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Abstract
We present a theoretical overview and experimental demonstration of a continuous-wave, cavity-enhanced optical absorption spectrometry method to detect molecular gas. This technique utilizes the two non-degenerate polarization modes of a birefringent cavity to obtain a zero background readout of the intra-cavity absorption. We use a double-pass equilateral triangle optical cavity design with additional feed-forward frequency noise correction to measure the R14e absorption line in the 30012←00001 band of CO2 at 1572.655 nm. We demonstrate a shot noise equivalent absorption of 3 × 10−13 cm−1 Hz−1/2.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical cavity enhanced spectroscopy (CES) is a well-established family of analytical techniques which use an optical resonator to investigate the molecular signatures in both gas and condensed phases [1–5]. It provides a powerful, ultra-sensitive tool to detect and quantify trace gas concentrations by using the resonant enhancement of an optical cavity to extend the interaction length between matter and light [6,7]. Due to their high sensitivity, CES techniques can be applied to a wide range of applications including fundamental studies of molecular and atomic transitions [8], monitoring of hazardous pollutants [9–11], medical analysis of biochemical research [12–14], study of atmospheric carbon cycles [15,16] and the exploration of hydrocarbon reserves [17–19].
To date, various approaches of cavity enhanced spectroscopy have been demonstrated. Some representative examples include Cavity Ring-Down Spectroscopy (CRDS) [3,20–23], Off-Axis Integrated Cavity Output Spectroscopy (OA-ICOS) [24,25] and Noise-immune Cavity-Enhanced Optical Heterodyne Molecular Spectroscopy (NICE-OHMS) [26–28]. A continual goal in CES research is to improve the absorption sensitivity limit so that extremely weak absorption can be detected [29], with the ultimate goal of reaching quantum shot noise limited performance being demonstrated only by select techniques such as NICE-OHMS [27]. In this paper, we present a theoretical description and experimental validation of an alternative high sensitivity, quantum shot noise limited CES technique, Polarization Impedance Measurement Spectroscopy (PIMS) [30].
The PIMS readout is a zero background method that does not require laser modulation in its absorption signal extraction. The signal extraction instead relies on the polarization properties of a non-degenerate, birefringent cavity to obtain a measure of the cavity impedance matching condition [31,32]. It then uses the impedance measurement readout as a proxy for the intra-cavity absorption [32]. By using non-degenerate polarization states, PIMS is able to forgo the optical and electronic hardware overhead required for modulation based techniques and minimize the number of active optical components in the system. When used in conjunction with a modulation free laser frequency locking scheme, such as the Hänsch-Couillaud method [33], it in principle, allows for baseband operation without the need for any electro-optic components. As a result, this new technique is capable of being highly flexible in its choice of operating wavelengths and sample gas pressures, ideal for accessing the fundamental transitions of rare isotopologues.
2. Theoretical description
The basis for the PIMS setup is the use of a non-degenerate, birefringent, optical cavity, for which we use a three-mirror ring cavity. For such cavities, the resonance frequencies for s-polarized light and p-polarized light are different and the two modes are well separated. Interrogating the cavity, an incident laser beam is prepared to be linearly polarized and is composed of both s- and p- polarizations. This linear polarization makes an angle $\theta$ with the p- axis, illustrated in Fig. 1(a), which in Eq. (1) we write for an arbitrary polarization state in Jones vector form:
where $E_p$ and $E_s$ are the square root of optical power in p-polarization and s-polarization respectively.
Fig. 1. Conceptual setup for the PIMS technique. A ring cavity is used to enhance the absorption of the intra-cavity gas cloud ($\alpha L$). The cavity input at point (a) is linearly polarized at a polarization angle of $\theta$, and can be decomposed as a probe beam and a reference beam. At the cavity reflection, (b), the optical beam consists of the probe that interrogates the cavity resonance, and the reference that is promptly reflected. This cavity reflected field is then incident on a polarizing beam splitter (PBS). Its output axes, x and y, are aligned to diagonal polarizations. The polarization projections onto the x axis, (c), interfere destructively, while the projections onto the y axis, (d), experience constructive interference. The two outputs are measured by two photodetectors (PD$_x$ and PD$_y$), and the electronic signals are subtracted to extract the PIMS signal. The corresponding Jones vectors representing the polarization states at each point along the optical path are also listed accordingly.
