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Abstract
We report on the method of the sideband amplitude modulation (SAM) to achieve high-sensitivity spectroscopy with a fiber electro-optic modulator (fiber-EOM). This method increases the signal to noise ratio (SNR) by a factor of forty, comparing with conventional absorption spectroscopy. It is a temporal balanced detection to eliminate the intensity noise of the light source, and capable of preserving an undistorted Doppler profile for further quantitative analysis. Taking advantage of the newly developed fiber-EOM, SAM is applicable for various spectroscopies with a simple experimental setup. We performed SAM on $\rm {CH_4}$ $3\nu _3$ overtone band at 1170 nm using an external cavity Quantum dot laser. We demonstrated that one of the absorption lines buried in the other ten times stronger nearby lines was clearly extracted. SAM shows great potential on the molecular spectroscopy, where the spectrum is complicated and quantitative analysis is required.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High-sensitivity spectroscopies play a key role in physics and chemistry from both fundamental and applied aspects. Especially, molecular spectroscopy, which is the unique fingerprint of a chemical substance, is the cornerstone for gas sensing. Its applications include toxic gas detection, air pollution detections et al. Resolving the complicate and weak spectrum of molecules to reach high-sensitivity is a technical challenge. It is particularly interesting to develop a high-sensitivity spectrometer in the near-infrared region, where the compact semiconductor laser systems are widely available. In this paper, we report a newly developed technique, Sideband Amplitude Modulation (SAM), as a variation of the conventional Amplitude Modulation (AM) and Frequency Modulation (FM), based on the newly developed fiber Electro-optical modulator (fiber-EOM).
The Signal-to-Noise Ratio (SNR) of the absorption spectrum can be expressed as [1]:
The signal $S=k \Omega P$, where $k$ is related to the efficiency of the detector and $\Omega P$ was the diminished laser power by the absorption. The noise is considered to be composed of three different sources: $N_e$ representing the electronic noise of detection, $N_s P$ that is the incident radiation noise due to the laser intensity fluctuation, and $b\sqrt {P}$ that is the quantum noise. The quantum noise sets the ultimately achievable limitation of SNR, unless certain exotic techniques are applied, such as squeezed state [2]. Our focus of this paper is on reducing or eliminating the classical noise sources: $N_e$ and $N_s P$.There are several methods developed for improving the SNR. $N_e$, which is known as the flicker noise or 1/f noise, occurs in almost all electronic devices. By modulating the incident light source at a high frequency, then recovering the signal using a demodulator, the 1/f noise can be largely reduced, because its noise spectrum following the 1/f decreasing. The only residual noise is that within the narrow demodulation bandwidth. The most commonly used techniques are AM and FM. In conventional AM, the light source is intensity modulated by a suitable means, such as driving current modulation, acousto-optic modulator (AOM), EOM, or mechanical chopper. It can reduce the $N_e$ term and filter out the background noise, such as room light and scattering, but does not improve the light intensity noise, $N_s P$ [3].
For the intensity noise, the FM technique has a great advantage, because the modulation is on the frequency domain and only the frequency dependent signal will be extracted. Therefore, it is immune to the intensity fluctuation noise, and the flicker noise is also reduced by the modulation-demodulation process, as AM. However, the FM spectral profile is a mixture of absorptive and dispersive parts of the transition and depends on the demodulation phase. Such a complicated profile makes quantitative analysis difficult [4].
Balanced photodetection is also a commonly used detection method in high-sensitivity spectroscopy. It utilizes a dummy beam as a reference, which is spatially separated from the signal beam, to subtract the large intensity fluctuation background burying the small signal. The common noise appearing in both signal and reference beams can be canceled out. Its performance is characterized as the common mode rejection ratio (CMRR) [5–8]. However, because of spatial separation, the difficulty lies in maintaining a perfect balance and being totally identical between the reference and signal branches. Any asymmetry of them will strongly affect the performance of the noise suppression and result in the incomplete cancelation of the excess noise [9].
SAM is a “temporal” balanced photodetection that resolves the possible imbalance due to the spatial separation. It is also a variation of FM, but the spectrum profile (Doppler, Gaussian) is preserved for quantitatively analyses that provide information about the concentration and the temperature of the sample under test.
We demonstrate the SAM technique with $\rm {CH_4}$ that is one of the most important greenhouse gases. A highly sensitive and quantitatively accurate detection method is required to study its role in global warming. The $3\nu _3$ overtone band of $\rm {CH_4}$ in 1.1-1.6 $\mu$m region can be accessed using near-infrared diode lasers. We show that a weak absorption covered by the surrounding strong transitions can be extracted and recovered using SAM.
