of the ring-down curves, given that the profile of ring-down curves was similar to those of only saturated one-photon absorptions (with no two-photon absorption). The SCAR model can obtain smaller fitting residuals [see Fig. 4(d)]. However, due to the two-photon absorption is very small, the fitting residuals by the SCAR model (Eq. (A)37 in [29]) also shows the very similar profiles. The SCAR model can obtain the decay rate γc induced by cavity mirrors and the decay rate γg by the unsaturated gas absorption. However, due to the SCAR model has more fitting parameters than the exponential model, the signal-to-noise ratio obtianed by the the exponential model is much better than that by the SCAR model. We cannot observe the two-photon absorption when using the SCAR model. Considering the small absorption of the proposed two-photon transition, although there are available SCAR models and a two-photon ring-down model [7,16], we still adopt the exponential model to analyse spectra for reducing the number of degrees of freedom of fits, which might produce relative high signal-to-noise ratios.
Fig. 4. (a) Typical cavity decay signals of the empty cavity (single decay and average of 50 decays), on and off of the two photon absorption. (b) The exponential fitting residuals (Experiment − Fit) for cavity decay signals of the empty cavity (average of 50 decays). (c) The exponential fitting residuals for the decay signals on and off of the two photon absorption. (d) The fitting residuals for decay signal on and off of the two photon absorption by using the Eq. (A)37 in the Ref. [29].
It is also interesting to study the absolute transition position, line broadening and shift of the observed two-photon transition. To do this we made four repeated measurements of the two-photon absorption at two different pressures of 5(1) Pa and 0.1(0.1) Pa. The spectral baseline was modelled using an oblique line. Figure 5 shows the baseline-subtracted two-photon spectra, at the pressures of 5(1) Pa and 0.1(0.1) Pa, fitted by the Lorentzian profile and the fitting residuals. The effective frequency sweep rate of the cavity resonance in the Fig. 5(a) and the Fig. 5(c) was −6.6 kHz/s and −31 kHz/s, respectively, on the heating part of the cycle. We obtained a two-photon position of 182207682.645 MHz (6077.7940800 cm−1) with a standard deviation of 74 kHz from the 5 Pa spectra. We considered several sources of possible systematic errors affecting the measurement uncertainty. The 10 MHz GPS time base has a relative uncertainty below 1×10−11, which results in an uncertainty of 1.8 kHz in the absolute position. The position uncertainty induced by the shift of the time base of the oscilloscope is below 4 kHz. There was no light shift (AC Stark Effect) observed within this experimental uncertainty. The upper limit of the pressure induced shift is estimated to be 10 kHz in security since there were no obvious line shifting of the two-photon absorption at 0.1 Pa and 5 Pa (see Table 2). Assuming the aforementioned contributions to be independent, we find the combined uncertainty of the determined line position to be 75 kHz. The position difference between the proposed two-photon transition and the Lamb dip is 75.497(87) MHz. The obtained full width at half-maximum (FWHM) of the two-photon absorption was 276(26) kHz and 204(28) kHz at the pressure of 5Pa and 0.1Pa, respectively. This indicates that at both pressures the line broadening is dominated more by transit time than by molecular collisions. The FWHM of the Lorentzian fitted to the Lamb dip at the pressure of 5 Pa was 656 kHz. The FWHM of the two-photon resonance is narrower than that of the Lamb dip by a factor of about two.
Fig. 5. Two-photon absorption spectra at pressures of 5 Pa and 0.1 Pa at 182207682.645 MHz. Symbols: $\color{green}{\bullet}$ experimental spectrum; $\color{red}{}$ cavity temperature; —— Lorentizian fitting spectrum; • fitting residuals (Experiment − Fit).
Table 2. Positions and FWHM widths of the two-photon absorption at two different pressures.
We tried our best to confirm the assignment through both the newest spectral database [30] and the theoretical analysis [31]. However, owing to the complexity of the methane energy levels, we are unable at present to give quantum assignments of its levels.
4. Conclusions
In this study, we have demonstrated the direct observation of a possible two-photon absorption in the near-infrared region by cavity ring-down spectroscopy. A possible two-photon absorption of methane at two different ultra-low pressures of 0.1 Pa and 5 Pa near 1.6 µm was observed using a temperature-scanning cavity ring-down spectrometer. The cavity decays on and off of the two photon absorption were fitted by the exponential model and a SCAR model. Due to the weak absorption of the two-photon absorption, the limitation of apparatus, and the interference by the nearby Lamb dip, we did not observe visible profile differences between the two decays. The absorption peak of the proposed two-photon transition and the Lamb dip were of opposite sign. The FWHM of the two-photon resonance is narrower than that of the Lamb dip by a factor of about two. The position of the proposed two-photon transition has been determined with the help of an optical frequency comb. These methods and spectral data will likely have applications in the fields of two-photon processes, metrology, and the study of molecular hyperfine structures.
Funding
National Key Research and Development Program of China (2016YFF0200101); International Science and Technology Cooperation Programme (2015DFG71880); National Natural Science Foundation of China (51976206); Guangdong Basic and Applied Basic Research Foundation (2019A1515111199).
Acknowledgments
Lei Yang greatly appreciates the National Institute of Metrology, China that provided the interesting studentship.
Disclosures
The authors declare no conflicts of interest.
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