Assuming the s-polarization to be resonant, the ring cavity allows s-polarized light to circulate and probe the intra-cavity medium, with the reflected amplitude determined by the cavity impedance mismatch and zero amplitude corresponding to an impedance matched cavity [32]. We can write the polarization dependent cavity reflection response as the Jones matrix, given in Eq. (2):
In this matrix, the prompt reflection of the off-resonant p-polarization is represented by a reflectivity of 1. The cavity reflection response for s-polarized light, $R_s$ is given in Eq. (3) which can be used to characterize the impedance matching condition of the cavity:
where $r_1$, $r_2$ and $r_3$ represent the amplitude reflection coefficients of the three cavity mirrors, $\alpha$ is the intra-cavity absorption coefficient and $L$ is the round trip cavity length, assuming that the absorbent homogeneously fills the entire cavity. In the presence of a small absorption such that $\alpha L<<1$, and an impedance matched empty cavity, Eq. (3) can be approximated as follows: where $R_{\textrm {empty}}$ is the background impedance mismatch of the empty cavity, and the second term is the single round trip absorption $\alpha L$ enhanced by $\mathcal {F}/\pi$, with $\mathcal {F}$ being the cavity finesse [34]. From Eq. (4) we can see that the cavity response to the resonant s-polarization is therefore approximately linear with absorption.On resonance, there is also a $\pi$ radian phase difference in the reflected light field between over- and under-coupled states. While the amplitude could be inferred by measuring the optical power, due to its quadratic response to changes in absorption around the impedance matching condition, a direct power measurement is not sensitive to small changes in reflected amplitude. Furthermore, the phase information carried by the reflected field will also be lost. To therefore obtain a linear signal, PIMS uses the p-polarized light as a reference field, which is compared to the reflected probe beam. Due to the cavity birefringence, the p-polarized reference is promptly reflected and does not interact with the intra-cavity absorbing medium, yielding the total optical field on reflection shown in Fig. 1(b), and the Jones vector representation in Eq. (5):
where the expression for $R_s$ is given by Eq. (4).As the cavity reflected probe and reference beams are orthogonally polarized, a polarization analyzer is required to interfere the two fields. By introducing a diagonally aligned polarizing beam splitter (PBS), ideally at 45$^\circ$ to the laboratory s- and p-planes, and the latter of which is aligned with the s- and p- polarization of the optical cavity respectively, we project the fields onto the horizontal (x) and vertical (y) axes of the PBS, yielding the Eq. (6) and Eq. (7) for the horizontal and vertical projections respectively:
From Eq. (6), we see at the PBS reflection output, the projected components interfere destructively along the x axis, corresponding with Fig. 1(c). Meanwhile, at the PBS transmission output, given by Eq. (7), we have constructive interference for the projected components on the y axis, corresponding with Fig. 1(d). Two photodetectors (PDs) are used to monitor the power of the two outputs, which are then subtracted to give the interference term between the probe and reference light, yielding Eq. (8) when the s-polarized probe field is on resonance:
where $k$ is a constant that accounts for photodetector response and transimpedance gain. This differential amplitude is directly determined by the cavity reflection response ($R_s$) and therefore, the intra-cavity absorption via Eq. (4).To analyze this system in specific limits, we can first see that in the case of an exactly impedance matched cavity, the cavity reflection response for the s-polarized probe field from the cavity is zero. The photodetector readings are then solely due to the p-polarized reference field which is still present and is split equally between PD$_x$ and PD$_y$, and zero in the differential readout. Any impedance mismatch due to intra-cavity absorption then results in a non-zero s-polarized probe field, with the polarity of the differential readout, V$_{\textrm {res}}$, revealing whether the cavity is over-coupled or under-coupled. We can draw similarities with the Hänsch-Couillaud frequency stabilization technique [33], however PIMS measures in the amplitude quadrature where as the former measures in phase.
3. Double pass cavity interrogation
A common challenge with optical cavity techniques, including PIMS, is the susceptibility to alignment and mechanical noise, both of which can limit the resolution and accuracy of cavity loss measurements. A double pass cavity configuration can be used to suppress both of these noise sources [35]. As illustrated in Fig. 2, by locking the laser frequency to a cavity resonance, the transmission output can be retro-reflected to interrogate the same cavity, with the second pass used for sensing. In this arrangement, the first (forward) pass of the cavity acts as a mode cleaner cavity, removing non-resonant spatial modes, resulting in a single transverse mode output [36,37]. Furthermore, the first pass through the resonant cavity also passively filters laser frequency noise by the cavity resonance linewidth and eliminates the radio frequency side-bands used for example in Pound-Drever-Hall (PDH) error signal extraction. For PIMS, as we use a cavity with large polarisation mode non-degeneracy, this first pass through the resonant cavity also functions as a strongly polarising element ensuring both polarisation stability and purity of the second pass beam. Finally, the short injection path of the second beam minimizes the mechanical noise of the double pass PIMS (DP-PIMS) input beam.