2. Sideband amplitude modulation
SAM is to phase modulate the optical field with an RF $\omega _{rf}$ and a secondary amplitude modulation $\Omega$ is then applied to $\omega _{rf}$. The signal is demodulated at the frequency of $\Omega$. When an EOM modulates the optical field $E_0 e^{\imath \omega t}$ of the optical frequency $\omega$ by an RF $\omega _{rf}$ and a modulation index $\beta$, the resulted optical field can be approximated as three parts: one carrier and two sidebands:
Fig. 1. Illustration of the SAM concept. The detecting laser beam is composed of 3 frequency components: one carrier and two sidebands. While the spectroscopy is being performed, the laser frequency is scanned from off-resonance (red line) to on-resonance (blue line), where the carrier is within the absorption profile.
SAM also reduces the 1/f flicker noise by fast switching the modulation index $\beta$, as the conventional AM, and rejects all the common mode noise, the power fluctuation, whose time scale is longer than $2\pi /\Omega$. It is as the balanced photodetection, but in “temporal” way. In comparison with the conventional “spatial” balanced photodetection, the balance between the detection and reference beams (i.e., $\beta$ ON/OFF in SAM) is guaranteed, because both of them are in the exact same optical path. SAM preserves the absorption spectral profile without distortion, unlike FM spectroscopy, where the spectral profile depends on the modulation-demodulation parameters ($\beta$, $\omega _{rf}$ and demodulation phase).
SAM is as advantageous as the two-tone modulation technique which is to simultaneously modulate the laser with two different high frequencies. The first two-tone FM method was reported in 1986 [11] as a sensitive FM spectroscopy technique with high modulation frequencies, but using low-frequency detection. By high-frequency modulation, the two-tone modulation improves the 1/f noise and partially reduces the laser intensity fluctuation. From the point of view of the frequency domain, SAM is similar to the two-tone modulation.
Comparing with the amplitude-modulated phase modulation [10] that gives a distorted derivative Doppler profile, SAM requires the sidebands to be well separated to be larger than Doppler linewidth. Hence, in most cases, the primary phase modulation frequency $\omega _{rf}$ must be larger than several GHz that is easily achievable using a fiber-EOM, which allows SAM to be experimentally easy to implement. Meanwhile, neither fast detector nor delicate demodulation setup is needed, because the modulation-demodulation is at $\Omega$ that is tens of kHz. The optimum condition for SAM is a large $\beta$ to provide the best contrast between $\beta$ ON/OFF. However, a large $\beta$ will be accompanied with more high order sidebands that could induce superfluous signal by nearby absorption lines. It is worth to note that such superfluous signals give an opposite phase and can be removed using off-line data analysis.
3. Experiment setup
The schematic diagram of our experimental setup is shown in Fig. 2. The spectroscopy of $\rm {CH_4}$ $3\nu _3$ overtone transitions at 1170 nm was performed using an quantum dot external cavity diode laser (QD-ECDL) system [12] and a Herriott multi-pass cell [13] with both the conventional absorption spectroscopy and SAM, for comparison.
Fig. 2. Schematic diagram of the experimental setup. The output of the single frequency QD-ECDL is modulated using a fiber-EOM that is given with a frequency of 11.2 GHz from an 8x frequency multiplier. A 60 passes multi-pass cell is used to enhance the absorption length. QD-ECDL: Quantum dot laser external cavity diode laser, PD: photodetector, BS: beam splitter, DM: dichroic mirror, BP filter: bandpass filter
Typically the quantum dot diode laser has a lower threshold and wider tuning range relative to quantum well diode lasers in the near infrared region. The ECDL was constructed around a polarization-maintaining (PM) fiber-coupled gain module (Innolume, GM-1140-120-PM-130) with the Littrow configuration. The laser wavelength was selected using a 1200 grooves/mm blazed grating, which was mounted on a piezoelectric transducer (PZT) to fine-tune the angle of the grating. The wavelength of the ECDL can be tuned from 1100 to 1200 nm. The mode-hop-free range over 10 GHz and the output power around 80 mW is achieved in a typical operation current 500 mA. An optical isolator (OI) at the output of the ECDL was used to avoid the optical feedback.