Fig. 2. Schematic view of a double pass cavity configuration. The first pass reflection port can be utilized for monitoring or frequency locking detectors (not illustrated) while the sensing detection is carried out using the second pass reflection.
To implement DP-PIMS we must first excite the second pass mode. The most efficient method for achieving this is to initially transfer all the optical power into one polarization mode, which is made resonant with the cavity, maximizing the transmission on the first pass. The first pass reflection is used to lock the laser frequency to the optical cavity resonance, where in this demonstration we use the Pound-Drever-Hall (PDH) technique [38], though alternative techniques may also be employed [33,37]. On the first pass cavity transmission, a quarter-wave plate and retro-reflector is used to rotate half of the first pass transmitted power to the orthogonal polarization state, effectively preparing a new input state as per Fig. 1(a) and Eq. (1). We can then proceed with an analogous derivation to that described in the previous section.
A significant difference between the single pass and double pass implementations of PIMS is the calibration method. In a single pass system, the calibration can be carried out by comparing against the non-zero PIMS off-resonance readout. For a double pass system, the second pass field is disabled when off-resonance, and therefore this calibration method is unsuitable. Therefore, we apply an alternative calibration technique for DP-PIMS by normalizing to the total detected optical power, which we achieve by measuring the sum of both detector signals on-resonance $V_{x} + V_{y}$. The calibrated double pass PIMS readout is then given by $S_{\textrm {DP}}$ shown in Eq. (9).
where $V_x$ and $V_y$ are the voltage outputs of the $x$ and $y$ detection ports of the balanced detector respectively. This measurement captures the same optical and electronic gains as the DP-PIMS signal and is used for normalization. Here, we assume that the polarization angle $\theta$ is tuned to 45$^\circ$ and the cavity is impedance matched. The resonant DP-PIMS readout can be normalized to:Fig. 3. (a) A simulated plot of the DP-PIMS error signal around resonance as a function of laser frequency detuning. Under-coupled, impedance matched and over-coupled conditions have been shown as the green, red and blue traces respectively. (b) The DC readout of DP-PIMS on resonance gives a linear readout of the impedance matching condition of the cavity, The red trace shows the zero crossing point when the cavity is impedance matched. Molecular absorption leads to an effective under-coupling (green trace) which therefore leads to a positive readout while an over-coupling (blue trace) causes a negative readout using this technique.
When restricted to considering on-resonance frequencies, Eq. (10) can be simplified to give
Reorganising Eq. (11) and ignoring $R_{\textrm {empty}}$ as it is constant across all measurements, yields the fractional absorption:
The fundamental limit of the system is determined by quantum shot noise, which can be expressed in terms of the shot noise equivalent absorption, given by Eq. (13):
4. Experimental implementation
To demonstrate a DP-PIMS readout, an experimental demonstration was implemented using the setup shown in Fig. 4. We use a NKT Koheras fiber laser to interrogate the absorption lines of carbon dioxide (CO$_2$) at 1572 nm. The sensing cavity was designed and constructed by using stainless-steel spacers to rigidly hold the cavity mirrors in position. The spacers were also designed to act as a vacuum chamber, which allow ambient gas to be evacuated. By using a pressure gauge, the pressure of the vacuum chamber can be verified for analysis. The two polarization modes of the optical cavity had a finesse of 1943 and 523 for the s- and p- polarizations respectively.
Fig. 4. The DP-PIMS experimental setup in a double pass configuration. Measurements are made by frequency locking the laser on optical resonance using the first pass reflection for a PDH frequency locking scheme. We initially transfer all input optical power into the resonant polarization mode, maximizing the first pass transmission. The quarter wave plate before the retro-reflector then selects the ratio of the two polarization states used for the DP-PIMS readout implemented on the cavity second pass. This readout is extracted from the second pass cavity reflection using a polarization analyzer and balanced detector setup.
The laser is frequency locked using the first pass reflection to the s- polarization mode of the cavity. For frequency locking, the Pound-Deriver-Hall locking technique was used throughout this paper, with the required phase sidebands generated using a fiber coupled JDSU dual Mach-Zehnder electro-optic modulator. Frequency control was implemented through both piezo actuation on the laser and a fibre coupled acousto-optic modulator (AOM), IntraAction FCM-801E5C operating at an RF frequency of 80MHz.