A fused optical fiber coupler splits 10% of the laser power into a wavelength meter (Bristol instruments 521 series) for diagnosis. In order to reduce residual amplitude modulation (RAM) effects resulted from the variation of the laser polarization, the other 90% passed through a crystal polarizer (GT10-C-Glan-Taylor Polarizer) aims to retrieve better extinction ratio before coupling into the fiber-EOM (EOSPACE, PM-0K5-10-PFU-PFU-130) and was collimated as a 1.38 mm $1/e^2$ diameter beam spot. A beam splitter (BS) splits part of the light to the reference cavity for monitoring the laser operation condition and ensuring all of the experiments performed under single mode operation.
A computer-controlled RF synthesizer (HP-8648B, 9 kHz to 2000 MHz) generating 1.4 GHz was as our fundamental RF source. It was referenced to the 10 MHz reference from a GPS disciplined Cs clock and also monitored using a spectrum analyzer. The three stages of frequency multipliers were used to have a total multiplication factor of 8, and the final frequency coupled into the EOM was 11.2 GHz. The 9.8 GHz to 12.4 GHz bandpass filter was installed to eliminate the other harmonic frequencies and to ensure that only two sidebands are generated after the fiber-EOM, as shown in Fig. 3. The RF output was then switched ON/OFF by a 60 kHz square wave.
Fig. 3. Schematic of one carrier and two sidebands generated using the EOM and observed with the reference cavity, which has a free spectral range of 1.42(2) GHz. The cavity was scanned with a triangle wave by using a PZT. The input laser beam was carefully mode-matched to the cavity, but there is still a small residual high order transverse mode (not completely suppressed), as the peak C. The peaks A were carriers and the peaks B were sidebands. The amplitude of peak B was one-third of peak A. Because the frequency difference between the carrier and the sidebands was 11.2 GHz, which equals to 8 $\times$ FSR - 0.16 GHz, the separation between peak A and peak B is 0.16 GHz. The red line in the inset is without any modulation and shows only the carrier and its higher-order transverse modes.
There are three frequency components, one carrier and two sidebands, generated by fiber-EOM. The amplitude of sidebands was one-third of the carrier, as shown in Fig. 3. Two mode-match lenses (f = 30 mm and f= 60 mm) focused the 1170 nm beam into a multi-pass cell with a 0.1 mm beam waist radius at the center of the cell (new focus 5612). The cell was 80 cm long, and the light reflected 60 times in the cell to increase the absorption length to interact with $\rm {CH_4}$ molecules.
To align the invisible 1170 nm light into the multi-pass cell, a 543 nm He-Ne laser was overlapped with the 1170 nm beam path using a dichroic mirror (DM). We can confirm the number of passes in the cell by counting the green pattern. Two mode-match lenses (f = 50 mm and f= 100 mm) shaped the 543 nm beam as the 1170 nm beam. The multi-pass cell equipped with Brewster windows was filled with 99.99% $\rm {CH_4}$ gas at 5.44 Torr by using a rotary vane pumps to control the working flow. The output beam was detected using an InGaAs photodetector (PD) which was not sensitive to 543 nm light and then demodulated using a lock-in amplifier (SR830) to acquire a Doppler-broadened profile.
4. Result
The experiment was performed on the $3\nu _3$ overtone band of $\rm {CH_4}$. We focused on the vicinity of 8602.5 $\rm {cm^{-1}}$. There were four absorption lines as listed in Table 1 and denoted as A, B, C, and D. This region was chosen to have no nearby transition with comparable strength covered by both the sidebands. The C-line has line strength that is an order of magnitude weaker than the neighboring B and D lines, which overlap and bury it with the Doppler-broadened profiles. Our result shows that the weak buried C-line can be extracted using SAM. We fitted the experimental data with multi-peaks Gaussian profiles using Origin (OriginLab). The mathematical model is:
where $x_c$ is the center of the profile, $w$ is the full width at half maximum (FWHM), and $A$ relates to the peak height. In our fitting, we have set all the parameters to be free but with a constraint: $w_1=w_2=w_3=w_4$. The optimized parameters were found using the least Chi-square.
Table 1. $3\nu _3$ overtone transitions of ${\textrm {CH}}_4$ molecule from HITRAN
Figure 4 shows the spectrum using the conventional direct absorption spectroscopy of $\rm {CH_4}$ with a pressure of 5.44 Torr. The red curve is the experimental result. The reference cavity being the frequency marker was made of Invar material with a plano-concave configuration. Its free spectral range (FSR) is 1.42(2) GHz. In this spectrum, there are three clearly observable transitions that have line intensities stronger than $10^{-24}$ cm/mol, corresponding to A, B, and D lines as listed in Table 1. The experimental result can be well fitted with three individual Gaussian profiles of the same linewidth. However, C-line was not observed at all. The black dash line is the combination of the three fitting curves. Comparing with the fitting and experimental data, the R-square of the fitting result is 0.945, and the noise is estimated to be $\sim 0.8 \%$ that gives an SNR 5.5, as shown in the residual of Fig. 4. The measured FWHM is 0.65(1) GHz. That is smaller than the theoretical value, 0.79 GHz, calculated using the standard expression:
where $\nu _0$ is the line center, T is the temperature, M is the molecular mass and k is the Boltzmann constant. This disagreement may be due to the poor SNR of the spectrum, as indicated by the SAM result.Fig. 4. $\rm {CH_4}$ direct absorption spectrum and the fitting residual. The orange, blue and purple lines are fitting curves of $\rm {CH_4}$, corresponding to absorption peak A, B, and D respectively in the $3\nu _3$ overtone band. The black dash is the combination of the three fitting peaks. The conventional AM spectrum with a lock-in amplifier is showed in the inset and gives an SNR of 20.
Figure 5 shows the $\rm {CH_4}$ spectrum with a largely improved sensitivity using SAM. This spectrum includes only a single scan with a scanning time of 20 sec. The SNR was increased up to 205, which is forty times higher than the previous conventional direct absorption spectroscopy and ten times higher than conventional AM-lock-in absorption spectroscopy (see Fig. 4). The derived detection limit of $\rm {CH_4}$ is 70 ppm. Multiple scans could further improve the SNR and push the sensitivity to a lower limit. According to the four peaks in Table 1, we analyzed the experimented spectrum with two different fitting procedures: 3 peaks without C-line and all 4 peaks fitting. For the three peaks fitting, we considered only A, B and D. The fitting result gave an R-square of 0.99874, and a fitting residual shows a weak absorption line between B and D, as illustrated in the inset of Fig. 5. It is clear evidence of the existence of C-line.
Fig. 5. $\rm {CH_4}$ absorption spectrum and the four peaks fitting residual with SAM. We fitted this spectrum with four peaks, instead of three peaks. The C-line was marked at the green solid line. In the inset, we show the difference between these two curves: three peaks (A, B, and D) fitting curve and four peaks (A, B, C, and D) fitting curve. Setting the three peaks fitting curve as a baseline, it is obvious that the four peaks fitting curve is much better fitted to the data. The red line is the lock-in demodulation signal, the blue line is the four experimental peaks fitting curve, and the black line is three peaks fitting curve as the baseline.
By the 4 peaks fitting, as shown in Fig. 5, the fitting result gave a better R-square, 0.99929. The weak absorption line mentioned above is very well fitting as C-line. The resulted FWHM is 0.76(1) GHz, that is in a better agreement with the predicted value, 0.79 GHz, and the residual noise is improved to be $\sim 0.1\%$. The line intensity ratio of A: B: C is 1: 0.69: 0.13. The SNR of C-line is estimated to be 6.3 using the inset in Fig. 5.
The measured frequency separation from peak A - B and peak A-C are 1.05(1) GHz and 1.76(1) GHz, respectively. Comparing the HITRAN prediction [14], they are given as 1.0490 GHz and 2.1579 GHz, respectively. Although the non-linear response of the reference cavity PZT would cause a certain error in the frequency spacing measurement, the peak separation A - C is not in agreement with the HITRAN prediction for unknown reasons. It also detects weak fringes, as shown in the residual of Fig. 5, which could be caused by the optical interference in the light path, possibly the etalon effect of two collimation lenses. Due to the high sensitivity, SAM reveals the existence of Peak C, which cannot be noticed in the direct absorption spectrum.
5. Conclusion and future work
We demonstrate that the method of SAM largely enhances SNR more than an order of magnitude, increases the sensitivity, and maintains the original spectrum profile. A $\rm {CH_4}$ weak transition in the near-infrared spectroscopy can be extracted from background noise and becomes measurable. Without any fast photodetector or complex modulation-demodulation, SAM provides an efficient approach to maintain an undistorted Doppler spectrum with high sensitivity and is especially advantageous to the experiment of the quantitative analysis. The high sensitivity of SAM can be applicable to $\rm {H_2}$ molecular spectroscopy, which is located at 1162 nm and has an important implication for fundamental chemical physics [15]. The capability of maintaining an undistorted Doppler profile can be favored for the Boltzmann constant measurements [16,17].
Funding
Ministry of Science and Technology, Taiwan (MOST) (105-2112-M-007-027-MY3, 106-2112-M-007-021-MY3).
Acknowledgments
This work was financially supported by the Center for Quantum Technology from the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan.
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