For optimal absorption sensitivity, the performance of the frequency control system was critical and the system we implemented achieved a unity gain bandwidth of $\sim$ 200 kHz, with a crossover frequency of approximately 6 kHz between the two actuators. Figure 5(a) plots the closed-loop suppression function of the frequency locking servo where the red trace is the measured data, compared with the blue trace showing the servo design response. The servo design features a $1/f^2$ response for the PZT actuator arm and a $1/f$ response for the AOM where the AOM dominates above the 6 kHz crossover frequency. At $\approx$ 35 kHz there is a small dip in both the designed response and the experimentally measured data. This is where the first PZT resonance occurs with a significant out of phase component compared to the AOM actuator.
Fig. 5. (a) The close-loop suppression functions of the servo control loop. The red trace represents the in-loop frequency noise suppression from measurement, which agrees well with the simulation result (trace in blue). (b) A conceptual illustration of frequency noise suppression in a double-pass system, including by the optical cavity filtering effect (blue trace) and by active frequency locking (red trace). The residual frequency noise is indicated with the gray area. As the licking bandwidth is higher than the cut off frequency of the cavity filtering, the frequency noise is suppressed across all frequency bands.
In addition to the active servo suppression of laser frequency noise with respect to the optical cavity, the transmitted field also passively filters laser frequency noise beyond the cavity half width half maximum (HWHM). Figure 5(b) illustrates the combined effect of passive cavity filtering (blue trace) cascaded with the suppression function from the active feedback control loop (red trace). The residual frequency noise is illustrated as the grey area in Fig. 5(b). With the bandwidth of the servo ($\sim$200 kHz) higher than the cavity HWHM (75 kHz), the entire broad-band frequency noise has been reduced.
We can quantify the residual noise floor in terms of the noise equivalent absorption (NEA), spectral density plot in Fig. 8, trace (a). As shown in this plot, the minimum NEA reaches 2$\times$10$^{-12}$ cm$^{-1}$ Hz$^{-1/2}$ for signal frequencies below 10 kHz. When compared with the expected shot noise equivalent absorption (dashed green trace) of $\alpha _{SN}$ = 2.8$\times$10$^{-13}$ cm$^{-1}$ Hz$^{-1/2}$, calculated using Eq. (13), the experimental data is seen to be a factor of $\sim$7 away from the fundamental shot noise limit.
5. Feed-forward frequency correction
Although the active frequency locking servo in conjunction with the cavity filtering effect has substantially reduced the laser frequency noise, due to the limits in control loop gain and feedback bandwidth, a small part of residual frequency noise still remains. This residual frequency error results in a time-varying detuning between the laser frequency and the cavity resonance which in turn causes a PIMS readout error as per Eq. (10) with detuned laser frequency. In our system we however have a concurrent measure of the frequency detuning from resonance courtesy of the PDH error signal, which is plotted in Fig. 6 (top blue trace) with the DP-PIMS signal (bottom red trace). For small frequency excursions around cavity resonance (0 MHz in Fig. 6), the DP-PIMS signal response is predominately quadratic, transforming linear PDH frequency errors into both DC and second harmonic DP-PIMS errors. Therefore, even though the required DP-PIMS signal bandwidth may be modest, all dynamic frequency errors produce DC errors in the DP-PIMS signal. Whilst DP-PIMS benefits from the low pass, passive filtering of transmission through the sensing cavity prior to DP-PIMS, in addition to active PDH frequency suppression, it proves practically difficult to reduce the residual frequency noise, shaded gray area of Fig. 5, to a level where DP-PIMS can operate at the shot noise limited sensitivity given by Eq. (13).
Fig. 6. A conceptual view of our feed-forward frequency noise correction method. As the laser frequency is slightly detuned from cavity resonance (0 MHz), the PDH error signal (upper blue trace) varies linearly with the frequency fluctuation. While the double pass PIMS signal (lower read trace) shows a quadratic response. These theoretical plots assume a cavity finesse of 200 with a phase modulation frequency of 35 MHz for PDH error signal.
As Fig. 6 also shows, when the sensing signal detuning is well within the cavity linewidth, the laser frequency fluctuations can be well approximated by the PDH error signal. By comparing it to the corresponding DP-PIMS quadratic response, the relationship between the frequency detuning response of DP-PIMS signal and that of the PDH signal can be used for a feed-forward correction to mitigate the effects of frequency detuning on the absorption readout.
The basic principle of our feed-forward method is therefore to use the PDH error signal as a measure for the laser frequency detuning and feed it into the DP-PIMS frequency response function to generate an accurate estimate of the DP-PIMS error signal due to residual frequency fluctuations. Subtracting this estimate from the total DP-PIMS error signal then provides a corrected virtual on-resonance value for the DP-PIMS readout. We use a heuristic model of the DP-PIMS frequency response to give an estimate of the PIMS error signal $S_{\textrm {Est-PIMS}}$ due to frequency fluctuations:
where $f_{\textrm {PDH}}$ is the residual frequency error as recorded by the PDH error signal, $a$ is a calibration coefficient dependent on the cavity finesse and scales the quadratic error term, $b$ is a coefficient that scales the residual linear frequency error of the PDH error signal, and $c$ is a coefficient that scales the DC offset due to the empty cavity impedance mismatch.The coefficients of Eq. (15) were experimentally determined by firstly tuning the laser to a cavity resonance with an optical frequency away from any absorption transition. Then we applied a triangular waveform to the laser PZT actuator which scans the optical frequency across the cavity resonance. This scanning range was constrained within the HWHM of the cavity to ensure a linear PDH response. The PDH and DP-PIMS signals were simultaneously recorded during the frequency scanning, obtaining the traces plotted in Fig. 7(a) where trace (i) is the PDH error signal $f_{\textrm {PDH}}$ and trace (ii) is the uncorrected DP-PIMS error signal $S_{\textrm {DP-PIMS}}$. The fluctuations on both traces are dominated by laser frequency variation.
Fig. 7. The (i) PDH and (ii) DP-PIMS signal from direct measurement as the laser frequency was linearly scanned across the cavity resonance compared with (iii), the feed-forward frequency corrected PIMS readout. In the bottom figure, trace (iv) is the modelled DP-PIMS signal generated from the PDH error signal using Eq. (15) which shows close agreement with the measured DP-PIMS signal (ii). The feed-forward correction is carried out by subtracting trace (iv) from trace (ii).
The trace (iv) in Fig. 7(b), is the estimated frequency noise induced in the PIMS readout $S_{\textrm {Est-PIMS}}$, computed using the recorded PDH signal trace (i) in Fig. 7(a) and Eq. (15). For comparison with the feed-forward estimate, we replot trace (ii), the uncorrected PIMS signal in Fig. 7(b). Trace (iii) in Fig. 7(a) is the subtraction of these two traces: $S_{\textrm {Corr DP-PIMS}} = S_{\textrm {DP-PIMS}} ~- ~S_{\textrm {Modelled DP-PIMS}}$. The value of all coefficients was numerically determined by iterating coefficient values in order to minimising the resultant RMS PIMS error signal $S_{\textrm {Corr DP-PIMS}}$. The optimum value of coefficient $a$ was determined to be $a$ = -0.101, whilst coefficients $b$ and $c$ were negligibly small. As the empty cavity was designed to be impedance matched and the frequency locking loop was optimised, it is unsurprising that the optimum values of coefficients $b$ and $c$ is close to zero. The substantial elimination of frequency noise demonstrated in trace (iii), shows that our model of frequency noise induced DP-PIMS noise is accurate and useful. We verify this by applying our DP-PIMS feed-forward model to the initial measured NEA plotted in Fig. 8. The residual noise floor of our DP-PIMS spectrometer without feed-forward noise reduction is shown in trace (a) and, after applying feed-forward correction in trace (b).
Fig. 8. The absorption sensitivity comparison between (a) before and (b) after feed-forward correction, quantified by using the matrix of noise equivalent absorption. The measurement was over 2 seconds at a sampling rate of 2MHz. The result shows almost an order of magnitude improvement in sensitivity with feed-forward compensation applied, reaching 3$\times$10$^{-13}$ cm$^{-1}$ Hz$^{-1/2}$ with the red trace. The shot noise is calculated to be around 2.8$\times$10$^{-13}$ cm$^{-1}$ Hz$^{-1/2}$, which is shown in blue dashed green.
The minimum NEA of DP-PMIS, using feed-forward correction, reaches 3$\times$10$^{-13}$ cm$^{-1}$ Hz$^{-1/2}$ for signal frequencies below $\sim$ 1 kHz. This is in close agreement with the expected shot noise equivalent absorption ($\alpha _{SN}$ = 2.8$\times$10$^{-13}$ cm$^{-1}$ Hz$^{-1/2}$), demonstrating that with both active laser frequency stabilisation and feed-forward laser frequency noise correction, our DP-PIMS spectrometer is able to reach quantum shot noise limited performance for a cavity finesse of 2000. At frequencies of a few kHz and above, the NEA spectrum is contaminated by the non-linear response of the PDH error signal at high frequencies relative to the cavity line width. Below frequencies of $\sim$500 Hz, the NEA shows technical noise features including electronic pick-up from the main power supply at 100 Hz and 150 Hz in addition to acoustic mechanical pick-up from the optical cavity.
6. Absorption measurements
To demonstrate the efficacy of the DP-PIMS spectrometer configuration, we measure the R14e absorption line in the 30012$\leftarrow$00001 band of CO$_2$ at 1572.655 nm, shown in Fig. 9, trace (a). Figure 4 shows a simplified schematic of our experiment where the subtracted signal from the balanced PD was recorded by a data acquisition system and, using Eq. (9)–(12), was subsequently calibrated to give the intra-cavity fractional absorption $\alpha$. By implementing this calibration routine at both the beginning and end of each data run we ensure the fractional absorption calibration remained stable and was found to be highly repeatable across measurements.
Fig. 9. Spectroscopic measurement using double-pass configuration on an equilateral triangle cavity. (a) The red dots represent the direct DP-PIMS spectroscopic result, measuring the R14e absorption line in the 30012$\leftarrow$00001 band of CO$_2$. This experimental result was fitted with (b), a Voigt profile to extract the partial pressure of CO$_2$. (c) The blue stem plot is the difference between the experimental data and the Voigt fit curve. Traces (a), (b) and (c) share the same vertical axis scale. This measurement of atmospheric CO2 level was made at 294 K at atmospheric pressure (1008 mbar).
Due to the limited resolution of the discrete spectrum obtained by operating at cavity resonances, the absorption line under measurement needs to be pressure broadened so that it crosses several cavity FSRs. Thus we measured the absorption line at a room temperature of 294 K and pressure of 1008 mbar, with a cavity finesse of 1943. To prevent the saturation in the absorption signal, a weak transition line, the R14e in the 30012 $\leftarrow$ 00001 band of CO$_2$ at 1572.66 nm was chosen.
The fractional loss data from our measurement is plotted as red dots in Fig. 9, trace (a), with each dot being the average of 10,000 data points acquired at a sampling rate of 1 kHz. The absorption coefficient was calculated using Eq. (4) and Eq. (11), and the wavelength has been calibrated by using a wavelength meter.
As the transition line is expected to obey a Voigt line shape at an ambient pressure of around 1000 mbar, a Voigt profile is calculated to fit the spectrum with a corresponding line intensity of 1.767$\times$10$^{-23}$ cm$^{-1}$ / (mol cm$^{-2}$) [39], and is shown in Fig. 9, trace (b). In addition, Fig. 9, trace (c) shows the residual after the Voigt fit is subtracted from the experimental data. From the Voigt fit, the partial pressure of CO$_2$ was estimated to be 0.366 $\pm$ 0.006 mbar, with a total pressure of 932.36 $\pm$ 24.85 mbar. This spectral result agrees with the independent measurement from the pressure gauge. The uncertainty for this estimation was dominated by wavelength calibration error attributed to thermal drift of cavity resonances during the full measurement cycle which was dominated by the need to manually tune between cavity resonances. This effect can be significantly reduced through automation, and the subsequent speed increase of the data acquisition process.
7. Conclusion
We have presented a CES method, Polarisation Impedance Measurement Spectroscopy (PIMS), which achieves a continuous-wave, zero background readout with a base-band architecture. We have also demonstrated the experimental implementation of this method with the double pass configuration. A proof-of-concept trace gas measurement was conducted on the R14e absorption line in the 30012$\leftarrow$00001 band of CO$_2$ at 1572.66 nm, with cavity finesse of 1943. From the Voigt fit, the partial pressure from detection is 0.366 $\pm$ 0.006 mbar which is in agreement with the theoretical value of atmospheric air. Through optimisation of the feed-back frequency control scheme, together with a non-linear feed-forward frequency noise correction, we achieved a shot noise limited noise equivalent absorption sensitivity of 3$\times 10^{-13}$ cm$^{-1}$ Hz$^{-1/2}$, with a modest cavity finesse of $\sim 2000$. This result indicates that double-pass PIMS has the potential to be a competitive, ultra-sensitive spectroscopic measurement technique and is capable of molecular gas transition measurements with ultra-low concentrations.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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